Quantification study of mental load state based on AHP–TOPSIS integration extended with cloud model: methodological and experimental research

Abstract

Mental load affects the work efficiency and mental health of operators, and it has a vital effect on the efficiency and reliability of human–machine systems. In this study, the evaluation index system of operators’ mental load was used to quantitatively evaluate the mental load state of workers. The system was established by selecting indices from the operators’ physiological parameters, subjective feelings, and time perception. We propose an extended cloud evaluation model of mental load states that combines cloud model (CM) theory with analytic hierarchy process (AHP) and technique for order preference by similarity to ideal solution (TOPSIS) and provides mental load levels. An energetic material initiation experiment was conducted to evaluate the mental load state of the operators using the proposed method, and the results of a fuzzy comprehensive evaluation and subjective questionnaire were used to verify the performance of the method. The results show that the extended CM evaluation method scientifically and reliably quantified the mental load state. Applying the AHP-TOPSIS integration extended with the CM theory evaluation method in mental load state evaluation provides a new scientific method for studying the quantification of the mental load state and occupational health of workers in hazardous environments. The results of this study are a reference for assessing the mental state of personnel and analyzing occupational suitability for dangerous posts.

Introduction

From the perspective of system reliability, humans as system elements raise reliability issues. For example, a human error is said to occur when an individual fails to perform a prescribed function under certain conditions within a determined period of time [1]. Catelani et al. [2] reported that human error accounts for approximately 70–80% of the causes of accidents. The devastating Chernobyl and Three Mile Island nuclear power plant accidents were attributed to human error [3]. Mental load is a vital cause of human error and refers to the amount of mental work that an individual bears per unit of time, which is manifested as the load of cognition, thinking, judgment, or emotion [4]. Mental load is closely related to human work efficiency, operational reliability, and job satisfaction, making it an important index that reflects the state of human–machine systems. Human emotions, perception, fatigue, and other mental states affect enterprise production safety. In 2010, the “13 consecutive jumps” that occurred at Foxconn reflected that workers under mental load can cause large production safety hazards in a company. Similarly, working in high-risk industries, such as mining, high-altitude operations, and hazardous chemical industries, will aggravate the mental load of operators and cause an overload. Furthermore, excessive mental load will affect the work efficiency as well as physical and mental health of personnel, and subsequently, the efficiency and reliability of the entire human–machine system. Therefore, it is crucial to study mental load thoroughly.

The quantitative study of mental load sate has been an important direction in mental load research. However, progress has been relatively slow because of technical limitations and complex factors that affect mental load. Many scholars have used subjective questionnaires to quantify mental load state. Da la Torre et al. [5] used the modified National Aeronautics and Space Administration-Task Load Index (NASA-TLX) scale to measure the mental load of drone operators and found that the scores of the questionnaire can reflect mental load state in the training task. DÖnmez et al. [6] measured the workload perception of pseudo pilots using NASA-TLX, which reflected the mental load of the pilots during simulation courses. Mansikka et al. [7] successfully used NASA-TLX and the Modified Cooper Harper (MCH) scale to quantify the mental load state of pilots under different task difficulty conditions. Physiological indices of mental load have been studied, and changes in the indices have been used to reflect mental load state. Moon et al. [8] examined the mental load sensitivity indices of nuclear power plant workers using fuzzy algorithms. The authors found that electroencephalography (EEG) (α-energy and β-energy,) and heart rate variability (HRV) signals can efficiently reflect changes in mental load. Sugimoto et al. [9] studied the relationship between an operator’s mental load and HRV when operating a ship handling simulator. The authors found that the inter-beat interval (IBI) and low frequency/high frequency (LF/HF) ratio can effectively assess the operator’s mental load level. Richter et al. [10] studied the physiological index changes of drivers’ mental load when driving on rural roads. The study showed that heart rate (HR), HRV, blink frequency, and other indices can adequately reflect people’s mental load and evaluate reliability. Hertzum and Holmegaard [11] found that perception time decreases with increasing mental load through subjective load assessment and pupil diameter measurement. The authors noted that mental workload should not exceed the capacity of a worker. To obtain mental load sensitivity parameters, namely HR, RRn, SDNN, RMSSD, pNN50, CV, HF, SD1, SD2, and B–, Hao et al. [12] performed linear analysis, Poincare plot, scatter plot, and sample entropy analysis on HRV signals under mental load and resting states. They judged whether the participants were in the mental load state by observing the parameter changes. These studies show that the physiological parameters and questionnaire survey methods effectively and reliably reflect the mental load state.

However, the mental load state is not a well-defined concept. It is impossible to perform an accurate mental load evaluation by only changing a certain physiological index or questionnaire survey. As a multiple decision-making method, the fuzzy comprehensive (FC) evaluation method integrates the influence of various factors and effectively addresses fuzzy and uncertain factors. The method has been successfully used for evaluating human physiological health and mental fluctuations. Zheng et al. [13] selected skin temperature, systolic blood pressure, rectal temperature, sweating rate, and HR as evaluation indices; used sensitivity analysis to determine weights; and established a quantitative evaluation model of the physiological state. Jing et al. [14] determined the evaluation indexes using physical fatigue and mental fatigue. They constructed a comprehensive evaluation model of personnel fatigue based on the multi-level FC evaluation principle, realizing a quantitative and hierarchical evaluation of fatigue. Li et al. [15] selected θ/β, LF/HF, SampEn and effective working hours as evaluation indices. They calculated the weight using the analytic hierarchy process (AHP) and proposed an evaluation model of the working fatigue state based on the FC evaluation method. Zhang et al. [16] established a multi-level safety mental evaluation system for coal mine workers and calculated the factor weight using the AHP. They also obtained the safety mental evaluation level of coal mine workers using the FC evaluation method in combination with the safety level table.

Overall, the AHP and FC evaluation methods have been widely used to analyze human fatigue and mental characteristics, demonstrating their applicability and reliability. However, the membership function of the traditional fuzzy theory contains uncertainty and fuzziness, which uniquely and accurately determine the membership of indices when quantifying the linguistic terms provided by experts, resulting in the contradiction of accurate modeling of fuzzy concepts [17]. Meanwhile, the AHP inevitably contains fuzziness, uncertainty and dispersion when used to calculate factor weights [18]. The cloud model (CM) theory is used in this study to solve the uncertainty problem of the above methods. The CM theory was proposed by Chinese researcher Li Deyi [19]. The model combines the fuzziness, randomness and dispersion of factors under uncertain conditions to describe uncertain indices quantitatively. Currently, the CM theory are widely used in risk assessment, environmental protection and other fields [20,21,22]. Cui [20] and Zhang [21] proposed the use of the CM theory for improving the AHP algorithm to assess the sustainability of mineral resources and environmental vulnerability. Xie et al. [18] assessed the fire and explosion risk of oil depots, considering the research of Cui et al., and proposed a Cloud-AHP algorithm based on the fuzzy cloud membership function. The algorithm addresses the numerical dispersion problem of the weight cloud models (WCMs), making the work more scientific and objective. Therefore, the CM theory was selected for the quantitative assessment of mental load in this study.

When applying the CM theory in the quantitative evaluation of the mental load state, the evaluation factor set is first determined. According to the studies highlighted above, subjective questionnaires, EEG, HRV, and electrooculogram (EOG) are potential indices for evaluating the mental load state. Additionally, the time perception test can determine the mental load state of personnel. Therefore, subjective questionnaire, EEG, HRV, EOG and time perception test were selected in this study to construct the evaluation index system of mental load state. Furthermore, reasonable and scientific determination of the index weight is crucial to quantifying mental load accurately. Thus, the multi-dimensional Cloud-technique for order preference by similarity to ideal solution (MDCT) and Cloud-AHP were used to determine the weight of the evaluation index. Finally, virtual cloud algorithm (VCA) was used to calculate the mental load level cloud and determine the mental load level. According to the extended cloud (EC) evaluation model that combines the CM theory with AHP and TOPSIS, an evaluation model of the mental load state was constructed. The mental load state of workers can, therefore, be quantified to the extent of the mental load feedback. A case study involving mental load experiments was considered on the new evaluation model of the mental load state using a cloud model. The mental load induction experiment was the energetic material initiation experiment, which collected the subjective and objective evaluation data of the study participants. The research contents are illustrated in Fig. 1.

