1 Introduction

Population and consumption growth leads to at least 50% larger demand for food within the next 50 years (Ehrlic and Harte 2015). In the face of growing pressure on agricultural production, agriculture is one of the most critical sectors in providing global food security for the next generations (Schiefer et al. 2016). While the total number of farmers worldwide is dramatically decreasing, to feed an increasing global population, which is more likely to reach 9 billion by 2050, food production would be enhanced more than its current level (Antony et al. 2020). Once almost the whole anticipated rise in the population is expected to occur among developing countries (Le Mouël and Forslund 2017), this tremendous population boost will require more agriculture productivity, notably for less-developed and developing countries. Nevertheless, agriculture in these countries mostly depends on smallholder farmers, who use generational knowledge in their farming and agricultural practices and depend on several challenges, such as unpredictable weather patterns and seasons due to climate change (Kavga et al. 2021). Herein, since smallholder farmers have an essential role in providing genetic diversity of food supply and decreasing the potential risks like nutritional deficiencies and degradation of an ecosystem (Fanzo 2017), it is crucial to mitigate the challenges putting pressure on their shoulders.

Undoubtedly, agriculture is facing the fourth revolution by incorporating information and communication technologies in traditional farming throughout the last few decades. As a new way of farm management, precision agriculture backed up by technological developments, has started to address some of the agricultural challenges in recent years (Gray et al. 2018). Internet of things (IoTs) and artificial intelligence (AI) applications have contributed significantly to the rise of precision agriculture and its application in the agriculture sector (Ayaz et al. 2019; Hosseinnia Shavaki and Ebrahimi Ghahnavieh 2022; Kwaghtyo and Eke 2022; Wang et al. 2021;). Notably, utilizing IoTs, physical objects are easily identified and tracked by gathering relevant data, which will be turned into fruitful information and disseminated over a network (Gaspar et al. 2021). Accordingly, since alerts can be created for agricultural situations that need corrections, IoTs effectively plan and control agricultural processes (Farooq et al. 2020).

As per IoTs, unmanned aerial vehicles (UAVs), namely drones, which are aircraft where there is not any human pilot on board, are one of the most versatile devices (Gaspar et al. 2021). UAVs are able to resolve the drawbacks in the physical IoT infrastructure already established (Srivastava and Prakash 2022). Using a ground controller and a communication system, UAVs are usually used for aerial surveillance to monitor crops, weeds, and irrigation (Tsouros et al. 2019). Herein, precision agriculture with the use of UAVs enables farmers to make better decisions with more information about local climate, water, soil, and crop (Gray et al. 2018). Accordingly, the application of UAVs in smart agriculture, also widely known as Agriculture 4.0, with exceptionally microelectromechanical systems (MEMs) sensors has made them extremely attractive in recent years (Boursianis et al. 2022). However, agricultural UAVs still have a relatively low percentage among all types of UAVs (Petkovics et al. 2017), while they have undoubtedly had a crucial role in agricultural crops for a few years. It is expected that the improvement in UAV technology will further expand the application of agricultural UAVs in the upcoming years to establish Agriculture 4.0. Therefore, UAV technology used for collecting information that enables agricultural practitioners to take effective decisions is currently a promising research avenue today and future.

In the relevant literature, several investigations have been conducted on UAVs in Agriculture 4.0 to provide fruitful information about their critical applications (Boursianis et al. 2022; Tsouros et al. 2019) and challenges against their application (Coppola et al. 2020). Besides, there are also several research studies on agricultural UAVs concerning their types and classifications (del Cerro et al. 2021; Dileep et al. 2020), comparison of UAVs concerning supporting technologies (Sharma and Hema 2021) and the latest technologies regarding them (Kim et al. 2019). Though these studies provide a general perspective on UAVs, they still have some drawbacks in providing practical contributions for smallholder farmers. Besides, most prevailing studies on using UAVs in the agriculture sector are exploratory and descriptive in nature, and primarily based on a systematic literature review (Daponte et al. 2019). Hence, most of these studies have a limited scope; e.g., concentrating only on farm monitoring and pesticide spraying (Hafeez et al. 2022) and weed management (Roslim et al. 2021). Differently from them, there are also several experimental research on tasks of UAVs such as mapping (Johansen et al. 2020; Zhang et al. 2020), path planning (Freitas et al. 2020), remote sensing (Tokekar et al. 2016), spraying (Meng et al. 2020), crop monitoring (Fu et al. 2020; Tetila et al. 2020; Ye et al. 2020), field monitoring (e.g., Elmokadem 2019), irrigation (Romero et al. 2018), and weed detection (Stroppiana et al. 2018). Undoubtedly, previous studies’ findings mainly enhance farmers’ awareness of using agricultural UAVs for several agricultural tasks. However, still little has been known about selecting optimum agricultural UAVs to be used in in-field operations from the perspective of smallholder farmers.

Concerning their typology and main sensorial and performance features, there is a great variety of agricultural UAVs in the marketplace (del Cerro et al. 2021). Therefore, a wide range of catalogs of agricultural UAVs, which are tailored for specific applications, enable smallholder farmers to make each of these operations more straightforward and provide cost and time efficiency for them to implement (Abbasi et al. 2022b). However, since there is a lack of knowledge among most of the elderly and low-educated smallholder farmers to uptake new knowledge, the selection of the best UAV for their agri-food production becomes difficult for them. Besides, the choice of the best UAVs has been well-documented in some specific sectors, such defense sector (Hamurcu and Eren 2020; Radovanović et al. 2021) and the civil sector (Akpınar 2021; Ulukavak and Miman 2019). Unfortunately, choosing which agricultural UAV is the best for smallholder farmers to be used in their in-field operations is still questionable due to the lack of adequate research in this promising research area. Those motivations lead to some research questions as follows:

  1. (i)

    What are the key criteria regarding UAVs for smallholder farmers?

  2. (ii)

    Which main criteria do smallholder farmers mainly consider when buying UAVs?

  3. (iii)

    Which existing UAVs in the marketplace are the best for smallholder farmers?

Building on the abovementioned discussion, a model is developed in this study to effectively perform UAV evaluation and selection for agricultural applications in uncertain environments. Herein, nine critical criteria for UAVs used in the agriculture sector are determined based on the review of relevant literature. Then, based on a detailed survey and experts’ opinions, five existing agricultural UAV brands are selected regarding their specifications. As mentioned, there are several studies on UAV selection in the literature. The techniques adopted in these studies to select, evaluate or rank the aircraft types with different specifications and sizes include fuzzy Choquet integral (Akpınar 2021), even swap method (Dožić and Kalić 2013), novel approach to imprecise assessment and decision environments (NAIADE) (Gomes et al. 2014), analytical hierarchy process (AHP) (Bruno et al. 2015; Dožić and Kalić 2015; Ulukavak and Miman 2019), fuzzy logic and even swaps method (Dožić and Kalić 2014), fuzzy AHP (Ozdemir and Basligil 2016), AHP, complex proportional assessment (COPRAS) and multi-objective optimization on the basis of ratio analysis method (MOORA) (Kiracı and Bakır 2018), AHP and technique of order preference similarity to the ideal solution (TOPSIS) (Hamurcu and Eren 2020; Kiracı and Akan 2020), fuzzy reference ideal method (FRIM) (Sánchez and Rodríguez, 2020), fuzzy AHP-VIKOR hybrid model (Radovanović et al. 2021), feuristics (Maywald et al. 2019), fuzzy AHP and efficacy method (Ahmed et al. 2020) and additive ratio assessment (ARAS) and full consistency method (FUCOM) (Hoan and Ha 2021). Differently from these studies, this study employs an integrated decision framework under the q-rung fuzzy context to select the best agricultural UAV for precision agriculture.

