1 Introduction

Increasing demand for food at a global level has contributed to the ongoing degradation of native ecosystems, associated with growing greenhouse gas emissions and biodiversity losses caused by the agricultural sector (Smit and Smithers 1993; Godfray et al. 2010; Foley et al. 2011). This is a situation that can be clearly observed in the Brazilian agriculture-forest frontier, mainly located in the transition between the Amazon and the Cerrado biomes, and where extensive livestock, high GHG emissions, changes in land cover, abandonment of degraded lands, and low farm incomes are among the main environmental and developmental challenges (Cohn et al. 2014; Garrett et al. 2017; Gil et al. 2018). Livestock is believed to be the main driver of deforestation in the Brazilian agriculture-forest frontier (Barona et al. 2010; Lapola et al., 2014; Margulis, 2003). Traditional livestock systems characterized by large areas with low production levels and limited economic competitiveness remain the predominant land-use strategy for most cattle ranches in the Brazilian agriculture-forest frontier (Strassburg et al. 2014; zu Ermgassen et al. 2018; Mandarino et al. 2019). However, particularly after 2008 with the intensification of China’s participation in the Brazilian exports, intensive crop production systems were expanded onto pasturelands, with large-scale production using high levels of external inputs such as fertilizers, pesticides, and machinery, while livestock production kept moving toward frontier regions (Barona et al. 2010; Macedo et al., 2012).

In this context, the adoption of sustainable intensification of agricultural practices that may improve productivity per unit of input, thus avoiding the need for further land expansion, is critical for protecting the fragile Amazonian environment while enhancing the quality of life for society (Ikerd 1993; Schaller 1993; Hansen 1996; Tilman et al. 2011; Pretty 2018). Sustainable farming systems are those that seek sustainability goals by simultaneously preserving or enhancing the productive capacity of the environment, helping the protection of biodiversity, displaying positive economic returns, generating increasing levels of social welfare, and maintaining their capacity to continue producing over time (Smit and Smithers 1993; Ikerd 1993; Schaller 1993; Hansen 1996; Pretty 2008). Hence, policy-makers are increasingly interested in stimulating research and encouraging the adoption of sustainable agricultural systems (UNEP 2011; IPCC 2013; United Nations 2015; Steffen et al. 2015).

Sustainable agricultural intensification is particularly relevant in the Brazilian agriculture-forest frontier because this region is, simultaneously, one of the largest and fastest-growing agricultural frontiers in the world (Spera et al. 2014; Kastens et al. 2017; Picoli et al. 2018) and a hotspot for global commodity production (Morton et al. 2006; Gil et al. 2018) that is undergoing extensive deforestation (da Cruz et al. 2021; Silva Junior et al. 2021). Furthermore, it is also home to the largest terrestrial and freshwater biodiversity in the world (Lewinsohn and Prado 2005; Malhi et al. 2008) and is vital for the ecosystem services it provides (Morton et al. 2006; Urzedo et al. 2020), including climate regulation at a global level (Ruiz Agudelo et al. 2020). On the other hand, agricultural intensification may increase deforestation as a potential negative consequence, “a rebound effect”, resulting in further agricultural expansion as a response to increased land productivity and value (Lambin and Meyfroidt 2011; Ceddia 2019). The empirical evidence about the final results of the agricultural intensification is ambiguous, but highlights the relevance of the institutional setting and environmental governance to promote sustainable land use in agriculture-forest frontiers (Lambin and Meyfroidt 2011; Ceddia et al. 2013; Garrett et al. 2018).

Since sustainability is a multidimensional concept encompassing complex and interchanging economic, environmental, and social (EES) issues (Shearman 1990; Mebratu 1998; Purvis et al. 2019), agricultural sustainability assessment requires multi-criteria decision analysis (MCDA) approaches (Munda et al. 1994; Sadok et al. 2009; Pelzer et al. 2012; Craheix et al. 2015). Such approaches often have to handle qualitative and quantitative information, mixed measurement levels of criteria, efficient rule-based consideration of experts’ knowledge and preferences, and conflicting interests underlying the different dimensions of sustainability (Munda et al. 1994; Cornelissen et al. 2003; Sadok et al. 2008; Pashaei Kamali et al. 2017). A set of models based on DEXi (Bohanec 2015), a computer program for multi-attribute decision-making (e.g., MASC, DIAMOND, and DEXiPM), has been proposed to evaluate agricultural sustainability considering those issues (Sadok et al. 2008, 2009; Pelzer et al. 2012; Bockstaller et al. 2015). In general, these models (i) manage large sets of indicators; (ii) encompass EES dimensions organized hierarchically; (iii) use qualitative information; (iv) focus on small scale (e.g., crop system, specific components or products within farms); (v) offer qualitative final results; and (vi) are used for ex-ante evaluations of the impacts of innovative agricultural systems. However, they are less sensitive than models based on quantitative variables, and do not satisfactorily consider the fuzziness that is inherent in sustainability assessment (Sadok et al. 2008; Craheix et al. 2015).