Fig. 1

Block diagram of research content

The major contributions of this study are as follows: (1) we establish a quantitative model for the comprehensive evaluation of mental load state; (2) we use the MDCT algorithm to rank the importance of evaluation factors and the Cloud-AHP to determine the weight of the evaluation factors; (3) we determine the evaluation index level cloud and mental load level cloud; (4) we compare the consistency with the results of the subjective questionnaire and FC evaluation, and we judge the accuracy and scientificity of the evaluation level of mental load state based on the EC evaluation model. The scientific evaluation of the impact of mental load on the mental health of operators is an important way to reduce the incidence of human errors and accidents. Thus, this study is of far-reaching significance to occupational suitability analysis as well as safe and efficient production in global industries.

Basic theories and concepts

Cloud model (CM)

Definition 1

Cloud is a conversion model that connects the uncertainty between the qualitative concepts of language terms and their corresponding quantitative expressions [23]. Assuming a universe $U=\left\{x\right\}$, $\widetilde{A}$ is a qualitative concept in the universe U. For any element x in the universe U, there is a stable tendency in $\widetilde{A}$. The random number ${\mu }_{\widetilde{A}}\left(x\right)$ is the membership degree of x to $\widetilde{ A}$. The distribution of the membership degree in the universe U is the membership cloud, which also forms the cloud, and each x is the cloud drop. The value range of ${\mu }_{\widetilde{A}}\left(x\right)$ is [0, 1], and the cloud is a mapping of the qualitative concept $\widetilde{A}$ from the domain U to the interval [0, 1], given as: ${\mu }_{\widetilde{A}}\left(x\right):U\to \left[0, 1\right], \forall x\in U, x\to {\mu }_{\widetilde{A}}\left(x\right)$ [19].

Expected value (${E}_{x}$), entropy (${E}_{n}$), and hyper-entropy (${H}_{e}$) reflect the uncertainty and ambiguity of the qualitative concept, respectively. The calculation of the cloud model includes forward and reverse cloud generators [23, 24]. The forward cloud generator determines the normal distribution cloud map according to the three numerical characteristics and the number of cloud drops to realize the conversion from qualitative concept to quantitative information. However, the reverse cloud generator does the opposite. In this study, the assessment of the mental load state of the personnel mainly determined the transformation of uncertainty from qualitative to quantitative, which is suitable for forward cloud converter calculation. Figure 2 illustrates the normal cloud calculated using the forward cloud generator; the three characteristic values are annotated.

Fig. 2

Cloud diagram

Basic operations of the CM

Definition 2

Suppose in universe U there are two clouds: ${C}_{\alpha }=\left({E}_{{x}_{\alpha }}{, E}_{{n}_{\alpha }},{ H}_{{e}_{\alpha }}\right)$, ${C}_{\beta }=\left({E}_{{x}_{\beta }}{, E}_{{n}_{\beta }},{ H}_{{e}_{\beta }}\right)$, ω is a real number; the following operation rules exist [18, 25, 26].

$$C_{\alpha } + C_{\beta } = \left( {E_{{x_{\alpha } }} + E_{{x_{\beta } }} ,\sqrt {E_{{n_{\alpha } }}^{2} + E_{{n_{\beta } }}^{2} } ,\sqrt {H_{{e_{\alpha } }}^{2} + H_{{e_{\beta } }}^{2} } } \right)$$

(1)

$$C_{\alpha } - C_{\beta } = \left( {E_{{x_{\alpha } }} - E_{{x_{\beta } }} ,\sqrt {E_{{n_{\alpha } }}^{2} + E_{{n_{\beta } }}^{2} } ,\sqrt {H_{{e_{\alpha } }}^{2} + H_{{e_{\beta } }}^{2} } } \right)$$

(2)

$$C_{\alpha } \times C_{\beta } = \left( {E_{{x_{\alpha } }} \times E_{{x_{\beta } }} ,\left| {E_{{x_{\alpha } }} E_{{x_{\beta } }} } \right| \times \sqrt {\left( {\frac{{E_{{n_{\alpha } }} }}{{E_{{x_{\alpha } }} }}} \right)^{2} + \left( {\frac{{E_{{n_{\beta } }} }}{{E_{{x_{\beta } }} }}} \right)^{2} } ,} \right. \left. {\left| {E_{{x_{\alpha } }} E_{{x_{\beta } }} } \right| \times \sqrt {\left( {\frac{{H_{{e_{\alpha } }} }}{{E_{{x_{\alpha } }} }}} \right)^{2} + \left( {\frac{{H_{{e_{\beta } }} }}{{E_{{x_{\beta } }} }}} \right)^{2} } } \right).$$

(3)

$$C_{\alpha } \div C_{\beta } = \left( {\frac{{E_{{x_{\alpha } }} }}{{E_{{x_{\beta } }} }}, \left| {\frac{{E_{{x_{\alpha } }} }}{{E_{{x_{\beta } }} }}} \right| \times \sqrt {\left( {\frac{{E_{{n_{\alpha } }} }}{{E_{{x_{\alpha } }} }}} \right)^{2} + \left( {\frac{{E_{{n_{\beta } }} }}{{E_{{x_{\beta } }} }}} \right)^{2} } , } \right. \left. {\left| {\frac{{E_{{x_{\alpha } }} }}{{E_{{x_{\beta } }} }}} \right| \times \sqrt {\left( {\frac{{H_{{e_{\alpha } }} }}{{E_{{x_{\alpha } }} }}} \right)^{2} + \left( {\frac{{H_{{e_{\beta } }} }}{{E_{{x_{\beta } }} }}} \right)^{2} } } \right)$$

(4)

$$\omega C_{\alpha } = \left( {\omega E_{{x_{\alpha } }} , \sqrt \omega E_{{n_{\alpha } }} , \sqrt \omega H_{{e_{\alpha } }} } \right)$$

(5)

$$C_{\alpha }^{n} = \left( {E_{{x_{\alpha } }}^{n} ,\sqrt n \times E_{{x_{\alpha } }}^{n - 1} \times E_{{n_{\alpha } }} ,\sqrt n \times E_{{x_{\alpha } }}^{n - 1} \times H_{{e_{\alpha } }} } \right)$$

(6)

Similarly, cloud computing satisfies the commutative and associative laws.

Cloud model conversion of uncertain language value

Definition 3

Experts must use appropriate language evaluation scales when making qualitative evaluations. Each language scale can be represented by a quantitative uncertainty linguistic value. Let $\widetilde{X}=\left[{X}_{\mathrm{min}}, {X}_{\mathrm{max}}\right]$ be the uncertainty linguistic value. ${X}_{\mathrm{min}}$ is the lower limit and ${X}_{\mathrm{max}}$ is the upper limit (the bilateral constraint value of the language scale). The language evaluation scale is vague and can be described as a normal cloud [27]. Figure 2 illustrates the relationship between the cloud and uncertainty linguistic value. Therefore, the digital feature value of the cloud is converted with the bilateral constraint value [28, 29]. The bilateral constraint conversion formula is:

$$\left\{\begin{array}{c}{E}_{x}=\frac{{X}_{\mathrm{min}}+{X}_{\mathrm{max}}}{2}\\ {E}_{n}=\frac{{X}_{\mathrm{max}}-{X}_{\mathrm{min}}}{6}\end{array}\right.$$

(7)

${H}_{e}$ was determined by the size adjustment of the bilateral constraint interval of the uncertainty linguistic value. Generally, the uncertainty of the language evaluation scale increases with increasing interval value, thus increasing ${H}_{e}$. On the contrary, the changing trend is the opposite.