Specifically, we propose novel approaches for the experts’ weights determination, criteria weights calculation, and personalized ranking of UAVs to support farmers in the age of Agri-Food 4.0. The weights of experts and criteria must be determined methodically to mitigate inaccuracies and biases, which are strongly emphasized by Kao (2010) and Koksalmis & Kabak (2019). Furthermore, the determination of personalized ranks along with cumulative ranks provides a feel of personalization that supports the decision process to intuitively focus on individuals’ opinions apart from cumulative preference choices. Since such points are lacking in extant UAV selection models, motivation is gained by authors to put forward some innovative research contributions such as:

  • Methodical calculation of experts’ weights is achieved by presenting the regret measure,

  • Weighted logarithmic percentage change-driven objective weighting (LOPCOW) is developed for criteria weight estimation, by considering experts’ opinions and weights of experts,

  • Personalized ranking of UAVs is achieved by proposing an algorithm for rank estimation that integrated visekriterijumska optimizacija i kompromisno resenje (VIKOR) and Copeland strategy. Weights of criteria as well as experts are both considered during rank formulation along with personalized preferences from each expert on UAVs based on potential criteria.

A combination of the regret measure with LOPCOW, VIKOR, and Copeland strategy is developed in the present study to rationally select suitable UAVs for promoting smart farming. Some rationale for presenting these approaches are (i) regret measure closely mimics human behavioral characteristics and can effectively determine the essential values of experts by considering criteria type in the process. Besides, LOPCOW is an objective weight calculation procedure that does not require a-priori information about criteria and can effectively capture the hesitation of experts during a preference-sharing process; further, (ii) LOPCOW can considerably reduce the effects of extreme values by adopting a logarithmic operator, and finally, (iii) the well-known VIKOR approach is used, which is a compromise solution that considers distance norms for rank assessment resembling close to human-driven ranking in the present ranking algorithm for obtaining personalized and cumulative rank values of UAVs for rational ordering of UAVs via choice vectors from experts and Copeland strategy to aid farmers in their agro-business.

Before proceeding further, the authors briefly compare the proposed approaches with state-of-the-art methods in the context of weight determination and ranking. Though the studies in the literature provide methods such as entropy, criteria importance through intercriteria correlation (CRITIC), and so on, the LOPCOW has the following merit points such as (i) criteria type are taken into consideration, unlike other methods, which accounts for rationality in the weight estimation phase; further, (ii) the log function is the LOPCOW formulation provides a flexibility to experts to express their views in the \(\mp \infty\) space, which effectively aids in the symmetric preference expression context, especially in linguistic contexts, and finally, (iii) the LOPCOW technique provides flexibility to experts to experiment with different log bases to understand its effects on criteria weights, which are lacking in other methods. Apart from this, there are different ranking methods available in the literature, such as AHP and TOPSIS, but the VIKOR ranking method is a popular approach to rank alternatives (UAVs here) in a compromise fashion and the following merit points can be inferred such as (i) closely resembles human-driven decision-making, (ii) less computational complexity compared to AHP that follows pair-wise comparison strategy, (iii) also problems of consistency are incurred by AHP, which is not there is VIKOR; besides, (iv) Opricovic & Tzeng (2007) clearly demonstrated that advantages of VIKOR over TOPSIS in terms of the ranking strategy and other parameters that add potential to the VIKOR approach, and finally, (v) Opricovic & Tzeng (2007) showed that VIKOR can represent some special cases of outranking approaches as well, which is lacking in other ranking methods. As a result, these merit points motivate authors to present these approaches in the decision model for the rational selection of UAVs.

The rest of the study is organized as follows. Section 2 reviews the relevant literature on UAVs in smart agriculture to detect evaluation criteria and methodology. Section 3 precisely explains the methodological framework and research methodology. Section 4 demonstrates the application of the developed group decision-making approach and the final results. Section 5 discusses the results, and the managerial and practical implications are given in Sect. 6. Finally, the study's limitations and recommendations for further research are described in Sect. 7.

2 Literature review

In line with the purpose of the study, the place of UAVs in Agriculture 4.0 is tried to be revealed within the scope of the literature review. Moreover, the focus is on the factors considered in selecting agricultural UAVs.

2.1 UAVs in agriculture 4.0

In the production of agricultural goods, a conventional agri-food value chain has three key stages, including pre-field, in-field, and post-field stages (Abbasi et al. 2022b). Although all the stages are essential for the success of the agri-food value chain, as per these stages, the in-field stage, which contains many crop-growing processes such as sowing, spraying, and harvesting, particularly has a vital role in food security. On the other hand, the in-field stage is mainly based on traditional agricultural methods, which are labor-intensive and require farmable land, a respectable amount of time, and too much water for irrigation (Abbasi et al. 2022a). Accordingly, the disuse of sophisticated technologies and computer-based applications, particularly in the in-field stage, is more likely to cause harm to crops, eventually leading to agricultural waste.

Given the world population growth, demands for agricultural food are substantially growing, making agricultural waste one of the most significant problems for the next generation. Thence, agricultural production requires transformation from traditional agriculture to smart agriculture today more than ever (Aceto et al. 2019). Smart agriculture, also known as precision agriculture, is a recent farm management approach that rests on observation, measurement, and immediate response to internal challenges, such as illnesses and external parameters, such as wild animals, rodents, and drought (Petkovics et al. 2017). With information and communication technology, smart agriculture aims to utilize limited sources of farms efficiently and enhance agricultural productivity by decreasing costs related to agricultural production and boosting yield (Rakhade et al. 2021). As a result, farmers can successfully check the agricultural conditions and processes using smart agriculture without being present on the field 24 h a day as in conventional farming (Sinha and Dhanalakshmi 2022).

Besides, for farmers, particularly elder and low-educated smallholder farmers, who have no information about using different devices to measure the optimal ecological conditions for their crops, smart agriculture devices provide an automatic system that functions without any human direction (Antony et al. 2020). Thence, by equipping agricultural practitioners with a diversified set of tools, smart agriculture enables them to increase the number of crop yields, minimize costs, and improve the quality of agricultural products to overcome food security issues (Ozdogan et al. 2017). Additionally, since smart agriculture decreases the ecological footprint of traditional agricultural practices, it is considered a novel green technology approach for sustainable agriculture (Walter et al. 2017).

Aerial robots are at the heart of smart agriculture, among which, UAVs have been extensively applied to address various issues in agri-food production (Kim et al. 2019). As competent vehicles, their usage has significantly contributed to several areas of agriculture, including mapping, seed planting, pesticide and fertilizer prospecting and spraying, fertility assessment, weed recognition, and crop forecasting (Mogili and Deepak 2018). Utilizing UAVs, farmers can execute assigned tasks in minutes (Khelifi and Butun 2022). Thus, their use decreases working hours and enhances productivity with stability and measurement accuracy. Unlike other smart agriculture devices, which require a wide range of smart sensors to monitor infield operation, UAVs are flexible, easily operated, and less costly (Petkovics et al. 2017).