Given the complexity of agricultural processes and associated trade-offs, the threshold to differentiate “sustainable” from “unsustainable” is not crisp, but rather fuzzy (Mebratu 1998; Cornelissen et al. 2001). Therefore, a suitable approach to assess sustainability is using fuzzy logic to develop appropriate indicators (Dunn et al. 1995; Phillis and Andriantiatsaholiniaina 2001; Ocampo-Duque et al. 2006; Liu 2007). The fuzzy set theory (Zadeh 1965) is useful to deal with problems in which the source of fuzziness is the absence of sharply defined criteria (Kosko 1990; Klir and Yuan 1995; Zimmermann 2001), and a fuzzy inference is especially useful when experts’ knowledge is a valuable or the sole source for building a system or model (Zadeh 1989; Cornelissen et al. 2003; de Vos et al. 2013). Furthermore, fuzzy logic allows for the translation of human expectations and scientific knowledge about sustainability into linguistic variables, and clearly enunciated sustainability indicators (Kosko 1990; Dubois and Prade 1998; Zimmermann 2001). In fuzzy logic, numerical and categorical variables of different scales can be merged (Dunn et al. 1995; de Vos et al. 2013), facilitating the expression of sustainability assessment indices (Phillis and Andriantiatsaholiniaina 2001; Prato 2005; Sami et al. 2014).

The sustainability assessment literature offers several examples of Fuzzy Inference Systems usage to evaluate distinct agricultural production models mainly at the cropping systems level of aggregation (Cornelissen et al. 2001; Ocampo-Duque et al. 2006; Sattler et al. 2010; Gao and Hailu 2012; Liu et al. 2013; Sami et al. 2014; Santos et al. 2017; Bockstaller et al. 2017; Li et al. 2020). Nonetheless, there is a paucity of tools based upon objective data at farming system level, encompassing EES dimensions to assess farming sustainability. Moreover, we identify a lack of comprehensive models applicable to broad agricultural conditions in different environments and socioeconomic contexts, to serve as decision support systems for policy making regarding sustainable farm management and farming systems design.

The objectives of the study are twofold: to present an indicator-based fuzzy logic model for assessing the sustainability of agricultural systems and to carry out case studies onto 22 reference farms with contrasting production systems in the Brazilian agricultural-forest frontier region to demonstrate the models’ applicability and flexibility (Fig. 1). We chose this method since it encompasses all positive characteristics of models based on DEXi, offers the advantage of dealing with both continuous and categorical variables, considers the fuzziness inherent to sustainability assessments, and provides a numerical result for the sustainability assessment.

Fig. 1
figure 1

Most common farming systems in Brazilian agriculture — forest frontier: large-scale crop farms, extensive livestock, and integrated systems (photos: Gabriel Faria, Embrapa Agrossilvipastoril)

The present work advances on the existing literature on sustainable agricultural systems assessment by providing a comprehensive fuzzy inference model to deal with information at the farm level that is suitable for handling diversified agricultural, livestock and integrated systems and applicable to different environmental or socioeconomic contexts. The indicators set and assessment model were built on integrating production activities and their effective economic, environmental, and social outcomes, implying that sustainability is considered as a whole, not as the sum of individual components (Rodrigues et al. 2003, 2010; Sattler et al. 2010; Gómez-Limón and Sanchez-Fernandez 2010).

2 Methods

2.1 A Fuzzy Inference System to assess agricultural sustainability

The framework proposed is an indicator-based approach built as a hierarchical Fuzzy Inference System (Phillis and Andriantiatsaholiniaina 2001; Liu 2007; Sami et al. 2014) developed with the MATLAB Fuzzy Logic Toolbox. For details about Fuzzy set theory and its applications, please refer to Zimmermann (2001) and a summary can be found in the supplementary material I. The model structure provides a partial indicator for each EES dimension and a sustainability index (SI) for each case study (farm). Each partial indicator is formed by 6 sub-indicators calculated using input variables surveyed at on-farm level (Fig. 2). This structure is useful because it allows comparisons across different farming systems and favors stepwise analysis of the contributions of each indicator to the corresponding sustainability dimension and that to the final result. Details about the indicator set are available in Table 1 and the supplementary material III.

Fig. 2
figure 2

Fuzzy Inference System representation of the interrelations between the sub-indicators, the economic, social, and environmental (EES) partial indicators and the sustainability performance index

Table 1 The set of economic, social, and environmental indicators and their assumed contribution to farming system sustainability

The selection of indicators is not straightforward and may be highly context-specific. This indicator set was selected since it can be straightforwardly linked with the farmer’s management decisions, allowing sustainability assessment considering on-farm issues. Also, all EES input variables are derivable from usual farming records and are solved without higher mathematical or computational requirements (Sami et al. 2014). Moreover, this indicator set considers most up-to-date issues concerning farming systems sustainability (Sattler et al. 2010; Gómez-Limón and Sanchez-Fernandez 2010; Pelzer et al. 2012; Sami et al. 2014; Santos et al. 2017; Li et al. 2020). Hence, the indicators were selected taking into account the following principles: (i) the farms as the proper management analytic level; (ii) economic, environmental, and social (EES) as the three main sustainability dimensions; (iii) data availability and practicality for obtaining reliable information; (iv) the use of the assessment system must be possible for different regions and contexts with minor adjustments; (v) the system must be appropriate for assessing different farming systems to allow comparisons and; (vi) the indicators set must be sufficient and complete to assess sustainability at the farm level (Bossel 2002; Gómez-Limón and Sanchez-Fernandez 2010).