Definition 4

A comprehensive cloud is the combination of two or more uncertain linguistic values of the same type to a broader uncertainty linguistic value. Suppose there are n base clouds [${C}_{1}=\left({E}_{{x}_{1}}{, E}_{{n}_{1}},{ H}_{{e}_{1}}\right)$, ${C}_{2}=\left({E}_{{x}_{2}}{, E}_{{n}_{2}},{ H}_{{e}_{2}}\right)$,…, ${C}_{n}=\left({E}_{{x}_{n}}{, E}_{{n}_{n}},{ H}_{{e}_{n}}\right)$] in the universe U, we can generate a comprehensive cloud ($C=\left({E}_{x},{E}_{n}{,H}_{e}\right)$). When the correlation between the underlying indices represented by each base cloud is small, the integrated cloud computing of the base cloud uses the floating cloud algorithm in the virtual cloud [30]. The calculation formula of the digital feature value is given as:

$$\left\{\begin{array}{c}{E}_{x}=\frac{\sum_{i=1}^{n}{\omega }_{i}{E}_{{x}_{i}}}{\sum_{i=1}^{n}{\omega }_{i}} \\ {E}_{n}=\sum_{i=1}^{n}\frac{{\omega }_{i}^{2}{E}_{{n}_{i}}}{\sum_{i=1}^{n}{\omega }_{i}^{2}}\\ {H}_{e}=\sum_{i=1}^{n}\frac{{\omega }_{i}^{2}{H}_{{e}_{i}}}{\sum_{i=1}^{n}{\omega }_{i}^{2}}\end{array}\right.$$

(8)

where ${\omega }_{i}$ is the weight value of the index.

To identify the comprehensive cloud of the highest-level index, the comprehensive cloud algorithm in the virtual cloud was used [31]. The calculation formula of the digital characteristic value of the integrated cloud is given as:

$$\left\{\begin{array}{c}{E}_{x}=\frac{\sum_{i=1}^{n}{\omega }_{i}{E}_{{x}_{i}}{E}_{{n}_{i}}}{\sum_{i=1}^{n}{\omega }_{i}{E}_{{n}_{i}}}\\ {E}_{n}=n\sum_{i=1}^{n}{\omega }_{i}{E}_{{n}_{i}} \\ {H}_{e}=\frac{\sum_{i=1}^{n}{\omega }_{i}{H}_{{e}_{i}}{E}_{{n}_{i}}}{\sum_{i=1}^{n}{\omega }_{i}{E}_{{n}_{i}}}\end{array}\right.$$

(9)

where n indicates the number of indices, and ${\omega }_{1}+{\omega }_{2}+{\dots +\omega }_{n}=1$.

Definition 5

Suppose there are two clouds ${C}_{\alpha }=\left({E}_{{x}_{\alpha }}{, E}_{{n}_{\alpha }},{ H}_{{e}_{\alpha }}\right)$ and ${C}_{\beta }=\left({E}_{{x}_{\beta }}{, E}_{{n}_{\beta }},{ H}_{{e}_{\beta }}\right)$ in the universe U, then the Hamming distance between two clouds is [32]:

$$\begin{aligned}D\left({C}_{\alpha },{C}_{\beta }\right) & =\left|\left(1-\frac{{E}_{{n}_{\alpha }}^{2}+{H}_{{e}_{\alpha }}^{2}}{{E}_{{n}_{\alpha }}^{2}+{H}_{{e}_{\alpha }}^{2}{+E}_{{n}_{\beta }}^{2}+{H}_{{e}_{\beta }}^{2}}\right){E}_{{x}_{\alpha }}\right.\\ & \quad \left.-\left(1-\frac{{E}_{{n}_{\beta }}^{2}+{H}_{{e}_{\beta }}^{2}}{{E}_{{n}_{\alpha }}^{2}+{H}_{{e}_{\alpha }}^{2}{+E}_{{n}_{\beta }}^{2}+{H}_{{e}_{\beta }}^{2}}\right){E}_{{x}_{\beta }}\right|\end{aligned}$$

(10)

Research method

Cloud-AHP algorithm

The Cloud-AHP algorithm was used to calculate the weight of evaluation dimensions and indices. The specific calculation steps are given below:

Step 1: Establish a hierarchical structure.

First, determine the evaluation target. Next, outline the various indices related to the evaluation target and analyze the logical relationship between them. Finally, draw the tomographic structure diagram of the evaluation indices.

Step 2: Construct the judgment matrix A.

The importance scale based on the CM is presented in Table 1 [18, 22]. Experts compare and assign the importance of the two indices as shown in Table 1, and obtain matrix A.

Table 1 Importance scale table based on CM

$${\left[{A}_{ij}\right]}_{n\times n}=\left[\begin{array}{c@{\quad}c@{\quad}c}\begin{array}{cc}{A}_{11}\langle {E}_{{x}_{11}}{,E}_{{n}_{11}},{H}_{{e}_{11}}\rangle & {A}_{12}\langle {E}_{{x}_{12}}{,E}_{{n}_{12}},{H}_{{e}_{12}}\rangle \\ {A}_{21}\langle {E}_{{x}_{21}}{,E}_{{n}_{21}},{H}_{{e}_{21}}\rangle & {A}_{22}\langle {E}_{{x}_{22}}{,E}_{{n}_{22}},{H}_{{e}_{22}}\rangle \end{array}& \cdots & \begin{array}{c}{A}_{1n}\langle {E}_{{x}_{1n}}{,E}_{{n}_{1n}},{H}_{{e}_{1n}}\rangle \\ {A}_{2n}\langle {E}_{{x}_{2n}}{,E}_{{n}_{2n}},{H}_{{e}_{2n}}\rangle \end{array}\\ \vdots & \ddots & \vdots \\ {A}_{n1}\begin{array}{cc}\langle {E}_{{x}_{n1}}{,E}_{{n}_{n1}},{H}_{{e}_{n1}}\rangle & {A}_{n2}\langle {E}_{{x}_{n2}}{,E}_{{n}_{n2}},{H}_{{e}_{n2}}\rangle \end{array}& \cdots & {A}_{nn}\langle {E}_{{x}_{nn}}{,E}_{{n}_{nn}},{H}_{{e}_{nn}}\rangle \end{array}\right]$$

When two factors are compared, i is less important than j, the importance value is the reciprocal of the importance in Table 1, and the calculation formula is $\frac{1}{{C\left( {E_{{x_{ij} }} ,E_{{n_{ij} }} ,H_{{e_{ij} }} } \right)}} = C\left( {\frac{1}{{E_{{x_{ij} }} }},\frac{{E_{{n_{ij} }} }}{{\left( {E_{{x_{ij} }} } \right)^{2} }},\frac{{H_{{e_{ij} }} }}{{\left( {E_{{x_{ij} }} } \right)^{2} }}} \right)$.

Step 3: Multiply the rows.

Multiply each row of the cloud of elements in matrix A to obtain a new vector A’.

$$\left\{\begin{array}{l}{E}_{{x}_{i}}=\prod_{j=1}^{n}{E}_{{x}_{ij}} \\ {E}_{{n}_{i}}=\prod_{j=1}^{n}{E}_{{x}_{ij}}\sqrt{\sum_{j=1}^{n}{\left(\frac{{E}_{{n}_{ij}}}{{E}_{{x}_{ij}}}\right)}^{2}}\\ {H}_{{e}_{i}}=\prod_{j=1}^{n}{E}_{{x}_{ij}}\sqrt{\sum_{j=1}^{n}{\left(\frac{{H}_{{e}_{ij}}}{{E}_{{x}_{ij}}}\right)}^{2}}\end{array}\right.$$

(11)

$$\left[ {A^{\prime}_{i} } \right]_{1 \times n}^{T} = \left[ {A^{\prime}_{1} E_{{x_{1} }} ,E_{{n_{1} }} ,H_{{e_{1} }} , A^{\prime}_{2} E_{{x_{2} }} ,E_{{n_{2} }} ,H_{{e_{2} }} , \ldots A^{\prime}_{n} E_{{x_{n} }} ,E_{{n_{n} }} ,H_{{e_{n} }} } \right]$$

Step 4: Calculate the n-th root.