Two basic types of UAV platforms, fixed-wing and rotary-wing, are usually used in agriculture. Fixed-wing UAVs fly through thrust and aerodynamic lifting force and seem like an airplane, while rotary-wing UAVs are categorized as helicopter and multi-rotor types (Kim et al. 2019). Compared to rotary-wing UAVs, fixed wings are consistently larger and are utilized primarily for photography over a broad area (Pederi and Cheporniuk 2015). A rotary-wing UAV is extensively adopted for aerial photography and spraying. It has a big propeller at the top of the aircraft (Lan et al. 2017), whereas multi-rotor models are classified based on several rotors they have. We can refer to quadcopter, hexacopter, and octocopter, which comprise four, six, and eight rotors, respectively. In several cases, rotary-wing UAVs are mostly favored for agricultural tasks over those with fixed wings (Mistry et al. 2022).

Overall, the market growth for agricultural UAVs has been remarkable recently (Kim et al. 2019). Nevertheless, agricultural UAVs still have several technical limitations regarding battery efficiency, low flight time, payload, and so on (Von Bueren et al. 2015). Thence, to select the optimum agriculture UAV, it is crucial to determine the critical specifications of agricultural UAVs.

2.2 Key selection criteria for UAVs used in smart agriculture

Agriculture production has various complex requirements. To address these requirements, agricultural UAVs can vary in aspects such as flight time in minutes, drive type, payload, range, and so on. Thus, it is essential to determine the criteria for selecting the most suitable agricultural UAV.

2.2.1 Crop spraying

To enhance the yield and quality of crops against pests and diseases, pesticides are seen as the key means for prevention and control, but the more the pesticides are used, the more the ecological environment and human health are endangered (Wen et al. 2018). To deal with this problem, one of the most common applications of UAVs for smart agriculture is crop spraying (Xue et al. 2016). For spraying tasks, UAVs are designed with variable aerial spraying technology. Nozzle size and spray volume are critical because they can influence deposition and pesticide control efficacy (Wang et al. 2019). Besides, effective spraying width is another crucial specification in planning operation routes and improving spraying quality (Chen et al. 2017). Additionally, since the pressure of the water pump is the most significant determinant of the size of the droplets, the water pump regarding is also an essential requirement for UAVs (Hu et al. 2022). Finally, droplet size is one of the substantial elements affecting droplet deposition and drift for spraying (Chen et al. 2020). Herein, since flow rate can affect the size of droplets (Balsari et al. 2019), it is better to design UAVs equipped with a flowmeter that detects flow rate with high accuracy and high accuracy stability. Overall, agricultural UAVs should have some specifications regarding spraying technology including nozzle size, operating tank volume, effective spray width, water pump, and flowmeter in this work.

2.2.2 Radar system

Any collision of UAVs in environments with distinctive obstacles should be prevented (de Melo et al. 2021). To avoid collisions, UAVs require an obstacle avoidance radar that detects possible threats (Yasin et al. 2020). Further, UAVs should frequently move and replace their positions based on new flight conditions (Khelifi and Butun 2022). To monitor specific targets and carry out the assigned tasks in the areas of interest precisely, UAVs should also have particular radar systems, such as spherical radar system, which has several functions, including terrain following, obstacle sensing, and obstacle circumventing in all directions. Finally, UAVs should have top-view radar, which stands at the upper part of the UAV’s fuselage, to sense obstacles and plan a route to effectively avoid obstacles, as well as a spherical radar system (Wang et al. 2022b).

2.2.3 Camera

Image analysis has been extensively adopted in crop production for different purposes, including quality assessment, irrigation, and weed identification to enhance production efficiency (Sinha and Dhanalakshmi 2022). So, UAVs used in agriculture should be designed to capture visible and multi-spectral images of crops while they are growing (Petkovics et al. 2017). For capturing high spatial and temporal resolution images, agricultural UAVs should also have some specifications and sensors, such as view angle (Huang et al. 2021). Another important specification regarding agricultural UAV camera is image resolution which depends on the light intensity. Herein, UAVs’ digital camera exposure settings should be manually or automatically arranged depending on overall light intensity (Delavarpour et al. 2021). Finally, a first-person view (FPV) camera is an essential specification for UAVs to take the current supply from the flight controller and record the video (Shaw and Vimalkumar 2020). Hence, to monitor live agricultural operations, such as spraying and controlling pest attacks on fields, the FPV camera is almost a must for agricultural UAVs (Yallappa et al. 2017).

2.2.4 Remote control

Concerning crop management systems, UAVs, which can operate in conjunction with sensors and GPSs, can be commanded remotely to facilitate wireless surveillance and control (Sinha and Dhanalakshmi 2022). Recent advancements in wireless cellular systems also enable UAVs to be effectively remotely controlled beyond the visual line of sight (Galkin et al. 2016). Using Wi-Fi and Bluetooth technology, a remote controller generates and transmits the remote signal, and UAVs can be remotely controlled for several tasks (Meivel et al. 2016). In this regard, the remote controller should also have some specifications regarding display screens, operating memory, and storage space (Chen et al. 2019). For instance, the larger the display screen, the more the operator follows the UAVs’ tasks (Sadraey 2017).

2.2.5 Power system

Since UAVs are aerial devices with a highly long-range operation capability in terms of altitude and distance, they can fly for many hours in the air without any physical intervention (Khelifi and Butun 2022). Accordingly, to cover large agricultural areas, the flight time of UAVs should be long, and their speed should be as high as possible (Petkovics et al. 2017). Herein, to improve the power system of UAVs, the interaction between the motor and propeller is essential. For instance, for larger UAVs with massive payloads, big propellers and low-KV motors can work better for having more rotational momentum and maintaining UAVs’ stability (Anand and Dineshkumar 2016). Therefore, the motors, propellers, flight time, and electronic speed controllers are also vital when deciding the best agricultural UAV.

2.2.6 Technology

As a component of spraying and radar systems, UAVs can also be equipped with other technologies, such as branch targeting technology which can be utilized for spraying areas of interest precisely with the assistance of a radar system. Some UAVs are equipped with a flight laser function, which enables UAVs to measure the distance from the camera to a specific point in the field (McLeod et al. 2013). Finally, the intelligent return function allows UAVs to return along the original route quickly. So, through the intelligent return function, UAVs can land on the spoofing position (Li et al. 2018). All in all, to select the best agricultural UAV, its technology is also one of the vital selection criteria.

2.2.7 Battery

Although some petrol-driven types exist, today’s UAVs are usually electric-driven (Petkovics et al. 2017). Thus, energy limitation is also one of the main constricts in UAVs as there is a limited capacity for onboard batteries, reducing the flight time and autonomy of UAVs (Coppola et al. 2020). In this regard, battery capacity for maximum flight time becomes one of the vital specifications of UAVs (Nishiura and Yamamoto 2021). Moreover, to enhance the battery capacity, UAVs can have a removable battery that remains stable during flight (Zhao et al. 2018). Besides, long battery life is extremely required for longer flights and higher speeds (Petkovics et al. 2017). Finally, charging specifications such as charging time and temperature can be considered within the battery criterion.

2.2.8 Efficiency

To understand the performance of UAVs, there are also some other criteria, such as operating load, hourly work efficiency, maximum spray flow, and rotation speed. Per these criteria, the operating load is especially critical for the operational efficiency and endurance of UAVs used in agriculture (Li et al. 2022). Second, hourly work efficiency in terms of spraying area should be also an important performance criterion because UAVs’ hourly work efficiency increases, if they have the potential to spray large areas (Wang et al. 2022b). Third, since an increase in the liter of flow sprayed in a minute leads to an increase in UAVs’ spray flow efficiency, another efficiency criterion should be maximum spray flow as a critical spraying parameter (Wang et al. 2022c). Finally, the rotation speed should be crucial for UAV’s efficiency because nozzle rotation speed and rotor rotation speed play a critical role in droplet size, affecting the quality of spray of agricultural UAVs (Zhu et al. 2019).