To assess the efficiency in their use, environmental inputs were calculated as ratios relative to the total energy of all production items (Rodrigues et al. 2002; dos Reis et al. 2021). Because farms are thermodynamic systems (Giampietro 1997), this measure is applicable when comparing the production of distinct agricultural goods, even if the energy returned is of different qualities (Odum 1984; Jordan 2016). For the economic dataset, monetary inputs were expressed as ratios relative to farms’ production area. All monetary values were expressed in 2019 USD (1 USD = 3.94 REAIS), a conversion applying exchange data from official Brazilian Government databases provided by the Institute of Economic Applied Research (IPEADATA 2021).

To perform the Fuzzy Inference Systems, we chose the “Mamdani method” (Mamdani and Assilian 1975; Mamdani 1977) due to its robustness as well as for being the most used in environmental assessments. Also, this method better represents experts’ knowledge (Cornelissen et al. 2001; Prato 2005; Sattler et al. 2010). A typical Mamdanis’ Fuzzy Inference System has basically four steps: (i) fuzzification; (ii) fuzzy rules base definition; (iii) inference and, (iv) defuzzification (Klir and Yuan 1995; Dubois and Prade 1998; Zimmermann 2001).

Since the interrelation among the input variables over a sustainability assessment process is fuzzy, the fuzzification step consists of framing each input of the variable set — a crisp value — as a linguistic variable and decomposing it to one or more fuzzy sets by means of the membership functions that define soft thresholds of each element into the interval [0,1], and enables to assess the contribution of each element using functions to operate linguistic variables (Cornelissen et al. 2001). Triangular and trapezoidal membership functions were used in this study because (i) they are consistent with EES information; (ii) they offer consistent data representation, even for small samples; (iii) they are easier to derive, and (iv) they do not require higher computational resources to be estimated (Pedrycz 1994; Sami et al. 2014). For a better differentiation of studied farms, and based on a recursive process to define the fittest structure to represent the fuzzy sets, as well as on experts’ knowledge, we used five linguistic variables to express the inputs and the performance of the partial (EES) indicators: Very Low (VL), Low (L), Medium (M), High (H) and Very High (VH). For the sustainability index, however, only four linguistic variables were used: Very Low (VL); Low (L), Medium (M) and High (H).

To operate and describe the interrelations among the linguistic variables, a fuzzy rule set was created applying approximate reasoning based on scientific and/or experts’ knowledge and human perception to represent the connection between variables using the linguistic variables mentioned above (Cornelissen et al. 2003; Pashaei Kamali et al. 2017). For this study, the experts’ group was formed by all eight senior researchers from the multidisciplinary sustainable agriculture research group of Embrapa Agrossilvipastoril, located in Sinop (state of Mato Grosso) focused on research and technological transfer in sustainable agricultural farming systems for the Amazon and Cerrado regions. This sustainable agriculture research group was instituted in 2011 and includes senior experts in agronomy, veterinary, forestry, environmental sciences, and economics. It is an advisory committee for the definition of Embrapa’s research agenda on sustainable agricultural systems adoption in the Brazilian agricultural-forest frontier in the state of Mato Grosso.

The fuzzy rules for the sustainability index, following the premises that higher sustainability is achieved when the values in all EES dimensions are high and balanced, are described as follows:

  • If any partial indicator shows a value “Very Low” then the Sustainability Index is “Very Low”

  • If any partial indicator shows a value “Low” then the Sustainability Index is “Low”

  • If the farm shows at least two values “Medium” then the Sustainability Index is “Medium”

  • If the farm shows at least two values “High” then the Sustainability Index is “High”

Further details about the fuzzy sets and fuzzy rules for EES partial indicators and for the sustainability index are presented on supplementary material I.

To run the fuzzy rules, the inference step was performed using MIM-MAX method (Mamdani and Assilian 1975; Mamdani 1977) since it is the most suitable to represent experts’ knowledge, it is the most used in environmental assessments, and it does not require higher computational resources (Prato 2005; Sattler et al. 2010). Centroid was chosen for defuzzification as it is the most commonly used (Klir and Yuan 1995; Dubois and Prade 1998; Zimmermann 2001). Similarly, the resulting crisp values after processing the raw data were further used to calculate the membership degrees in the fuzzy sets for partial dimensional EES indicators and the sustainability index as well. Finally, the partial and sustainability indices are dimensionless values ranging between 0 and 100, and highest values indicating highest sustainability (Fig. 3).