Take each element in vector A′ to the power of n to obtain a new vector A″.

$$A_{i}^{{^{\prime\prime}}} = A{^{\prime}}_{i}^{\frac{1}{n}} = \left( {\sqrt[n]{{E_{{x_{i} }} }} ,\sqrt{\frac{1}{n}} \cdot E_{{x_{i} }}^{{\frac{1}{n} - 1}} \cdot E_{{n_{i} }} ,\sqrt{\frac{1}{n}} \cdot E_{{x_{i} }}^{{\frac{1}{n} - 1}} \cdot H_{{e_{i} }} } \right)$$

(12)

$$\left[ {A{^{\prime\prime}}_{i} } \right]_{1 \times n}^{T} = \left[ \begin{gathered} A_{1} ^{\prime\prime}\left\langle {\sqrt[n]{{E_{{x_{1} }} }},\;\sqrt{\frac{1}{n}} \cdot E_{{x_{1} }}^{{\frac{1}{n} - 1}} \cdot E_{{n_{1} }} ,\;\sqrt{\frac{1}{n}} \cdot E_{{x_{1} }}^{{\frac{1}{n} - 1}} \cdot H_{{e_{1} }} } \right\rangle ,\; \hfill \\ A_{2} ^{\prime\prime}\left\langle {\sqrt[n]{{E_{{x_{2} }} }},\;\sqrt{\frac{1}{n}} \cdot E_{{x_{2} }}^{{\frac{1}{n} - 1}} \cdot E_{{n_{2} }} ,\;\sqrt{\frac{1}{n}} \cdot E_{{x_{2} }}^{{\frac{1}{n} - 1}} \cdot H_{{e_{2} }} } \right\rangle ,\;\;.... \hfill \\ A_{n} ^{\prime\prime}\left\langle {\sqrt[n]{{E_{{x_{n} }} }},\;\sqrt{\frac{1}{n}} \cdot E_{{x_{n} }}^{{\frac{1}{n} - 1}} \cdot E_{{n_{n} }} ,\;\sqrt{\frac{1}{n}} \cdot E_{{x_{n} }}^{{\frac{1}{n} - 1}} \cdot H_{{e_{n} }} } \right\rangle \hfill \\ \end{gathered} \right]$$

Step 5: Normalize.

Normalize the resulting vector to form the weight matrix W.

$$E^{\prime}_{{x_{i} }} = \frac{{\sqrt[n]{{E_{{x_{i} }} }}}}{{\mathop \sum \nolimits_{i = 1}^{n} \sqrt[n]{{E_{{x_{i} }} }}}}$$

(13)

$$\begin{aligned}& E^{\prime}_{{n_{i} }} = \frac{{\sqrt[n]{{E_{{n_{i} }} }}}}{{\mathop \sum \nolimits_{i = 1}^{n} \sqrt[n]{{E_{{n_{i} }} }}}}\\ &\quad = \frac{{\sqrt[n]{{E_{{x_{i} }} }}}}{{\mathop \sum \nolimits_{i = 1}^{n} \sqrt[n]{{E_{{x_{i} }} }}}}\sqrt {\left( {\frac{{\sqrt{\frac{1}{n}} \cdot E_{{x_{i} }}^{{\frac{1}{n} - 1}} \cdot E_{{n_{i} }} }}{{\sqrt[n]{{E_{{x_{i} }} }}}}} \right)^{2} + \left( {\frac{{\mathop \sum \nolimits_{i = 1}^{n} \sqrt{\frac{1}{n}} \cdot E_{{x_{i} }}^{{\frac{1}{n} - 1}} \cdot E_{{n_{i} }} }}{{\mathop \sum \nolimits_{i = 1}^{n} \sqrt[n]{{E_{{x_{i} }} }}}}} \right)^{2} }\end{aligned}$$

(14)

$$\begin{aligned}& H^{\prime}_{{e_{i} }} = \frac{{\sqrt[n]{{H_{{e_{i} }} }}}}{{\mathop \sum \nolimits_{i = 1}^{n} \sqrt[n]{{H_{{e_{i} }} }}}}\\ &\quad = \frac{{\sqrt[n]{{E_{{x_{i} }} }}}}{{\mathop \sum \nolimits_{i = 1}^{n} \sqrt[n]{{E_{{x_{i} }} }}}}\sqrt {\left( {\frac{{\sqrt{\frac{1}{n}} \cdot E_{{x_{i} }}^{{\frac{1}{n} - 1}} \cdot H_{{e_{i} }} }}{{\sqrt[n]{{E_{{x_{i} }} }}}}} \right)^{2} + \left( {\frac{{\mathop \sum \nolimits_{i = 1}^{n} \sqrt{\frac{1}{n}} \cdot E_{{x_{i} }}^{{\frac{1}{n} - 1}} \cdot H_{{e_{i} }} }}{{\mathop \sum \nolimits_{i = 1}^{n} \sqrt[n]{{E_{{x_{i} }} }}}}} \right)^{2} } \end{aligned}$$

(15)

$$W^{T} = \left[ {W_{1} \left( {\begin{array}{*{20}c} {E^{\prime}_{{x_{1} }} ,} & {E^{\prime}_{{n_{1} }} ,} & {H^{\prime}_{{e_{1} }} } \\ \end{array} } \right),W_{2} \left( {\begin{array}{*{20}c} {E^{\prime}_{{x_{2} }} ,} & {E^{\prime}_{{n_{2} }} ,} & {H^{\prime}_{{e_{2} }} } \\ \end{array} } \right), \ldots ,W_{n} \left( {\begin{array}{*{20}c} {E^{\prime}_{{x_{n} }} ,} & {E^{\prime}_{{n_{n} }} ,} & {H^{\prime}_{{e_{n} }} } \\ \end{array} } \right)} \right]$$

Step 6: Consistency check [22].

Calculate the consistency ratio (C.R.) using Eq. 16. When C.R. < 0.1, the consistency of the judgment matrix is considered acceptable. When C.R. > 0.1, the consistency of the judgment matrix cannot be exceeded, and experts should make evaluation adjustments.

$$\mathrm{C}.\mathrm{R}.=\frac{1}{n\left(n-1\right)}\sum_{i=1}^{n}\frac{{H}_{{e}_{ij}}}{{E}_{{x}_{ij}}}$$

(16)

Step 7: Calculate the weight value.

The cloud expected value (Eq. 17) can be used as the weight value [22].

$${\omega }_{i}={E}_{{x}_{i}}$$

(17)

Group cloud multi-dimensional comprehensive decision-making (GC-MCDM) algorithm

The weighted average cloud aggregation algorithm accounts for the evaluation ability of each expert; it calculates the weight and evaluation result of the element of each expert. Based on this algorithm, this study evaluates elements from multiple evaluation dimensions. Suppose the weights of n experts are ${\omega }_{E1}$, ${\omega }_{E2}$,…, ${\omega }_{En}$, each expert evaluates each element from n evaluation dimensions. Using Cloud-AHP, the cloud of the evaluation dimension is ${D}_{1}=\left({E}_{{x}_{1}}{, E}_{{n}_{1}},{ H}_{{e}_{1}}\right)$, ${D}_{2}=\left({E}_{{x}_{2}}{, E}_{{n}_{2}},{ H}_{{e}_{2}}\right)$,…, and ${D}_{n}=\left({E}_{{x}_{n}}{, E}_{{n}_{n}},{ H}_{{e}_{n}}\right)$. Equation 5 is used to calculate the single-dimensional weighted cloud (${E}_{wa}$). The multi-dimensional aggregate cloud (${C}_{wa}$) is calculated using Eq. 18 and the basic operation rules of the cloud [33].

$${C}_{wa}=\sum_{i=1}^{n}{D}_{i}{E}_{wai}$$

(18)

Multi-dimensional cloud-TOPSIS (MDCT) algorithm

Using the traditional TOPSIS algorithm, we propose an innovative multi-dimensional TOPSIS method based on the CM. A fuzzy membership function based on the cloud model was used as the language evaluation scale in this study. The cloud diagram of each evaluation scale is shown in Fig. 3. The specific calculation steps of the MDCT algorithm are given below:

Fig. 3

Membership function of fuzzy clouds

Step 1: Build a multi-attribute decision matrix.