2.2.9 Sales price

There are certain costs related to the utilization of IoTs in agriculture (Banerjee 2019). However, the cost of adopting smart technologies and systems, which usually includes deployment and operation and maintenance costs, is the main barrier to digitization in the agriculture sector (Abbasi et al. 2022b). Deployment costs are relatively higher because these costs are particularly related to the installation and implementation of hardware, such as UAVs, to perform specific agricultural operations (Sinha and Dhanalakshmi 2022). Thence, since implementation costs, including hardware costs such as IoT devices and sensors, are among the main costs for IoT in smart agriculture (Gaspar et al. 2021), it is also crucial to consider the price of UAVs while selecting the best agricultural UAV.

Overall, the criteria determined for UAVs used in agriculture are outlined in Table 1. Regarding Table 1, nine key criteria are identified based on relevant literature on agricultural UAVs.

Table 1 Evaluation criteria utilized and their descriptions
Full size table

3 Research methodology

In this section, the basic ideas pertaining to q-rung orthopair fuzzy set (qROFS) are presented, and then, the execution steps of the integrated approach are explained.

3.1 Preliminaries

Let us provide certain rudimentary concepts of qROFS that sets the ground for the integrated approach.

Definition 1

(Atanassov 1986): \(G\) is a fixed set with \(H\subset G\) also being fixed. Then, \(\overline{H }\) is an IFS in \(G\) such that.

$$\overline{H} = \left\{ {g,\mu_{H} \left( g \right),v_{H} \left( g \right)\left| {g \in G} \right.} \right\},$$
(1)

Where \(\mu_{{\overline{H} }} \left( g \right)\), \(v_{{\overline{H} }} \left( g \right)\), and \(\Pi_{{\overline{H} }} \left( g \right)\)\(= 1 - \left( {\mu_{H} \left( g \right) + v_{{\overline{H} }} \left( g \right)} \right)\), \({\mu }_{H}\left(g\right),{\upsilon }_{H}\left(g\right)\) are the hesitation, preference, and non-preference grades, \(\mu_{{\overline{H} }} \left( g \right)\), \(v_{{\overline{H} }} \left( g \right)\), and \({\pi }_{H}\left(g\right)\) poses values in the unit interval \(\mu_{{\overline{H} }} \left( g \right)\)\(+ \le 1\).

Definition 2

(Yager 2017): \(G\) is as before and \(g\in G\). Then, the qROFS \(GX\) on \(G\) is considered as.

$$GX = \left\{ {g,\mu_{GX} \left( g \right),v_{GX} \left( g \right)\left| {g \in G} \right.} \right\},$$
(2)

where \({\mu }_{GX}\left(g\right)\) and \({\upsilon }_{GX}\left(g\right)\) yield unit interval values representing preference and non-preference grades, respectively. Moreover, \(0\le {\left({\mu }_{GX}\left(g\right)\right)}^{q}+{\left({\upsilon }_{GX}\left(g\right)\right)}^{q}\le 1\) with \(q\ge 1\). When \(q=1\), we get IFS [1], and when \(q=2\), we get PFS [3].

Note 1: For convenience, \(GX=\left({\mu }_{x},{\upsilon }_{x}\right) \forall x=\mathrm{1,2},\dots ,\tau\) is considered as a q-rung orthopair fuzzy number (q-ROFN). Collectively, they form q-ROFN.

Definition 3

(Yager 2017): \({GX}_{1}\) and \({GX}_{2}\) are two q-ROFNs. Arithmetic operations are given by,

$$GX_{1} \oplus GX_{2} = \left( {\left( {1 - \left( {1 - \mu_{1}^{q} } \right)\left( {1 - \mu_{2}^{q} } \right)} \right)^{1/q} ,v_{1} v_{2} } \right),$$
(3)
$$GX_{1}^{\rho } = \left( {\mu_{1}^{\rho } ,\left( {1 - \left( {1 - v_{1}^{q} } \right)^{\rho } } \right)^{1/q} } \right)\rho > 0,$$
(4)
$${}_{\rho }GX_{2} = \left( {\left( {1 - \left( {1 - \mu_{2}^{q} } \right)^{\rho } } \right)^{1/q} ,\upsilon_{2}^{\rho } } \right)\rho > 0,$$
(5)
$$GX_{1} \oplus GX_{2} = \left( {\mu_{1} \mu_{2,} \left( {1 - \left( {1 - v_{1}^{q} } \right)\left( {1 - v_{2}^{q} } \right)} \right)^{1/q} } \right),$$
(6)
$$S\left({GX}_{2}\right)={\mu }_{2}^{q}-{\upsilon }_{2}^{q},$$
(7)
$$A\left({GX}_{2}\right)={\mu }_{2}^{q}+{\upsilon }_{2}^{q}.$$
(8)

Operations such as addition, power operation, scalar multiplication, multiplication, score, and accuracy are presented in Eqs. 3, 4, 5, 6, 7, and 8, respectively.

3.2 Weights of experts and criteria

This section provides a stepwise procedure for determining the weights of two crucial entities in the decision-making process. Both experts and criteria have a substantial role in the decision process. Weight estimation relates to the critical determination of these entities. In reality, an implicit competition and trade-off exist, which cannot be well modeled by assigning equal weights or different weights at random. Works from Kao (2010) and Koksalmis and Kabak (2018) are supportive evidence for the claim that the determination of weights through methodical aspects not only reduces biases and subjectivity but also provides rational values.

Two main categories of weight determination include ‘partially known weight information’ and ‘fully unknown weight information’ (Krishankumar et al. 2022a). The former needs additional information, which may not be commonly available and to handle such issues, the latter is introduced. In this work, we adopt the latter context and approaches with their steps presented below. Popular methods in the latter context include AHP (Anbuudayasankar et al. 2020) and entropy (Kumar et al. 2021; Namdari et al. 2019) that cannot effectively capture the hesitation of experts and also the variability in the distributions. Furthermore, a method such as AHP faces the overhead of consistency, thereby increasing complexity.

Taking these challenges into account, in this section, we put forward two approaches that can methodically determine the weights of both experts and criteria. Regret theory (RT) (Loomes and Sugden 1982) and LOPCOW (Ecer and Pamucar 2022) are presented under the q-ROFN context to better manage the issues expressed above and to determine weights methodically.

RT is an interesting concept from the psychology domain that aims to choose options so that it gives less regret than other options in the candidate set. The procedure can capture experts' hesitation during the preference-sharing phase and also determines the regret value associated with an expert that reflects the behavioral attitude of the expert (Aggarwal 2021). Besides, the procedure is elegant and straightforward with less computational complexity than the extant method mentioned above. The steps for the calculation of experts' weights are described as follows:

  • Step 1: Consider \(T\) matrices of \(A\times B\) with q-ROFN as the rating information to rate \(A\) alternatives based on \(B\) criteria. \(T\) expert provides her/his rating to form decision matrices.

  • Step 2: Determine the accuracy by applying Eq. (8) to the q-ROFNs from Step 1. This yields \(T\) accuracy matrices of order \(A\times B\).