Fig. 3
figure 3

Example of a Mamdani’s Fuzzy Inference System representation for a hypothetical farm with the following inputs values for partial EES indicators: Economic: 60; Social: 20; Environmental: 50, resulting in Sustainability Index 22.64. Dotted lines illustrate the membership degree for each input on the respective fuzzy set represented by the membership functions µ(x). Ec economic, So social, En environmental, Su Sustainability Index. Very Low (VL), Low (L), Medium (M), High (H), and Very High (VH) are the linguistic variables to express the inputs and the performance of the partial (EES) indicators. X axes indicate input values for partial EES indicators and Y axes indicate their membership degree; both axes ranging between 0 and 100. The Fuzzy Inference System is carried out through steps as follows (A): Fuzzification and membership functions, the process of decomposing an input variable to one or more fuzzy sets. The next step (B) is to run the fuzzy rules and process the fuzzy inference. This process has three sub-steps; B.1: Fuzzy rules and linguistic operators (IF-THEN); B.2: Fuzzy rules activation (MIM-Method); B.3: Fuzzy rules aggregation (MAX-Method). Finally, at step (C) Defuzzification, the values of the fuzzy set outputs are converted into a single crisp value.

2.2 Field application of the model toward the sustainability assessment of farming systems in the Brazilian agricultural frontier

The indicator-based fuzzy logic model was applied to assess the sustainability performance of diversified farming systems in the state of Mato Grosso, Brazil (Fig. 4), one of the largest and most productive agricultural frontiers in the world (IBGE 2020; IMEA, 2021; MAPA, 2021) in order to test its applicability, flexibility, and robustness. Presently, Mato Grosso state accounts for 28% of the soybean, 33% of the corn, and 71% of the cotton produced in Brazil (IMEA 2021). Furthermore, it contains 15% of the Brazilian beef cattle herd, i.e., 30.1 million heads (IBGE 2020). In the 2018/2019 season, Mato Grosso allocated 23 million hectares to livestock and 16 million hectares to crops (IMEA 2021). This remarkable agricultural dynamism yielded a Gross Value Added (GVA) of USD 20.5 billion in the 2018/2019 season (IMEA 2021), as a result of intense commercialization with external markets, especially China and the Arab countries (MAPA 2021).

Fig. 4
figure 4

Regional position, biome distribution, and location of the 22 case studies evaluated in the study

These economic results, however, do not express the considerable negative environmental impacts associated with commodity agricultural production in the state, particularly deforestation (Malhi et al. 2008; Barona et al. 2010). In 2020, deforestation in Mato Grosso reached 1767 km2 in the Amazon biome and 727 km2 in the Cerrado biome and contributed with 15.9% and 9.9% of the total area deforested in each biome, respectively (INPE 2021; INPE (TerraBrasilis) 2021). Moreover, recent public and private investments in infrastructure in the Amazon Southeastern region, such as the paving of the highway BR-163 and the implementation of silos and warehouses in export harbors in Santarém and Miritituba (in neighboring Pará state), have resulted in further pressure to expand croplands over existing pasturelands and to advance pasture-based cattle ranching into newly deforested areas (Schielein and Börner 2018). Therefore, the need for a harmonious coexistence of these biodiverse rich biomes with the booming agricultural sector makes this region of special concern and demands the development of tools to support decision makers in promoting sustainable farming strategies.

We assessed twenty-two case studies (farms) with diverse productive activities. They illustrate the most common productive systems in the Brazilian agricultural frontier and the three biomes of Mato Grosso (Fig. 4), and included nine case studies with soybean-corn rotation and one with soybean-corn-pinto beans rotation (pure crop farms); seven case studies with cattle ranching for beef production (pure livestock farms); and five case studies with integrated farms, i.e., four with soybean-corn rotation integrated with cattle ranching (integrated crop-livestock farms - ICL), and one with cattle ranching integrated with teak (Tectona grandis) for timber (integrated livestock-forest farm - ILF). The data were collected for the 2018/2019 season and detailed information about the case studies is available in the supplementary material - dataset. We personally contacted all 35 farmers who partake as Embrapa’s partners in the Technological and Economic Reference Units Project (TERU Project) in state of Mato Grosso. However, some of them were not willing to participate in the study since the survey was extensive and involved subjects that farmers may consider sensitive, such as economic performance, use of external inputs, and deforestation. The final dataset was collected with 22 farmers, in direct interviews through a structured survey.

3 Results

3.1 Input set: economic, social, and environmental data

The input set used to build the partial indicators and the sustainability indices for the 22 case studies are summarized in Table 2. They showed a wide variability in terms of size, technological level, production system adopted, and productive efficiency. A detailed table describing all values is available in supplementary material II – Table I.

Table 2 Descriptive statistics for the economic, social, and environmental input datasets from the 22 case studies. Monetary values were converted to 2019 USD (1 USD = 3.94 REAIS). Production values are expressed as energy content for all product items in the farms (Joules)

In general, pure crop farms presented the largest production areas (average of 2648.50 ha), the longest period in activity (average of 20 years), the largest gross profits (average of 607.03 USD ha-1), and high farm manager wages (average of 2474.62 USD month-1). The high technology level used in these farms can be inferred considering their higher production costs (average of 962.52 USD ha-1), as consequence of their expenditures in external inputs such as fertilizers (325.81 kg ha-1), pesticides (6.28 kg ha-1 active ingredients), and fuel (15.50 l ha-1). As a consequence, these farms presented the highest yields (supplementary material II - Table 2). In addition, these farms used more formal managerial practices to improve financial and operational activities, and invested more in staff training (supplementary material II - Table I).