Experts construct a multi-attribute decision matrix R according to the language evaluation scale [34, 35] shown in Table 2, where ${Z}_{j}$ and ${y}_{i}$ represent the evaluation dimension and candidate index, respectively. The form of the matrix R is given as:

Table 2 Cloud model language evaluation scale

$${R=\left[{Z}_{j}\left({y}_{i}\right)\right]}_{m\times n}= \left[\begin{array}{ccc}\begin{array}{cc}C\langle {E}_{{x}_{11}}{,E}_{{n}_{11}},{H}_{{e}_{11}}\rangle & C\langle {E}_{{x}_{12}}{,E}_{{n}_{12}},{H}_{{e}_{12}}\rangle \\ C\langle {E}_{{x}_{21}}{,E}_{{n}_{21}},{H}_{{e}_{21}}\rangle & C\langle {E}_{{x}_{22}}{,E}_{{n}_{22}},{H}_{{e}_{22}}\rangle \end{array}& \cdots & \begin{array}{c}C\langle {E}_{{x}_{1n}}{,E}_{{n}_{1n}},{H}_{{e}_{1n}}\rangle \\ C\langle {E}_{{x}_{2n}}{,E}_{{n}_{2n}},{H}_{{e}_{2n}}\rangle \end{array}\\ \vdots & \ddots & \vdots \\ \begin{array}{cc}C\langle {E}_{{x}_{m1}}{,E}_{{n}_{m1}},{H}_{{e}_{m1}}\rangle & C\langle {E}_{{x}_{m2}}{,E}_{{n}_{m2}},{H}_{{e}_{m2}}\rangle \end{array}& \cdots & C\langle {E}_{{x}_{mn}}{,E}_{{n}_{mn}},{H}_{{e}_{mn}}\rangle \end{array}\right]$$

Step 2: Multi-dimensional ideal cloud computing.

Generate a multi-dimensional positive ideal cloud and a multi-dimensional negative ideal cloud based on the positive and negative ideal evaluation clouds, respectively, in each evaluation dimension.

Multi-dimensional positive ideal cloud:

$$\begin{aligned} {y}^{+} & =\left\{{Z}_{j},\underset{i}{\mathrm{max}}\langle s\left({Z}_{j}\left({y}_{i}\right)\right)\rangle | j=1, 2,\dots ,n\right\}\\ & =\left\{\langle {Z}_{1}, C\left({E}_{{x}_{1}}^{+}{,E}_{{n}_{1}}^{+},{H}_{{e}_{1}}^{+}\right)\rangle ,\dots ,\langle {Z}_{j}, C\left({E}_{{x}_{n}}^{+}{,E}_{{n}_{n}}^{+},{H}_{{e}_{n}}^{+}\right)\rangle \right\} \end{aligned}$$

(19)

$$\left \langle {Z}_{j}, C\left({E}_{{x}_{j}}^{+}{,E}_{{n}_{j}}^{+},{H}_{{e}_{j}}^{+}\right)\right \rangle =\left(\underset{i}{\mathrm{max}}{E}_{{x}_{ij}},\underset{i}{\mathrm{min}}{E}_{{n}_{ij}},\underset{i}{\mathrm{min}}{H}_{{e}_{ij}}\right)$$

(20)

Multi-dimensional negative ideal cloud:

$$\begin{aligned} {y}^{-} & =\left\{{Z}_{j},\underset{i}{\mathrm{max}}\left \langle s\left({Z}_{j}\left({y}_{i}\right)\right)\right \rangle | j=1, 2,\dots ,n\right\}\\ & =\left\{\langle {Z}_{1}, C\left({E}_{{x}_{1}}^{-}{,E}_{{n}_{1}}^{-},{H}_{{e}_{1}}^{-}\right)\rangle ,\dots ,\langle {Z}_{j}, C\left({E}_{{x}_{n}}^{-}{,E}_{{n}_{n}}^{-},{H}_{{e}_{n}}^{-}\right)\rangle \right\} \end{aligned}$$

(21)

$$\left\langle {Z_{j} ,C\left( {E_{{x_{j} }}^{ - } ,E_{{n_{j} }}^{ - } ,H_{{e_{j} }}^{ - } } \right)} \right\rangle = \left( {\mathop {{\text{min}}}\limits_{i} E_{{x_{{ij}} }} ,\mathop {{\text{max}}}\limits_{i} E_{{n_{{ij}} }} ,\mathop {{\text{max}}}\limits_{i} H_{{e_{{ij}} }} } \right)$$

(22)

Step 3: Hamming distance calculation.

Use Eq. 10 and the weight value of each dimension to calculate the Hamming distance between the ${E}_{\mathrm{wa}}$ of each index and the multi-dimensional positive and negative ideal clouds.

$$\begin{aligned}{D}^{+}\left({y}_{i} ,{y}^{+}\right) & =\sum_{j=1}^{n}{\omega }_{j}d\left({Z}_{j}\left({y}_{i}\right),{Z}_{j}\left({y}^{+}\right)\right)\\ & =\sum_{j=1}^{n}{\omega }_{j}\left(\left|\left(1-\frac{{E}_{{n}_{ij}}^{2}+{H}_{{e}_{ij}}^{2}}{{E}_{{n}_{ij}}^{2}+{H}_{{e}_{ij}}^{2}{+E}_{{n}_{j}}^{+2}+{H}_{{e}_{j}}^{+2}}\right){E}_{{x}_{ij}}\right.\right.\\ &\quad \left.\left.-\left(1-\frac{{E}_{{n}_{j}}^{+2}+{H}_{{e}_{j}}^{+2}}{{E}_{{n}_{ij}}^{2}+{H}_{{e}_{ij}}^{2}{+E}_{{n}_{j}}^{+2}+{H}_{{e}_{j}}^{+2}}\right){{E}^{+}}_{{x}_{j}}\right|\right)\end{aligned}$$

(23)

$$\begin{aligned}{D}^{-}\left({y}_{i} ,{y}^{-}\right)& =\sum_{j=1}^{n}{\omega }_{j}d\left({Z}_{j}\left({y}_{i}\right),{Z}_{j}\left({y}^{-}\right)\right)\\ & =\sum_{j=1}^{n}{\omega }_{j}\left(\left|\left(1-\frac{{E}_{{n}_{ij}}^{2}+{H}_{{e}_{ij}}^{2}}{{E}_{{n}_{ij}}^{2}+{H}_{{e}_{ij}}^{2}{+E}_{{n}_{j}}^{-2}+{H}_{{e}_{j}}^{-2}}\right){E}_{{x}_{ij}} \right.\right.\\ &\quad \left.\left.-\left(1-\frac{{E}_{{n}_{j}}^{-2}+{H}_{{e}_{j}}^{-2}}{{E}_{{n}_{ij}}^{2}+{H}_{{e}_{ij}}^{2}{+E}_{{n}_{j}}^{-2}+{H}_{{e}_{j}}^{-2}}\right){{E}^{-}}_{{x}_{j}}\right|\right)\end{aligned}$$

(24)

${\omega }_{j}$ represents the weight value of the evaluation dimension, ${\omega }_{1}+{\omega }_{2}+\dots +{\omega }_{m}=1, j=1, 2, \dots ,m$.

Step 4: Calculate the proximity coefficient ${D}_{ij}^{*}$.

$${D}_{i}^{*}=\frac{{D}^{-}\left({y}_{i} ,{y}^{-}\right)}{{D}^{+}\left({y}_{i} ,{y}^{+}\right)+{\mathrm{D}}^{-}\left({y}_{i} ,{y}^{-}\right)}$$

(25)

The proximity coefficient ${D}_{ij}^{*}$ can reflect the distance between the ${E}_{\mathrm{wa}}$ of each index and the multi-dimensional positive and negative ideal clouds. The larger the value of ${D}_{ij}^{*}$, the closer the ${E}_{\mathrm{wa}}$ of the index is to the positive ideal cloud of the comprehensive dimension. However, a wider distance between the ${E}_{\mathrm{wa}}$ of the index and the negative ideal cloud of the comprehensive dimension shows that the index is relatively optimal. Conversely, the smaller the ratio of ${D}_{ij}^{*}$, the lesser the index [36].