  • Step 3: Apply Eqs. 9, 10, and 11 to determine the von-Neumann values, regret values, and the utility measure for each expert, which eventually aids in determining the weights of the experts.

    $${vof}_{ij}^{l}={\left(A\left({GX}_{ij}^{l}\right)\right)}^{\alpha },$$
    (9)
    $${ref}_{ij}^{l}=1-{e}^{-\beta \left({vof}_{ij}^{l}\right)},$$
    (10)
    $${utf}^{l}=\sum_{i=1}^{A}\sum_{j=1}^{B}\left({vof}_{ij}^{l}+{ref}_{ij}^{l}-{vof}_{j}^{l*}\right),$$
    (11)

where \(\alpha\) and \(\beta\) are in the unit interval, \(l\) shows the index of expert, \(i\) stands for the index of alternative, and \(j\) represents the index of criteria. Moreover, \({vof}_{j}^{l*}\) denotes the value pertaining to the type of criteria that is maximum for benefit and minimum of cost type criteria.

From these equations, it is clear that an expert with a higher utility value gets higher weight and the utility measure is composed of von-Neumann values and regret values. As the von-Neumann measure improves, the regret reduces, and the rejoicing enhances for an expert, inferring that the expert is less unpleasant about the decision process. This is mathematically formulated with the help of the exponent function.

  • Step 4: Normalize the utility values by using Eq. (12) to form a weight vector of \(1\times T\) order. The values are in the unit range and sum to unity.

    $${wE}_{l}=\frac{{utf}^{l}}{\sum_{l=1}^{T}\left({utf}^{l}\right)},$$
    (12)

where \({wE}_{l}\) is the weight of expert \(l\).

Based on the steps presented above, experts' weights are determined methodically. Further, the stepwise procedure to calculate the weights of criteria is represented. LOPCOW is an objective weight determination method that works under no a-priori information context. The approach has the ability to understand the nature of criteria and also estimates hesitation during preference articulation via the variability distribution measure. Furthermore, the logarithmic function supports reducing the effect of extreme values by setting the bounds to undefined values or infinity. Finally, experts’ weights are also considered in the formulation for the weight calculation of criteria. Driven by these attractive benefits, the procedure is provided as follows:

  • Step 5: Consider a criteria matrix of \(T\times B\) order that uses q-ROFN for rating each criterion.

  • Step 6: Apply Eq. (8) to the q-ROFN from Step 5 to find the accuracy values and to construct an accuracy matrix of \(T\times B\) order.

  • Step 7: Normalize the accuracy values from Step 6 by using Eq. (13). The formulation is provided separately for benefit and cost types. Again the order of the normalized matrix is \(T\times B\).

    $$g_{{lj}} = \left\{ {\begin{array}{*{20}c} {\frac{{A\left( {GX_{{lj}} } \right) - A_{{min}} }}{{A_{{max}} - A_{{min}} }},\hspace{1cm} {\text{if }}j \in benefit,} \\ {\frac{{A_{{max}} - A\left( {GX_{{lj}} } \right)}}{{A_{{max}} - A_{{min}} }},\hspace{1cm} {\text{if }}j \in cost,}\hspace{0.6cm} \\ \end{array} } \right.$$
    (13)

where \(A\left({GX}_{lj}\right)={wE}_{l} \left(A\left({GX}_{lj}\right)\right)\) is the weighted accuracy measure, \({A}_{min}\) is the minimum accuracy value and \({A}_{max}\) denotes the maximum accuracy value.

  • Step 8: Determine the percentage value criteria-wise to form a vector of \(1\times B\) order. The mean square value as well as the percentage of deviation is determined in this step whose log measure is determined so as to mitigate the effects of extreme values. LOPCOW is applied for this purpose.

    $${pv}_{j}=ln\left|\frac{\sqrt{\frac{{\sum }_{l=1}^{T}{\left(A\left({GX}_{lj}\right)\right)}^{2}}{T}}}{{\sigma }_{j}}\right|\times 100,$$
    (14)

    where \(\sigma\) is the deviation measure

When all experts provide the same value to a criterion, the deviation is zero at that time, indicating no hesitation (hypothetical case), which will yield infinity and the natural log function will eventually produce infinity as a percentage value. Similarly, if the natural log value is to be determined for zero in a hypothetical situation, it is infinity again. So the extreme value effects are nullified by the natural log measure. The value is multiplied by 100 to determine the percentage value. The criterion \(w\)th high \({pv}_{j}\) yields high importance/weight.

  • Step 9: Normalize the \({pv}_{j}\) values using Eq. (15) to identify the weights of criteria that form a vector of \(1\times B\) order in the unit interval and sum equal unity.

    $${wC}_{j}=\frac{{pv}_{j}}{\sum_{j}{pv}_{j}},$$
    (15)

where \({wC}_{j}\) is the weight of criterion \(j\).

3.3 Personalized ranking algorithm

The ranking is a critical step in the decision-making process that involves prioritizing the alternatives based on their rank values (Krishankumar and Ecer 2023), which is influenced by the performance/preference of the alternative over the criteria (Saha et al. 2022). With the help of the preference matrix and criteria weights, the rank values of alternatives are determined. Based on Kumar et al. (2017), it is clear that earlier ranking approaches rank alternatives without a-priori choices of the experts but only consider preference information. In practical cases, some experts have certain personal opinions on each alternative that must be regarded as potential information for the decision process (Rhudy et al. 2010; Krishankumar et al. 2022b; Saleem et al. 2014).

VIKOR is an attractive and popular ranking technique that works on the principle of \({L}_{p}\) norm (Opricovic 2011). It basically adopts a compromise solution driven by distance norms for ranking alternatives. The VIKOR method outperforms its close counterpart TOPSIS (Dammak et al. 2015) and can represent outranking methods as special cases (Opricovic and Tzeng 2007). Further, it can be inferred that VIKOR is simple and elegant and resembles close to human-driven decision-making. Integrating personal choices to VIKOR and aggregating personalized rank values from experts offers a powerful ranking algorithm that not only ranks alternatives rationally but also adheres to the human-driven decision process. Additionally, it must also be inferred that the ranking procedure takes into account the nature of criteria for rank estimation and experts’ personal choices to obtain a reasonable and rational ranking of alternatives. The proposed algorithm is presented below to obtain both individual and cumulative rankings of the alternatives based on experts’ rating data.

figure a
$${G}_{lj}^{+}={\mathrm{max}}_{j\in BT}\left(A\left({GX}_{ij}^{l}\right)\right) \mathrm{or} {\mathrm{min}}_{j\in CT}\left(A\left({GX}_{ij}^{l}\right)\right),$$
(16)
$${G}_{lj}^{-}={\mathrm{max}}_{j\in CT}\left(A\left({GX}_{ij}^{l}\right)\right) \mathrm{or} {\mathrm{min}}_{j\in BT}\left(A\left({GX}_{ij}^{l}\right)\right),$$
(17)
$${S}_{li}=\sum_{j=1}^{B}{wC}_{j}\frac{d\left({GX}_{ij}^{l},{G}_{lj}^{+}\right)}{d\left({G}_{lj}^{-},{G}_{lj}^{+}\right)},$$
(18)
$${R}_{li}={\mathrm{max}}_{j\in B}\left({wC}_{j}\frac{d\left({GX}_{ij}^{l},{G}_{lj}^{+}\right)}{d\left({G}_{lj}^{-},{G}_{lj}^{+}\right)}\right),$$
(19)
$${Q}_{li}=\theta \frac{{S}_{li}-{S}_{li}^{*}}{{S}_{li}^{-}-{S}_{li}^{*}}+\left(1-\theta \right)\frac{{R}_{li}-{R}_{li}^{*}}{{R}_{li}^{-}-{R}_{li}^{*}},$$
(20)
$${C}_{i}=\sum_{l=1}^{T}{{wE}_{l} (ro}_{l}),$$
(21)
$${F}_{i}={C}_{max}-{C}_{i},$$
(22)
$${FRO}_{i}={C}_{i}-{F}_{i},$$
(23)