In contrast, the livestock farms were characterized by large production areas (average of 1,120 ha) associated with low technological and productive levels (supplementary material II - Table 2), and poor environmental and economic performances. Livestock farms presented the lowest farm land values (average of 2994.54 USD ha-1), accounting for 30% and 21% of the land value of crop and integrated farms, respectively. They also showed the highest debt levels, spending around 50% of their gross revenue in financial expenses, and the lowest farm manager wages (average of 833.94 USD month-1), 66% lower than pure crop, and 73% lower than integrated farms. Moreover, livestock farms showed the lowest results for the environmental dimension, particularly in GHG emissions (average 1.95x10-08 ton CO2eq J-1). Even using smaller amounts of fertilizers and pesticides in absolute terms, indicating lower technology adoption, these farms reached the highest values for fertilizer/energy of products ratio (average 5.96x10-09 kg J-1), a value 3.7 times higher than observed for crop farms, and 6.6 times higher than the integrated farms. For pesticides/energy of products ratio (average 1.78 x10-10 kg J-1), livestock farms fared 5.6 times higher than crops, and 7 times higher than the integrated farms. These counterintuitive results are due to the lowest production volumes attained in livestock farms, with corresponding lower total energy content in their gross product.

Finally, the integrated farms showed higher yields (supplementary material II - Table 2) and efficiency in input uses for fertilizers (average 9.01x10-10 kg J-1), pesticides (2.54x10-11 kg J-1), and fuel (1.08x10-10 l ha-1 J-1). They also displayed the lowest topsoil losses (average 3.99x10-09 kg J-1) and GHG emissions (average -1.11x10-11 ton CO2eq J-1). The average runoff was 44%, and the average values for the land cover with natural forest areas were 58% and 17% higher than those observed for crop and livestock farms, respectively. Regarding the social dimension set, the integrated farms showed the highest owner’s schooling level (average of 12.6 years), and an average permanent/temporary employee ratio — a proxy for job quality — as high as 5.9, better than the 3.7 observed in crop and the 2.6 in livestock farms. In addition, for courses and training activities, integrated systems farms offered 12% more qualification events than crop farms and 3.3 times more than livestock farms. For profit sharing, a management instrument for encouraging productivity improvement, integrated farms showed values 20% higher than crop farms and 2.1 times higher than livestock farms. As a consequence of the improved performance in all EES dimensions, the integrated farms showed the highest market values (average of 13,961.10 USD ha-1), indicating that this productive system returns monetary gains due to investments in infrastructure and induced appreciation in land values.

3.2 Sustainability indices

The Fuzzy Inference System generated a similar pattern for the EES partial indicators set: high/medium values for integrated and crop system farms and lower values for livestock farms (Fig. 5). Hence, livestock farms presented the lowest values for the Sustainability Index (SI). Even the livestock farm that used best technological practices, such as pasture management, genetic improvement, and feedlot systems (i.e., farm #4) did not reach a high SI. Although this farm presented the best economic performance among the livestock farms, its poorer environmental and social performances explain its low SI.

Fig. 5
figure 5

Hierarchical clustering on principal components performed on economic, social, and environmental partial fuzzy-based indicators showing the main groups and subgroups: Best performing farms (A, in pink), medium performing farms (B, B1 and B2, in brown), and poorly performing farms (C, C1 and C2, in light green). Farms are identified by their case study number (1 to 22) and farm type (crop – pure crop farm, livestock – pure livestock farm, ICL – integrated crop-livestock farm, and ILF – integrated livestock-forest farm). Values for the partial fuzzy-based indicators are presented in the heatmaps where green represents the higher and red the lower estimated values. Ecn economic partial indicator, Soc social partial indicator, Env environmental partial indicator, SI sustainability index

In contrast, farms #19 and #17, representing an integrated forest - livestock and an integrated crop - livestock farm, respectively, showed the best SI values of the set (91.87 and 91.78) and very good performances for all three partial EES indicators. Farm #19 specializes in teak wood production for export, combined with high technology livestock husbandry. Although reaching intermediate profit and productive levels, its high organization and expertise in teak production explain its higher social and environmental indices. The efficiency in fertilizer and pesticide use and the ecosystem services provided by forests, such as low topsoil losses, CO2 sequestration, and low runoff (supplementary material II – Table I) were adequately expressed by the indicator-based fuzzy system and explain the excellent environmental results and the high SI. On its side, farm #17 displays highly productive performance based on managerial practices to improve financial and operational results, such as commercialization strategies to mitigate the negative impacts of commodities price volatility and profit share. Also, its livestock system is focused only on fattening, taking advantage of pastures intercropping with corn. Hence, this farm produces three harvests over one yearly growing season, consisting of two crops (soybean followed by corn) and a three-month animal fattening period in the same area. Farm #17 showed the second-largest profit (969.91 USD ha-1) and environmental performance similar to farm #19, particularly in topsoil loss, fertilizers and GHG emissions.