Step 5: Sorting indices.

The proximity coefficient ${D}_{ij}^{*}$ is sorted according to the calculation results. The order of ${D}_{ij}^{*}$ (from large to small) indicates the order of the merit and difference of the indices and reflects the relative importance of the indices.

Assessment integration mechanism based on CM

The research content of mental load assessment mainly includes the primary selection of evaluation indices, calculation of expert weights, prioritizing of the importance of evaluation indices, determination of index weights, and classification of mental load evaluation. The specific steps are explained below:

Step 1: Primary selection of evaluation indices.

Collect physiological parameter indices, subjective questionnaire indices, and time perception test indices of the workers. Use statistical optimization methods to select indices with considerable differences and relevance to represent mental load and construct a two-level mental load evaluation index system.

Step 2: Determine the weight of the evaluation dimension.

As shown in the language scale in Table 2, experts are required to evaluate the importance of the indices from three evaluation dimensions: availability, operability, and sensitivity. The weight cloud and weight value calculation are performed on the three evaluation dimensions using Cloud-AHP, as illustrated by the importance scale in Table 1.

Step 3: Determine the weight of experts.

The expert weight is calculated from the four aspects (title, experience, education, and age), using Renjith’s scoring basis method [37].

Step 4: Single-dimensional weighted cloud of second-level indices.

Use Eq. 5 and the evaluation results of the importance of indices from three dimensions by experts to calculate the ${E}_{\mathrm{wa}}$ of each index.

Step 5: Prioritization of the importance of the second-level indices.

Use the MDCT algorithm to calculate the proximity ${D}_{ij}^{*}$ of each evaluation index and prioritize the importance of the evaluation index.

Step 6: Multi-dimensional aggregation of second-level indices.

According to the GC-MCDM algorithm, the ${C}_{\mathrm{wa}}$ of evaluation indices is calculated using Eq. 18 and the basic operation rules of the cloud.

Step 7: Determine the weights of indices at all levels.

According to the multi-dimensional aggregated cloud computing result obtained in Step 6, Eqs. 11–17 in Cloud-AHP are used to obtain the second-level index weight cloud with ${E}_{x}$ as the index weight value. As shown in Table 1, Cloud-AHP is used to calculate the weight cloud and weight value of the first-level indices.

Step 8: Determination of the mental load level of the second-level index.

The K-means clustering algorithm is used to classify the mental load state threshold value of the collected subjective and objective index data under the mental load state, while a total of four levels (1, 2, 3, and 4) are divided. The index data of each operator is converted into the corresponding level. Based on the second-level index weight cloud obtained in Step 7, the corresponding level value of the second-level index is combined with the index weight cloud to generate a second-level index level cloud using Eq. 5.

Step 9: Determine the mental load level of the first-level index.

According to the influence weight value obtained in Step 7 and the second-level index level cloud in Step 8, Eq. 8 is used to calculate the first-level index level cloud.

Step 10: Determination of the mental load level cloud.

According to the first-level index level cloud obtained in Step 9, Eq. 9 is used to calculate the highest-level index level cloud—the mental load state-level cloud.

Step 11: Determination of the mental load level.

Equation 7 is used to calculate the uncertainty linguistic value corresponding to each mental load level cloud, taking the maximum value ${X}_{\mathrm{max}}$ of the bilateral constraint value as the threshold for each level to obtain the mental load evaluation level.

Methodology

This study demonstrated a mental load assessment method that combines traditional AHP and TOPSIS extended with CM theory. The evaluation model block diagram is shown in Fig. 4.

Fig. 4

Methodology of mental load assessment

Figure 4 illustrates the mental load assessment methodology demonstrated in this study, which was divided into three stages. Stage 1 used the MDCT algorithm to prioritize the importance of indices. Stage 2 determined the weight of the evaluation index based on the Cloud-AHP. Stage 3 determined the mental load assessment level. The relevant data results of Stage 1 were used to support the weight determination of Stage 2. The level cloud of Stage 3 was determined using the weight determination result of Stage 2. The multi-dimensional aggregated cloud computing results of Stage 1 were input into Stage 2 to form a new matrix A′. Furthermore, the second-level index weight cloud and weight value were obtained using the normalization process of Cloud-AHP. The second-level index level cloud of Stage 3 was jointly determined by the level threshold of the second-level index of Stage 1 and the weight value of the second-level index of Stage 2. The complete calculation process will be described in the experimental case study. Researchers aimed to obtain only the key indices of mental load, which can be achieved through Stage 1. To evaluate the mental load state of workers, researchers can apply the mental load evaluation model proposed in this study. The evaluation content should include Stage 1–3.

Case study (mental load test)

Experiment introduction

In the mental load induction experiment, 20 study participants completed the energetic material impact detonation operation which included charging, discharging, and detonating explosives. After completing the operation, the study participants were required to complete 60 oral arithmetic questions in the form of “1XX + XX” within 3 min. The participants were informed that ranking would be based on the oral arithmetic results. This operation was performed with an explosive impact sensitivity tester in the energetic materials sensitivity testing laboratory of China. The energetic materials in the operation were relatively small. The risk of the entire operation was controllable, and the personal safety of the study participants was guaranteed. Therefore, the experiment loaded the study participants’ mental load from the aspects of time required, mental stress, task difficulty, and performance level. During the experiment, the following instruments were used to collect objective evaluation data: BD-II-121 time perception tester, smart finger sensor, semi-dry EEG, semi-dry electrode cap, and Tobii eye tracker. A subjective questionnaire was used to collect subjective evaluation data. The experimental process is illustrated in Fig. 5. First, the study participants wore physiological measuring equipment for 7 min to obtain the physiological parameters during a resting state. Second, they were guided to complete the time perception test (3 min). Next, they were required to complete the subjective questionnaire in 2 min. Subsequently, they were guided to complete the energetic material test experiment, and the physiological parameters were recorded under a 7 min mental load. Finally, the study participants were guided to complete the time perception test and the subjective questionnaire under a mental load state.

Fig. 5

Experimental process

Preliminary selection of indices and hierarchical structure

This study aimed to provide a model for evaluating the mental load state of workers. Therefore, constructing a good mental load system hierarchy and index selection were the first conditions for developing the model. These two conditions facilitate the quick and accurate assessment of the mental load state. We conducted subjective and objective evaluations of the study participants. Using the analysis results of the evaluation data, we selected the characterization index and constructed the mental load evaluation index system.

Related indices of mental load include subjective and objective evaluation indices [38]. Subjective evaluation is typically in the form of a questionnaire that investigates the study participants’ physical feelings and external symptoms to determine the degree of mental load [39,40,41]. The subjective questionnaire used in this study included four aspects: time required, mental stress, performance level, and task difficulty. These four aspects served as the four indices of subjective evaluation. Objective evaluation primarily includes mental and behavioral evaluation methods and physiological parameter evaluation. The mental and behavioral evaluation method selected for this study was the time perception measurement method [42], whereas the selected physiological parameter evaluation methods were the HRV evaluation method, EEG evaluation method, and eye electrical evaluation method. We used a statistical optimization analysis method to perform Pearson’s correlation analysis and t test on the 23 subjective and objective parameters. We also selected characteristic parameters with p value < 0.05 and correlation coefficient within 0.4 and 0.9 as the mental load index. The results of the statistical optimization analysis are presented in Table 3. Based on the statistical analysis results, we selected 16 characteristic parameters from the 23 parameters [HRV index (meanIBI, meanHR, SDNN, LF/HF), EEG index (theta (θ), alpha (α), beta (β)), eye electrical index (pupil diameter, fixation time, blink frequency), time perception test index (Response time error, Total relative error rate), Questionnaire score (Time requirement, Mental tension, Performance level, and Task difficulty)] as mental load evaluation index to develop a two-level mental load evaluation index system as shown in Fig. 6. Table 4 outlines the final 16 evaluation indices and their corresponding descriptions.