where \(BT\) and \(CT\) are the benefit type and cost type, respectively. Moreover, \({G}_{lj}^{+}\) and \({G}_{lj}^{-}\) denote the ideal solution and anti-ideal solution, respectively. Here, \(d(a,b)\) shows the distance between \(a\) and \(b\), where \(\theta\) is the strategy value in the unit interval. Furthermore, \({S}_{li}^{*}\) and \({R}_{li}^{*}\) are the minimum values of \({S}_{li}\) and \({R}_{li}\), respectively. On the other hand, \({S}_{li}^{-}\) and \({R}_{li}^{-}\) stand for the maximum values of \({S}_{li}\) and \({R}_{li}\). We have also \({C}_{i}\), \({F}_{i}\), \({C}_{max}\) and \({ro}_{l}\) which show the win score, loss score, maximum win score, and the rank order of alternatives associated with the data from expert \(l\), respectively. Finally, \({FRO}_{i}\) displays the final rank order for an alternative \(i\). Eqs.  (21)–(23) represent the Copeland strategy (Ecer 2021) that helps in determining the final ordering of alternatives.

The framework of the proposed model is depicted in Fig. 1. It is observed that experts provide their ratings for UAVs and criteria. Initially, the rating is given in qualitative terms that are further converted to qROFNs based on tabular values. Experts’ weights are determined methodically to form an expert weight vector, which is used to calculate the criteria weights and rank the UAVs. Specifically, the experts’ importance values are utilized in both phases to gain rationale in the decision process intuitively. As it can be inferred that experts play a remarkable role in decision-making, embedding their importance is significant in the decision process. Both personalized ranking of UAVs based on each expert's data and cumulative ranking based on the Copeland strategy helps the stakeholders to understand the ordering of UAVs from both perspectives. The criteria weight vector is determined by considering the choice matrix from experts and the weights of experts. Lastly, the weight vectors of both experts and criteria are utilized for ranking UAVs.

Fig. 1
figure 1

Proposed agricultural UAV selection model with the qRONs

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4 Results: application of the agricultural UAV selection

Konya, the country’s largest province in terms of area, is located in the interior of Turkey and is known as “Turkey’s granary.” Due to its geographical structure consisting of plateaus and plains, wheat, barley, rye, oats, and sugar beet are grown in the region. Whereas the adverse impacts of the Covid-19 pandemic continued, the outbreak of the Russia-Ukraine war has caused incredible increases in oil and raw material prices. Herein, agriculture is one of the sectors directly affected by such negativities since increases in fertilizer, pesticide, and oil markets increase input prices in agriculture. A company in Konya provides farmers with spraying, fertilization, disease detection, seeding, and weed control services via UAVs. It aims to reduce the farmers' fuel, fertilizer, and pesticide costs and thus contribute to sustainability. Since the company needs professional agricultural rotary-wing UAVs, five alternatives have been identified (A1: DJI AGRAS T30, A2: VENUS 150, A3: Brouav D72L-8, A4: Helio T22, A5: Brouav D52L-8). To evaluate the alternatives and criteria, a decision-making team of four consisting of an agricultural engineer, an electronics engineer, a topographical engineer, and an academician is formed (DM1, DM2, DM3, DM4).

While three team members have bachelor’s degrees, the academician has a doctorate. Moreover, nine criteria in Table 1 are determined (C1, C2, …, C9) regarding the literature review and experts’ opinions. DM1, DM2, DM3, and DM4 rate five UAVs based on nine criteria C1, C2, C3, C4, C5, C6, C7, C8, and C9. Here, the first eight criteria are benefit-type, whereas C9 is cost-type. Experts adopt qualitative ratings via the Likert scale converted to the respective qROFN based on the tabular values. The stepwise procedure for ranking UAVs based on the competing criteria is discussed below:

  • Step 1: Form four preference matrices with the order of \(5\times 9\) with qualitative terms as rating information. Later, for the decision process, these terms are converted to their respective qROFNs. As discussed above, four experts rate five UAVs based on nine criteria (cf. Table 2).

  • Step 2: Use the data from Step 1 to determine the weights of experts. This is a vector of order \(1\times 4\) that represents the importance of each expert in the specified decision process. Table 3 provides the dataset associated with each UAV being rated by an expert over a particular criterion. Consequently, four matrices are obtained (cf. Fig. 2).

Table 2 qROFNs associated with qualitative terms
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Table 3 Rating data for UAVs from experts
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Fig. 2
figure 2

von-Nueman measure a DM1 b DM2 c DM3 d DM4

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From Figs. 3 and 4, it is clear that four matrices based on the von-Neuman measure and regret measure are obtained, each associated with an expert. The utility measure utilizes these values for determining the utility value of an expert. Hence, a vector of 1 × 4 order is obtained. Eqs. (8) and (11) are applied to calculate the von-Neuman values and regret values, respectively. Eqs.  (9) and (10) are applied to determine the importance of each expert and the values are obtained as 0.24, 0.28, 0.22, and 0.26, respectively. It is obvious that these values are in the unit interval and sum to unity. Based on these values, criteria weights are determined and given by 0.013, 0.063, 0.372, 0.022, 0.368, 0.057, 0.006, 0.008, and 0.103, respectively.

  • Step 3: Form four vectors each of order \(1\times 9\) by using linguistic terms, which are also further converted to qROFN based on the tabular values (cf. Table 4).

Fig. 3
figure 3

Regret measure a DM1 b DM2 c DM3 and d DM4

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Fig. 4
figure 4

Normalized criteria values

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Table 4 Opinions on criteria from experts
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Figure 4 depicts the normalized weighted accuracy values associated with each criterion. Eqs.  (11), (12), and (13) are utilized to determine the weights/importance of criteria. Equation (13) is particularly implemented to determine the normalized value based on the type of criteria. In the case example, as discussed earlier, seven criteria are benefit and the rest are cost type. By normalizing the probability value of each criterion, the weights are determined as 0.032, 0.092, 0.417, 0.018, 0.325, 0.039, 0.011, 0.003, and 0.087, respectively.

  • Step 4: Apply the procedure described in Sect. 3.3 to determine the rank values of UAVs that are of order \(1\times 5\). The ordering of UAVs is determined by the data from each expert and based on the Copeland strategy, the cumulative ordering is obtained.

Table 5 illustrates the ordering of UAVs based on individual ratings, which offers a sense of personalization lacking in other extant models. Each expert provides her/his rating on the UAVs based on diverse criteria and based on their rating, ranking values are obtained. It can be seen that the ordering of UAVs based on the data from DM1 is A1 \(\succ\) A5 \(\succ\) A3 \(\succ\) A2 \(\succ\) A4, DM2 is A5 \(\succ\) A1 \(\succ\) A3 \(\succ\) A2 \(\succ\) A4, DM3 is A1 \(\succ\) A5 \(\succ\) A3 \(\succ\) A4 \(\succ\) A2, and DM4 is A1 \(\succ\) A3 \(\succ\) A4 \(\succ\) A5 \(\succ\) A2. Based on these rank orders, the Copeland strategy is adopted to determine the cumulative ranking of UAVs and it is calculated as A1 \(\succ\) A5 \(\succ\) A3 \(\succ\) A4 \(\succ\) A2. It can be inferred that A1 is the most viable UAV for the problem considered and UAVs A5, A3, A4, and A2 follow the ordering for the decision problem that is regarded in the present study based on the rating data from the expert.