Crop farms displayed values for economic performance varying from 17.23 to 76.50 (mean of 53.35). Concerning the social indicator, except farms #13 and #22 that reached values around 70, most performed poorly in this dimension. Finally, all crop farms showed poor environmental performances, driven mainly by higher topsoil losses and GHG emissions, as a result of intensive use of farm machinery, fertilizers, and pesticides.

Worthy of note is the farm #7, an Amazon-located integrated crop-livestock venture that presented excellent economic and environmental performances but failed on social indicators, which compromised its SI. In fact, the precept guiding the structure of the decision rules of the Fuzzy Inference System was that true sustainability can only be achieved if all partial dimensions (EES) also comply with sustainable principles.

Hierarchical clustering on principal components applied to sustainability partial indicators identified three distinct clusters (Fig. 5). The first one (A) grouped the farms that showed the best performances for the partial dimensional indicators and encompasses farms #19, #17, and #2. All these farms adopted integrated systems and showed the best results for SI, and while farms #17 and #2 integrated crops and livestock, the farm #19, the best performing farm of the entire set, integrated forest with livestock. In this group, the farm #2 reached an SI value smaller than farms #19 and #17, but displayed good environmental and exceptional economic performances. This farm showed the highest land value and the second-best performance on GHG emission (-1.39x10-11 ton CO2eq J-1). However, its medium social performance reduced its SI.

Almost all crop farms were included in the second group (B) that showed medium performances for the partial EES indicators. Visual inspections of the dendrogram and the heatmap clearly indicate two subgroups: the first (B1) includes farms #22, #21, #14, #13, and #7. In general, these farms showed good economic performances associated with medium social and environmental indicators. Exceptions were observed for the farm #7, which showed the best productive performance (2.38x10+11 J ha-1) and higher efficiency in use of external inputs, high environmental and very high economic performances, but very poor social indicators. Also, farms #22 and #13 showed intermediate environmental indices, due to high use of external inputs for crop production, and high partial social indicators. The farm #22 showed the lowest debt level, high farm manager wage (five times the state’s average), lower fuel consumption values (3.97x10-11 l ha-1 J-1), higher job quality, and offered profit share, while the farm #13 presented the highest gross profit (USD 1,351.27 ha-1), high farm manager wage (four times the state’s average), the second-best performance in job quality, and offered health plans for permanent employees, which explain its good economic and social performances. The second subgroup (B2) composed by farms #20, #12, #9, #8, and #1 performed similarly to B1 except for lower economic indicators (except farm #9). Integrated farms included in group B (#7 and #9) showed a high economic performance, but failed to provide good social conditions.

All livestock farms were grouped in the third and poorly performing group (C), in which it was also possible to identify two subgroups. The first one (C1) included farms #18, #16, #15, #11, #4, and #3 and was characterized by low to very low values for two out of the three intermediate EES indicators. From these six farms, only two (farms #15 and #11) were not dedicated to livestock production. Finally, the subgroup C2 encompasses three farms (#10, #6, and #5), all dedicated to livestock production, yielding very poor results for all EES intermediate indicators and, consequently the lowest SI amidst the surveyed farms.

4 Discussion

The overview of farming systems sustainability performance shown in Fig. 5 illustrates the robustness and sensitiveness of the indicator-based fuzzy model proposed to assess sustainability performance of different farming systems. The model efficiently handles qualitative and quantitative information from EES dimensions, aggregating them in partial and synthesis indicators, providing useful and meaningful information for policy makers about sustainable land uses for the agricultural sector in an agriculture-forest frontier. Furthermore, even though based on an indicator set smaller than DEXi-based models (Pelzer et al. 2012; Craheix et al. 2015), the fuzzy model showed consistent data representation, demonstrating the suitability of the aggregation process, the decision rules, and the membership function used. Also, the premises set for the decision rules (Supplementary Material I) and the SI results (Fig. 5) highlighted the non-compensation as well as the frictions across EES dimensions. Accordingly, the proposed fuzzy indicator-based model encompasses the three requirements for relevance in sustainability assessment approaches - incomparability, incommensurability and non-compensation — highlighted by Sadok et al. (2008), more efficiently than other MCDA approaches used for sustainability assessment (Munda et al. 1994; Sadok et al. 2008, 2009; Bockstaller et al. 2009). This is true despite the limited direct comparison between the results found and the available literature, since we did not find studies evaluating on-farm sustainability using an indicator-based fuzzy model at farming system aggregation level such as the one we propose. However, our results strongly corroborate the agricultural sustainability assessment literature for the most relevant land use agricultural strategies adopted in the Brazilian agricultural-forest frontier (Costa et al. 2018; Gil et al. 2018; dos Reis et al. 2021).