Table 3 Statistical analysis results of subjective and objective indices

Fig. 6

Mental load evaluation index system

Table 4 Evaluation indices and corresponding descriptions

Prioritization of indices based on MDCT

It was crucial for experts to evaluate the 16 s-level indices from three evaluation dimensions (availability, operability, and sensitivity). Accessibility reflects the difficulty of index collection, operability reflects the difficulty of the collected indices in data analysis and processing, and sensitivity reflects whether the index changes considerably under the mental load state. Based on these three evaluation dimensions, the indices can be ranked more scientifically and rationally. As illustrated in Table 1, a pairwise comparison matrix among the three evaluation dimensions was constructed; the construction is presented in Table 5. Cloud-AHP was used to calculate the pairwise comparison matrix to obtain the weight cloud of each evaluation dimension. The calculation process is detailed in Table 6, and the calculation results are presented in Table 7. The weight cloud of each dimension is illustrated in Fig. 7, reflecting the relative importance of each evaluation dimension. It can be observed that sensitivity is a relatively important evaluation criterion with relatively low accessibility. ${E}_{x}$ of the weight cloud of the evaluation dimension represents the weight value of each dimension, and the results are presented in Table 7.

Table 5 Priority comparison between dimensions

Table 6 Dimensional weight cloud computing process table

Table 7 Weight cloud and weight values of dimension

Fig. 7

Cloud diagram of evaluation dimension

We formed a panel of three experts. According to Renjith’s scoring basis, we calculated the expert weights using the title, experience, education, and age. The results are presented in Table 8.

Table 8 Determination of expert weight coefficient

The panel had access to Table 4. As shown in Table 2, expert evaluation was performed on the three evaluation dimensions of the 16 indices. The ${E}_{\mathrm{wa}}$ of the index was calculated using Eq. 5. The expert evaluation results and ${E}_{\mathrm{wa}}$ of each index are presented in Table 9. Moreover, Eq. 18 was used to calculate the ${C}_{\mathrm{wa}}$ of each index under the three dimensions, as shown in Table 10.

Table 9 Expert evaluation and single-dimensional weighted cloud

Table 10 Multi-dimensional aggregation cloud and optimization ranking of indices

Next, Eqs. 19–22 were used to obtain the multi-dimensional positive ideal cloud ${y}^{+}$ and the multi-dimensional negative ideal cloud ${y}^{-}$.

$$\begin{aligned}{y}^{+} &=\left\{{E}_{\mathrm{wa}}\left(\mathrm{0.7477,0.0477,0.0143}\right),\right.\\ &\quad\;\; \left. {E}_{wa}\left(\mathrm{0.7582,0.0452,0.0136}\right), \right.\\ &\quad\;\; \left.{ E}_{\mathrm{wa}}(\mathrm{0.7058,0.0452,0.0136})\right\}\end{aligned}$$

$$\begin{aligned} {y}^{-}&=\left\{{E}_{\mathrm{wa}}\left(\mathrm{0.3082,0.0593,0.0178}\right),\right.\\ &\quad {E}_{wa}\left(\mathrm{0.4477,0.0667,0.0200}\right),\\ &\quad \left. {E}_{\mathrm{wa}}(\mathrm{0.2977,0.0593,0.0178})\right\} \end{aligned}$$

Finally, we used Eqs. 23 and 24 to calculate the Hamming distance between the ${E}_{\mathrm{wa}}$ of each index with ${y}^{+}$ and ${y}^{-}$. We calculated the proximity coefficient ${D}_{ij}^{*}$ of each index using Eq. 25 and ranked the advantages and disadvantages. The results are presented in Table 10. Additionally, the Hamming distance and sorting are illustrated in Figs. 8 and 9. It can be observed from Fig. 8 that when comprehensively considering the availability, maneuverability, and sensitivity of the indices, the top five mental load evaluation indices are X1, X2, X4, X8, and X16. The importance of EEG indices and subjective evaluation indices was relatively low.

Fig. 8

Hamming distance and proximity

Fig. 9

Index importance ranking

Determination of index weight clouds at all levels based on cloud-AHP

The panel compared the priority relationships of the first-level indices (F1, F2, and F3) and calculated the weight cloud. The results are presented in Table 11. Figure 10 shows the weight cloud diagram of the first-level indices. It can be observed from the figure that F1 has a higher weight, and F2 is relatively low. Based on ${C}_{\mathrm{wa}}$ of each index in Table 10, the normalization processing of the Cloud-AHP was used to calculate the weight cloud on the second-level indices at the three levels of physiological parameters, subjective evaluation, and time perception. The calculation process is demonstrated in Table 12. The second-level index weight cloud is presented as a cloud diagram, as illustrated in Figs. 11, 12, 13. It can be observed from Fig. 11 that X1, X2, and X8 have relatively high weights when evaluating mental load levels. In contrast, X5 and X10 have relatively low weights. Furthermore, by observing Figs. 12 and 13, it can be concluded that the weights of X12 and X15 are relatively high, whereas the weights of X11 and X16 are relatively low. ${E}_{x}$ of indices at all levels represents the weight value of each index, and the result is shown in Table 13. Meanwhile, the weight value of indices at all levels is plotted in Fig. 14.

Table 11 Pairwise comparison of the weight clouds of the first-level indices

Fig. 10

Cloud diagram of the weights of first-level indices

Table 12 Index weight normalization calculation process

Fig. 11

Weight cloud diagram of physiological parameters

Fig. 12

Weight cloud diagram of subjective evaluation indices

Fig. 13

Weight cloud diagram of reliability indices

Table 13 Index weight cloud and weight value at all levels

Fig. 14

Index weight values at all levels

Evaluation of mental load state based on CM

K-means was used to classify the subjective and objective evaluation data of the 20 study participants in mental load state into four levels. This study defined the highest and lowest levels of mental load as four and one, respectively, and quantitatively described the level values of each index level. According to the overall trend of each index in the resting state and mental load state, the threshold value of each level was determined. The level threshold directly corresponded to the questionnaire survey score because the subjective questionnaire was set to four points. The threshold division results of each second-level index are presented in Table 14.

Table 14 Level threshold division result of K-means clustering

The level values of each second-level index of 20 study participants were determined from Table 14, and the results are shown in Table 15. Based on the level value of each second-level index and the weight cloud of a second-level index, Eq. 5 was used to generate the second-level index level cloud. The first-level index level cloud and mental load state level cloud were calculated using Eqs. 8–9, respectively, and the results are shown in Table 15. Moreover, the same method was used to calculate the level cloud of the mental load state when the level value of each second-level evaluation index was 1, 2, 3, or 4, respectively. The results are presented in Table 16 and Fig. 15.

Table 15 Mental load rating and rating cloud of study participants at all levels

Table 16 Mental load state evaluation level

Fig. 15

Cloud map of evaluation level

We calculated the uncertainty language values $\left[{X}_{\mathrm{min}}, \right.\break\left. {X}_{\mathrm{max}}\right]$ corresponding to the four-level clouds in Table 16. To increase the strictness of mental load level evaluation, the bilateral constraint value ${X}_{\mathrm{max}}$ represented the threshold of mental load level classification to obtain the value range of mental load level evaluation, as shown in Table 16. The mental load level value ${X}_{\mathrm{max}}$ of the 20 study participants was calculated, and the evaluation level result of the mental load of each participant was obtained as shown in Table 15. To compare and analyze the scientificity and progressiveness of the EC evaluation results, we selected the FC evaluation for the same application example; the subjective questionnaire results are presented in Table 15. The results are better illustrated in Figs. 16 and 17.