Table 5 Personalized rank values of UAVs based on the experts’ data
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4.1 Sensitivity analysis and comparative examination

This section intends to understand the efficacy and limitations of the developed model by comparing it with extant models. Besides, the effects of criteria weights and strategy values in rank estimation are investigated by varying the values considerably. Figure 5 depicts the inference that readers can gain from the sensitivity analysis. In this section, an inter/intra sensitivity analysis by altering both criteria weights and strategy values are performed. We consider two types of weights, unequal or biased weights and equal or unbiased weights of criteria. The latter is computed based on the assignment of \(\frac{1}{B}\) where \(B\) is the number of criteria.

Fig. 5
figure 5

Sensitivity analysis of criteria weights and strategy values a DM1 biased; b DM1 unbiased; c DM2 biased; d DM2 unbiased; e DM3 biased; f DM3 unbiased; g DM4 biased; and h DM4 unbiased (group utility values)

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Figure 5a–h illustrate a detailed sensitivity analysis to understand the robustness of the proposed model. Both the weights of criteria and strategy values are altered systematically to determine the effect on the ranking orders. This infers that both inter/intra sensitivity analysis is performed with two cases of criteria weights, biased (unequal weights) and unbiased (equal weights), and nine strategy values from 0.1 to 0.9 with a single step size. The figures represent that the proposed model is robust even after adequate alterations are made to the weights and strategy values. Though the rank values change, the ordering of UAVs remains intact based on each expert’s rating data. This comprehensive analysis concerning the effect of weights and strategy values on the ranking order from the proposed model reveals the robustness of the model towards these parameters. Although each expert’s ranking order is based on diverse rating information, the changes in parameter values do not alter the ordering within the experts’ data space. Specifically, it can be seen that DM4’s data under unbiased weight conditions yields only group utility values and the merit function cannot be calculated owing to the same individual regret values, which causes divide by zero error as per the formulation of the merit function. Other experts' data yield the merit function values for UAVs under biased and unbiased weight categories.

Furthermore, we compare the proposed model from statistical and theoretical perceptions. Under the theoretical perception, extant methods viz., Nur et al. (2020), Radovanović et al. (2021), and Aktas and Kabak (2022) are compared with the suggested model. Table 5 describes the theoretical merits of the proposed model, which is further elaborated in a point-wise manner to clearly understand the innovative efficacy of the model proposed in this work. Moreover, we validate the model’s effectiveness via statistical perception by considering the consistency and discrimination tests. Extant methods such as Peng et al. (2019), Krishankumar et al. (2021), Riaz et al. (2020), and Yang and Pang (2019) are compared with this work. The Spearman correlation approach is employed to determine the correlation coefficients (cf. Figure 6) of rank orders from each method, which is further used to discuss the consistency of the developed model versus the other models.

Fig. 6
figure 6

Spearman correlation for consistency test (x-axis: 1. Proposed vs. Proposed; 2. Proposed vs. Peng et al. (2019), 3. Proposed vs. Krishankumar et al. (2021); 4. Proposed vs. Riaz et al. (2020), and 5. Proposed vs. Yang & Pang (2019))

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Table 6 summarizes the characteristics of the proposed and extant models, which clarifies the efficacy of the suggested model. Further, the novelties of the proposed framework are summarized as follows:

  • qROFN is the data structure adopted in the present study, which can model uncertainty from three dimensions: membership grade, non-membership grade, and hesitancy grade. Besides, experts can gain flexibility in sharing their preferences by adjusting the parameter q, which is lacking in other models.

  • The importance of experts is methodically identified by effectively capturing the hesitation of experts, which is lacking in the extant UAV selection models.

  • Furthermore, the weights of criteria are calculated by adequately considering the variability in the preference distribution and the importance of experts.

  • Moreover, the type of criteria is considered both during criteria weight estimation and ranking of UAVs, which is lacking in other models.

  • Unlike the extant UAV selection models, the proposed model allows the determination of both personalized and cumulative ranking orders of UAVs by considering criteria types and adopting distance norms that closely resemble human-driven decision-making.

  • Finally, it can be inferred that experts' importance is considered during both criteria weight estimation and rank estimation, which is lacking in the earlier UAV selection models.

Table 6 Summary of features of different models: the proposed model vs. others
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As discussed above, we perform the consistency test to realize the consistency of the proposed model concerning other models. For this purpose, the data from Sect. 4 is fed into all qROFN-based decision models and the rank orders are obtained. These orders are further fed into the Spearman correlation method for determining the coefficient values. For extant models, the data is initially aggregated using simple weighted geometry. Later, the fused data is given as input to the extant qROFN decision models. Figure 6 depicts the coefficient values that help determine the proposed model's consistency. Obviously, it can be figured out that the suggested model yields a unique rank ordering owing to the personalization mechanism adopted in the formulation. Nevertheless, the consistency is realized concerning other extant models with coefficient values 1, 1, 0.70, 0.50, and 0.50. In the discrimination test, the models are fed with 350 matrices of 5 × 9 order, and variability is measured within the rank vectors and plotted in Fig. 7. Weights of criteria are considered as determined above.

Fig. 7
figure 7

Discrimination test for proposed and other qROFN decision models

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Based on Fig. 7, it is clear that the proposed framework produces rank values that are broader compared to other extant models. Specifically, to determine the discrimination ability of the proposed model, personalized ranks from experts are aggregated by using the simple weighted geometry and the variance measure is calculated for each rank vector. In the extant models, the data is initially aggregated and the rank values are determined. Accordingly, 350 matrices are simulated, feeding to each qROFN decision model, and rank values are determined along with the variability of the vectors. This yields a vector of 1 × 350 for each model plotted in Fig. 7. The proposed model has superior discrimination ability than other extant models. Intuitively, this may be realized owing to the personalization of rank value determination that aids in determining ranks of UAVs based on each individual’s data that is finally fused to obtain the final rank vector. Following this, the models suggested by Peng et al. (2019) and Krishankumar et al. (2021) perform closely to the proposed model. The variability measure clarifies the experts use the model for better backup management at critical times. In the present application of UAV selection, the rank ordering with broader values associated with UAVs provides flexibility and ease to experts to plan backup UAVs in an emergency and urge.

5 Discussion of the results

Agricultural UAVs have become crucial, especially in recent years. These aerial vehicles can be utilized in many operations, including spraying, seed sowing, fertilizer spraying, weed recognition, mapping, and plant monitoring (Kim et al. 2019). Besides, they can fly without a pilot compared to manned aircraft, are easily used, and have a low purchase cost compared to other IoT devices (Tsouros et al. 2019). All of them have made UAVs attractive in the agriculture sector as well. However, selecting the best agricultural UAV is still a difficult decision because there are many alternative agricultural UAVs equipped with several technical specifications, and thus there are several criteria that influence purchasing of them.