4.1 Trade-offs across EES dimensions and the relevance of a comprehensive approach

Even though sustainable intensification holds the potential to improve the farm’s economic results and, simultaneously, to preserve environmental resources, the literature highlights possible trade-offs when adopting sustainable intensification practices (Sneessens et al. 2016; Rosa-Schleich et al. 2019; da Silveira Bueno et al. 2021). However, the related trade-offs, particularly between the economic and the environmental dimensions, can be associated with the analytical framework, focused on biophysical processes, without considering the impacts at farm scale as well as the complex interactions between subsystems (Wilkins 2008; Bell and Moore 2012; Bell et al. 2014; Sneessens et al. 2016; Szymczak et al. 2020; Vogel et al. 2021).

Our findings for the partial EES indicators and for the sustainability index indicate that the proposed fuzzy indicators system could capture the potential trade-offs among on-farm input variables as well as EES dimensions, facilitating their evaluation in a broader perspective in consonance with the objective of promoting agricultural sustainability. Moreover, the aggregation process of the fuzzy inference model proposed allows us to consider the win-win interactions in the integrated systems. Indeed, the best performing farms identified — group A: farms #19 #17 and #2 — are not top ranking in all EES indicators, but display high performance in all EES dimensions. These results contradict the literature about inherent trade-offs across EES dimensions and highlight the central role of the farmer’s management to take advantage of interactions between subsystems in integrated systems. The integrated systems require a high environmental management level to improve efficiency in resources use which, as a consequence, leads to better economic and social performances as well. The adoption of integrated systems is based on sustainable practices of soil and water conservation, lesser usage of external inputs, and optimization of land use with integration of various types of agricultural production (i.e., crops, livestock, and forestry) in the same area, via intercropping or rotations, to obtain synergies among agroecosystem components. To manage these more complex agricultural production systems, farmers need higher environmental management skills. Also, to take advantage of price fluctuations from different commodities markets, farmers must improve their financial management skills or hire highly skilled employees to deal with different agricultural practices and with the varying economic scenarios of commodity markets. As consequence, integrated systems farms tend to offer higher levels of training and courses, as well as higher wages.

The model was also able to highlight unbalanced performances, as illustrated by the results of farms #7 and #9, which showed high economic and environmental results, but poor social performances. The social performance of the farm #7, for example, is explained by its poor schooling and job attractiveness, while farm #9 showed low values for training and courses, and job quality. These contrasting results among integrated systems corroborate the assumption that it is challenging to support a general conclusion about the benefits of sustainable intensification, because they are context-specific (Ryschawy et al. 2012; Bell and Moore 2012; Rosa-Schleich et al. 2019; Szymczak et al. 2020; Vogel et al. 2021). However, the indicator-based fuzzy model proposed displayed enough sensitiveness to consider the wide variability of system performances and the interactions among their EES dimensions, expressing summarized results to enhance the assertion of indicators’ meanings and simplifying both policy-makers’ and farmers’ decisions toward sustainable farming.

4.2 Sustainability as balanced use of environmental resources and continuity over time

The sustainability indices highlight sustainability association with high and balanced interrelationships among the economic, environmental, and social dimensions (Mebratu 1998; Pretty 2008). These results also accentuate that sustainable farming systems can enhance productive capacity of environmental resources, ensuring their continuity over time (Smit and Smithers 1993; Schaller 1993; Hansen 1996).

The crop farms showed high economic performance (e.g., higher productivity, gross profit, and farm manager wages), but were based on extensive use of external inputs such as fertilizers and pesticides. In addition, the values obtained for topsoil losses and, particularly, for runoff provide evidence of the negative environmental impacts of continuous large-scale cropping, threatening the ability of this system to remain productive over time (Rieger et al. 2016; Anache et al. 2017). To keep high production levels, crop farms consume high and ever-increasing amounts of external inputs. As a result, to deal with increasing production costs, crop farms need to become larger, to take advantage of returns to scale. This pattern illustrates the unsustainability of the highly technological crop farms in the long run (Sneessens et al. 2016; dos Reis et al. 2021).

On the other hand, the top-ranking values for the integrated farms are explained by balanced interactions among all dimensions (Herrero et al. 2010; Lemaire et al. 2014; dos Reis et al. 2016). The economic results for gross profit, debt level, and farm manager wages are closely related with lower production costs, due to higher efficiency in input use. Also, these efficiencies explain the higher environmental performance, particularly lower GHG emissions, higher forest cover, and lower topsoil losses, ensuring the productive conditions for integrated farms to continue over time, and help explain their impressive results for land value, indicating that the market perceives and values the improved and balanced performance across all EES dimensions. Finally, the result for training and courses and job quality confirm the perspective that integrated farming demands more qualified workers and offers higher quality jobs, which is influenced by higher salaries and social insurance. The fuzzy indicator model highlighted that the harmonious interaction of economic, environmental, and social dimensions in integrated farming provides win-win situations and generates a continuous and sustainable trajectory (Lemaire et al. 2014; Rosa-Schleich et al. 2019; dos Reis et al. 2021).