Fig. 16

Maximum mental load level value of study participants

Fig. 17

Mental load state level of study participants

As shown in Table 15, the subjective questionnaire results of P5 and P19 are consistent with the mental load level. However, an observation of the second-level index level values of physiological parameters and time perception shows that the level values of P5 are higher than that of P9, which indicates that P5 has a higher mental load state than P9. Therefore, the EC and FC evaluation results are more scientific and reliable. Similarly, the mental load states of P1, P3, P4, P10, P13, and P17 were more scientifically quantified. FC evaluation is scientifically reliable in assessing personnel fatigue and mental health [13,14,15,16]. Table 15 shows that all the results were consistent, aside the inconsistency between the EC and FC evaluation results of P6, P8, P13, and P18, indicating that the EC evaluation can be used for mental load state evaluation. Meanwhile, the second-level index level values of physiological parameters and time perception of P6, P8, P13, and P18 and other participants (P15, P16, P17, etc.) with third-level mental load based on the FC evaluation method were observed. The level values of the physiological parameters were approximately at the same level, and the time perception indices values of participants with third-level mental load were significantly greater than that of P6, P8, P13, and P18. Therefore, the mental load level of these four participants should be lower than the third level. The EC evaluation method determined that the four mental load levels were second level, which indicates that the EC evaluation is more scientific than the FC evaluation.

Discussion

The mental load state is fuzzy and difficult to define. A scientific approach to analyzing and evaluating the mental load state is the use of the CM theory. A quantitative method based on the AHP-TOPSIS integrated CM theory is proposed in this paper for obtaining the mental load state of personnel. Using sample data from the energetic material initiation experiment, Pearson’s correlation analysis and t test were performed to reflect the scientific rationality of the selection of characteristic indexes of the mental load state. According to the K-means cluster analysis, the threshold of the mental load characteristic index was divided. The MDCT algorithm and expert consultations were used to determine the importance of each evaluation index from multiple evaluation dimensions. The weight of each evaluation index was then determined by combining the GC-MCDM algorithm and Cloud-AHP to reduce the fuzziness and uncertainty of the evaluation process. Experts were evaluated, and weights were calculated according to Renjith’s scoring system. Consequently, the dispersion of the evaluation index weights was reduced, and more comprehensive and reasonable evaluation index weights were obtained. In this study, the evaluation indices were selected from the subjective and objective perspectives. The results of the subjective questionnaire reflected the subjective feelings of the study participants under the mental load state. Physiological parameters (HRV, EEG, and EOG) reflected the physiological state of the participants under mental load. The results of the time perception test reflected the reliability of the participants’ behavior under mental load. Therefore, the mental load evaluation index system constructed in this study is reasonable and scientific as compared with others.

Mental load experiments have shown that pupil diameter exhibits a significant increasing trend under the mental load state of tension and fear [43]. The brain allocates attention during saccadic activities, decreasing blink frequency [44]. Under mental load conditions, meanIBI and SDNN decrease significantly while meanHR and LF/HF increase significantly. Shaffer et al. [45] noted out that meanIBI and SDNN are time-domain indices of HRV signals mediated and controlled by parasympathetic nerves. The decrease in meanIBI and SDNN indicates a decreasing trend in parasympathetic activity, and people experience negative mental states, such as stress, tension, and fear [12]. Meanwhile, LF/HF under mental load increases significantly and generally reflects the balanced control of autonomic nerves [46]. The significant increase in LF/HF indicates an increase in the sympathetic activity of the heart, a decrease in the parasympathetic activity, and an experience of a mental load state by the personnel. In the research on the EEG rhythm of mental load, α-energy, β-energy and θ-energy are sensitive to mental state changes [43]. An increase in the intensity of β-energy activities indicates high alertness and nervousness. During sleep or a lack of attention, α-energy activity of is weakened in the frontal lobe. During tiredness, θ-energy activity decreases. The test results obtained in this study show that under the mental load state, α-energy, β-energy and θ-energy activities exhibited an increasing trend, which can be used as a characteristic index of mental load. Therefore, meanHR, meanIBI, SDNN, LF/HF, α-energy, β-energy, θ-energy, pupil diameter and blink frequency can be used as meaningful indices for evaluating the mental load state.

This study proposed a multi-dimensional Cloud-TOPSIS algorithm. We improved the positive and negative ideal cloud evaluation and Hamming distance formulas in the traditional TOPSIS algorithm. We also proposed multi-dimensional ideal cloud evaluation and distance calculation formula. Based on this algorithm, this study prioritized the importance of mental load assessment indices from three evaluation dimensions of accessibility, operability, and sensitivity. The top five indices were HR, IBI, LF/HF, pupil diameter, and total relative error rate. Several scholars only consider the sensitivity of physiological indices to change under mental load when conducting mental load research [12, 43]. In this study, when the ranking was only based on the evaluation results of index sensitivity, the top five indices were pupil diameter, HR, IBI, θ-energy, and fixation time. It can be observed that the sorting results of the two methods differ. For example, although EEG indices showed substantial changes under mental load, the ranking of EEG indices under multiple evaluation dimensions decreased because of the difficulty in collecting and processing EEG data compared with HRV data. If conducting scientific research on the indices of the mental load is the only aim, it suffices to select the indices from the sensitivity. However, to obtain more scientific evaluation results of mental load degree, a multi-dimensional index evaluation should be performed.

The same degree of mental load was applied to 20 participants in this study through a mental load induction experiment. EC and FC evaluation methods were used to perform a quantitative evaluation of the mental load state, during which the 20 participants showed different mental load levels. A comparison of the results of the two evaluation methods and the subjective questionnaire shows that the EC evaluation method is more suitable for determining the evaluation level of the mental load state. The quantitative evaluation result of the mental load would aid the scientific, objective, and accurate evaluation of the mental load state of personnel. The result can also be used for mental health and occupational fitness evaluations of enterprise personnel. To minimize human errors caused by the mental load during the work process, operators with low levels of mental load are prioritized for emergency or high-risk jobs.

There are some limitations of this study and require further research. (1) More physiological signals, such as EMG and respiration, are needed to expand the integrity of the evaluation index system; (2) The sample size of the participants should be increased for continuous verification; (3) Mental load data were collected through experiments in this study. In the future, the mental load data of multiple types of workers on site should be collected and evaluated to enhance the practicability of the evaluation method.

Conclusion

In this study, significant change characteristics of physiological parameters, subjective evaluation, and time perception were selected as evaluation indices. A quantitative evaluation method of the mental load state of personnel based on the EC evaluation method was established using these indices. The priority and weight of each evaluation index were determined using the MDCT and Cloud-AHP algorithms. On this basis, the VCA and K-means clustering algorithm were used to divide the mental load levels. Finally, the evaluation method was applied in an experimental case study. The major contributions of this study are as follows:

• 1. The mental load level was divided into four levels. The meanHR, meanIBI, SDNN, LF/HF, α-energy, β-energy, θ-energy, pupil diameter, blink frequency, fixation time, time requirement, psychological tension, performance level, task complexity, response time error, and total relative error rate were selected as the mental load evaluation index set.

• 2. The multi-dimensional Cloud-TOPSIS algorithm was used to prioritize the importance of evaluation factors from multiple dimensions. To overcome personal knowledge and experience limitations, we calculated the weight of experts using Renjith’s scoring basis method. Additionally, experts were required to evaluate indices from the three dimensions of accessibility, operability, and sensitivity, and finally combined with the GC-MCDM algorithm to obtain multi-dimensional aggregation cloud and priority of importance. The algorithm avoids the one-sidedness of evaluating indices in a single dimension. It can more objectively integrate experts’ evaluation suggestions from various dimensions, reduce the subjectivity of experts’ personal evaluation, and eliminate the dispersion of evaluation data.

• 3. The threshold values of each index and mental load evaluation level were determined using K-means clustering and the bilateral constraint conversion formula. A calculation model of mental load degree based on the EC evaluation method was established to study the mental load state of personnel quantitatively. The method was verified by the FC evaluation method and subjective questionnaire. The results showed that the mental load calculation model can effectively quantify the mental load of personnel, and the EC evaluation method is more accurate and reliable.

• 4. The evaluation results of the mental load state can be used for mental health warning and occupational suitability evaluation. To reduce work-related human accidents, research should be performed from various aspects, such as physical and mental load, to further protect the work safety and physical and mental health of personnel.