Interestingly, there is no direct research on selecting the most desirable agricultural UAVs in the relevant literature. However, previous research studies on the selection of UAVs used in defense (Hamurcu and Eren 2020; Radovanović et al. 2021) and civil sector (Akpınar 2021; Ulukavak and Miman 2019) display that criteria such as payload capacity, maximum speed, maximum endurance, economic life, maximum altitude, and price are determinants in their selection. Based on the literature review on agricultural UAVs, evaluation criteria are especially determined based on their spraying and spreading systems (Hu et al. 2022; Wang et al. 2019), radar systems (Wang et al. 2022a; Yasin et al. 2020), camera (Kim et al. 2019; Petkovics et al. 2017), remote control (Sinha and Dhanalakshmi 2022), power system (Khelifi and Butun (2022), technology (Li et al. 2018), battery (Petkovics et al. 2017), efficiency (Li et al. 2022; Wang et al. 2022c), and price (Abbasi et al. 2022b).

The research results indicate that camera (0.417) is the foremost criterion according to its priority weight. Moreover, resolution (Kim et al. 2019), view angle (Sugiura et al., 2005), light intensity (Delavarpour et al. 2021), and FPV camera (Yallappa et al. 2017) specifications are determined as the foremost specifications to select the best agricultural UAVs. Regarding its priority weight, the following foremost criterion is found as the power system (0.325). Herein, agricultural UAVs’ motors, propellers, flight time, and electronic speed controllers also become essential specifications for picking up the best agricultural UAVs since they influence their flight time and speed (Petkovics et al. 2017). The radar system (0.092) is the third vital criterion concerning the priority weights. To avoid collisions, agricultural UAVs should also be equipped with radar systems such as obstacle avoidance (Yasin et al. 2020) and top-view radar (Wang et al. 2022b). To follow specific targets and perform the assigned tasks in specific areas, terrain following radar should be found in agricultural UAVs. As to the priority weights, the following key criterion is decided as price (0.087), which is followed by technology (0.039), spraying and spreading systems (0.032), remote control (0.018), battery (0.011), and efficiency (0.003), respectively.

In this research, each expert also provides his/her rating on agricultural UAVs regarding these evaluation criteria. Based on these results, DM1, DM3, and DM4 select A1 as the best agricultural UAV, while DM2 ranks A5 as the most optimum agricultural UAV. DM1 and DM2 also similarly rank A4 as the last optimum agricultural UAV, whereas DM3 and DM4 select A2 as the last optimum agricultural UAV. Based on all rank orders, the output of the proposed framework also shows that A1 is the optimum agricultural UAV. Thus, DJI AGRAS T30 is selected as the most proper UAV used in agriculture. Further, A5 is ranked as the second optimum agricultural UAV, followed by A3, A4, and A2. So, BROUAV D52L-8 becomes the second best UAV to be used in agriculture, whereas BROUAV D72L-8 is ranked as the third optimum agricultural UAV. Finally, Helio T-22 and Venus 150 are identified as the fourth and last-ranked agricultural UAVs, respectively.

6 Managerial and practical implications

A decrease in the agricultural labor force and an aging rural population lead to a decline in the efficiency of agricultural production. Thence, carrying out agricultural tasks requires more innovation today than ever to enhance efficiency in agricultural production. In the last few years, with Industry 4.0, agriculture has become one of the industries in which innovation and technological development play a critical role in its processes and operations. By integrating recent technologies such as IoT and robotics, agriculture has gained a more autonomous and intelligent environment. Accordingly, the transformation from traditional agriculture to smart agriculture, namely Agriculture 4.0, enhance agricultural productivity and food safety and decrease the negative environmental effect of improper agricultural practices and the use of excessive natural resources.

Herein, agricultural UAVs have an essential potential to carry out several agricultural tasks effectively, particularly in smart agriculture. Since they have high maneuverability and are good at working in rough areas and small plots efficiently, many agricultural practitioners are eager to use these modern vehicles in their agricultural practices, from spraying to monitoring, to enhance efficiency and maximize profit. On the other hand, selecting the best agricultural UAVs to be used in agricultural tasks is still a very tough decision for many smallholder farmers because there is a great variety of agricultural UAVs in the marketplace in terms of their typology, performance features, and costs. This paper brings some agricultural experts to help farmers determine the most critical evaluation criteria to select the optimum agricultural UAV. Based on their evaluation, the most important to least important criteria are ordered as camera, power system, radar system, price, technology, spraying and spreading systems, remote control, battery, and efficiency. Thus, firstly, the study's findings help many farmers by showing the most critical selection criteria for selecting the optimum agricultural UAV. Additionally, depending on the DMs’ rating, DJI AGRAS T30 is selected as the optimum UAV to be used in agriculture, followed by BROUAV D52L-8. Accordingly, secondly, the results of the paper directly present which agricultural UAV in the marketplace is optimum in terms of evaluation criteria. Hence, the results reduce the time farmers need to decide on the best agricultural UAV and guide them to select the optimum agricultural UAV to enhance their agricultural performance. Finally, to minimize costs and increase yields by reducing the use of fertilizers, pesticides, and other chemicals for improving plant health and providing food safety, the results of the paper attempt to make the use of agricultural UAVs ubiquitous in agriculture over the next several years.

7 Conclusion and outlook

The ongoing population growth, incorporated with changing consumption habits and increasing demand, is burdening agricultural systems. Thence, smart agriculture devices such as agricultural UAVs will undoubtedly play a pivotal role in smart agriculture for the next years. Principally, agricultural UAVs can be deployed for several agricultural tasks such as pesticide spraying, seed sowing, fertilizer spraying, weed recognition, mapping, and plant monitoring to save money and enhance the abilities of agricultural practitioners. Based on these various tasks, agricultural UAVs have very complex technical features that make it necessary to choose specific criteria to evaluate them. Nevertheless, selecting the best agricultural UAVs is a difficult task, particularly for agricultural practitioners, because this selection necessitates the consideration of several criteria, including spraying and spreading system, radar system, camera, remote control, power system, technology, battery, efficiency, and price. As a result, this work develops the q-ROFN-LOPCOW-VIKOR methodology to handle uncertainty and vagueness effectively. Regarding the findings, camera, power system, and radar system are the essential drivers for selecting an agricultural UAV. Further, the result shows that the best-suited agricultural UAV is DJ AGRAS T30. The overall conclusion is that adopting the q-ROFN methodology provides the optimum choice for picking up the optimum agricultural UAV.

As with all studies, this study also has some limitations. Some limitations of the proposed integrated approach are: (i) partial knowledge from the experts cannot be modeled by the decision system, (ii) non-availability of preference information due to pressure, hesitation, and unwillingness cannot be handled by the present framework, and (iii) proposed ranking model can handle divide-by-zero issue during final rank estimation only through a heuristic and an algorithmic solution is missing in the current decision system. As a part of a future drive for research, we first address the limitations of the proposed work. Later, we plan to extend the proposed model to solve diverse decision problems on sustainability and technological advancement. Further, plans are made to explore different fuzzy sets, such as neutrosophic fuzzy sets, Fermatean fuzzy sets, hesitant fuzzy sets, and so on, for UAV selection to help farmers achieve precision framing and sustainable crop cultivation. Moreover, plans are made to extract comments from web sources on different UAVs and integrate a recommender system with machine learning and MCDM for performing large-scale group decision-making for improving framers’ experience in a precision framing context. Mobile application-based UAV recommendation to farmers is also being planned in the future to considerably help farmers better plan the cultivation and earn a significant profit. Finally, the proposed methodology can be integrated with different AI tools (Ullah et al. 2018, 2021, 2022a, 2022b; de Paula Vidal et al. 2022) in order to improve the accuracy of such strategic decision-making processes.