Finally, the fuzzy indicator-based model results corroborate the literature indicating that increasing the economic returns while reducing environmental impacts is decisive for livestock farmers to improve sustainability. Previous researchers have highlighted the potential of sustainable intensification of pasture-based livestock to reconcile increased agricultural production and profitability while reducing negative environmental impacts, particularly GHG emissions per unit of production (zu Ermgassen et al. 2018; Gil et al. 2018; Mandarino et al. 2019). Sustainable intensification of pasture-based livestock to increase the productivity to 49–52% of its potential with currently available technologies would free enough land for the expansion of meat, crops, wood, and biofuel production, sufficing to meet demands for agricultural goods until at least 2040, while mitigating up to 14.3 Gt CO2eq — some 6.8 times the total Brazilian GHG emissions in 2019 (SEEG 2021) — without further conversion of natural ecosystems (Strassburg et al. 2014). This is especially relevant for those pasture areas in the Cerrado and Amazon biomes under extensive livestock production and which are not suitable for adoption of integrated crop - livestock or crop - livestock -forestry systems due to topographic limitations, soil type, and rainfall intensity and distribution along the year.

Furthermore, cattle ranchers have limited financial capacity to implement new and more expensive practices and, as the fuzzy-based indicator systems expressed, present higher debt levels (de Oliveira Silva et al. 2016, 2017). Therefore, public policies to promote wider adoption of technological practices associated with specific credit support are crucial for improving livestock performance in the Cerrado and Amazon regions. This is especially relevant to provide technology and credit access and environmental compliance by hundreds of thousands of small and medium farmers that are major suppliers of calves for large beef cattle finishing operations under confinement in these Brazilian biomes. Finally, it is important to consider that farms #3 and #5 are located in the Pantanal and that extensive livestock based on natural pastures is part of the tradition in the rural areas of this biome (Abreu et al. 2010). Hence, cattle ranchers in Pantanal, besides the general incentives indicated above, need specific consideration to improve their economic and environmental performances, without compromising their cultural connection with their environment (Santos et al. 2017).

4.3 Applications in other regions and countries

The possibility to be adjustable to different contexts is a central characteristic of assessment models based on fuzzy logic (Andriantiatsaholiniaina et al. 2004; Prato 2005; Ocampo-Duque et al. 2006). The Fuzzy Inference System proposed here was built aiming at being easily adjustable to varied environmental and socioeconomic contexts, to consider regional and farming systems specificities, sectoral experts’ knowledge, and locally availability of information, since its structure (i.e., membership functions or fuzzy rules), as well as the input variable set, can be easily modulated to reflect local sustainability conditions. Also, the results of our 22 case studies indicate that the set of indicators proposed is amenable to fit different farming systems, be they extensive such as the livestock farms; intensive, specialized and productivity-focused as we observed for the cropping farms; or highly technological, integrated farms.

4.4 Next steps and limitations

Sustainable development does not represent the endpoint of a process; rather, it represents the process itself (Shearman 1990; Mebratu 1998). Also, sustainability assessment based on scientific and/or experts’ knowledge tends to expose some bias both in the choice of indicators and in the definition of thresholds to differentiate “sustainable” from “unsustainable” situations. Therefore, models to evaluate sustainability are naturally incomplete, because human perceptions, expectations, and available knowledge are continuously evolving (Gómez-Limón and Sanchez-Fernandez 2010; Phillis et al. 2010; Van Passel and Meul 2012; Craheix et al. 2015; de Olde et al. 2016). The Fuzzy Inference System proposed here relies exclusively on data at the farm scale. Hence, a next step for this research would be to include information beyond the farms so as to upscale the assessment at regional level and investigate integrated systems’ contributions to land sparing or to agricultural expansion in agriculture-forest frontiers. Moreover, for this study, we focus on more objective aspects of sustainability assessment taking into account the farmers’ productive decisions. Next steps should include subjective aspects such as cultural heritage and information describing how the political context and environmental governance influence the farmers’ productive decisions. In addition, in locus measurements for inputs, particularly for the environmental dimension, would improve fuzzy model accuracy.

5 Conclusion

Sustainable agricultural intensification can play an essential role in addressing the global challenge of meeting the increasing worldwide demand for food while conserving and restoring natural ecosystems. Given the difficulty of understanding and incorporating all sustainability objectives and the fuzziness inherent to the concept of sustainability itself, the innovative indicator-based fuzzy logic model presented here can be a useful tool for policy- makers assessing sustainability of farming systems. The practical applicability of the model, tested and proven in the 22 case studies with varying degrees of complexity and intensity demonstrates its suitability to assess agricultural sustainability at farm scale, and testifies to the robustness and applicability of the proposed fuzzy indicator-based model to a wide range of farming systems.

Moreover, the model proposed here is dynamic and its development process is continuous, making it possible to harness both experts’ knowledge and scientific knowledge and incorporate future improvements and changes in sociopolitical objectives in order to implement land-use alternatives to boost agricultural productivity while maintaining/enhancing the productive capacity of the environment and promoting social welfare.