Kharif Crops Selection for Sustainable Farming Practices in the Rajasthan-India Using Multiple Attribute-Based Decision-Making

: Sustainability of agricultural practices depends on economic, environmental, and social conditions. The Rajasthan state of India has arid climatic conditions where kharif crops are commonly grown. In this work, the four major criteria are considered such as the farm area, crop yield per unit area, the cost prices, and the market sales price. Merged analytic hierarchy process (AHP) and entropy techniques have been employed to give reasonable weight coe ﬃ cients for the objective and subjective weights to each criterion. Multiple attribute-based decision-making models (MADM) have been developed using three proven techniques, namely the Exprom2, the technique for order of preference by similarity to ideal solution (TOPSIS), and the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR). The crop Pennisetum glaucum emerged as the most productive kharif crop in the arid climatic conditions of Rajasthan, India under the given criteria. The sensitivity analysis of the three methods identiﬁes the most signiﬁcant criteria and validates that Pennisetum glaucum is the ﬁrst ranked crop despite the interchange of the weights. The methodology used in this study may be applied across the globe to select appropriate crops for maximizing the proﬁt, optimizing the natural resources, and promoting sustainable agricultural practices. This study may be used to enhance the agricultural gross domestic product (GDP) to make the agriculturalists self-su ﬃ cient and to help the state policymakers in making e ﬀ ective regional policies.


Introduction
The kharif crops such as rice, Sorghum, Zea mays, cotton, ragi, Pennisetum glaucum, sugarcane, jute, etcetera, grow in dry and arid conditions. The soil and its nutrient value is an important component of sustainable farming [1]. Despite modern agricultural techniques, the high rate of population growth renders the crop yield inadequate [2]. The choice of a specific arrangement of crop patterns relies upon numerous criteria that differ from region to region [3]. The conception of the index was included in sustainability for the set of selected criteria and existing weather parameters by Dillon et al. [4]. Roy and Weng [5] examined the indicators of sustainable agriculture in Bangladesh.

Study Area
The important criteria considered in this study were the crop field areas, the yield of the crops, cultivation cost, and the market sales price of the crop. Figure 1 gives the ranking process of the kharif crops by MADM techniques.
Agronomy 2020, 10 The decision-makers (stakeholders) are farmers, service providers, regulators, the agriculture research institute, seed and fertilizer suppliers, agriculture brokers, and consumers. The policymakers include the department of agriculture, government of Rajasthan, ministry of agriculture, the agriculture minister, the minister of state, the department of irrigation, etcetera.

Study Area
The important criteria considered in this study were the crop field areas, the yield of the crops, cultivation cost, and the market sales price of the crop. Figure 1 gives the ranking process of the kharif crops by MADM techniques.

Criteria Weighting
The entropy and analytic hierarchy process (AHP) techniques were merged to obtain the normalized objective and subjective weights of the criteria. For the k th criteria, the synthesis weight w k is given as follows: In Equation (1), the k th criteria has the weight α k computed by AHP method and the β k is computed by entropy method [23].

AHP Technique
The AHP technique was proposed by Saaty [24]. The pairwise matrix A is used to compare the set of n alternatives according to the relative importance of the weights.
In Equation (2), a 1 , a 2 , . . . , a n represent the criteria. The relative significance of the two criteria are ranked using the digits from 1 to 9 [25], where 1 stands for equally significant, 3 for somewhat more significant, 5 for intensely significant, 7 for demonstrably more significant, 9 for absolutely more significant and 2, 4, 6, 8 stands for a compromise between slightly different judgments. The comparative weights are obtained by determining the eigenvector w concerning λ max that satisfies A w = λ max w.
Here, λ max is the highest eigenvalue of matrix A. The consistency index (CI) and the consistency ratio (CR) are calculated from Equations (3) and (4) to ascertain the accuracy of the comparative weights and consistency of the subjective perception. Here, n is a criteria number, the value of CI should be less than 0.1 for the results to be confident, and the random consistency index (RI) should be below 0.1 for the valid results.

Entropy Technique
The following Equation (5) gives the decision matrix A, having m alternatives (evaluation objectives) for n criteria (evaluation indexes) [12].
For normalization, the dimensionless values of different criteria are computed by Equation (6) to make a comparison among them.
where P ij is the normalized vector, a proportion of i th index value under criteria j. Equation (7) is used to compute the entropy E j of the j th criteria.
In Equation (7), constant k = 1/ ln m, ensures 0 ≤ E j ≤ 1 and m is the number of choices. Equation (8) can be used to calculate the degree of divergence (d j ) of the mean information contained in each criterion.

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The weight of the entropy of the j th criteria is given by Equation (9).

Exprom2 Technique
The updated version of the Promethee II technique is known as the Exprom2 technique, which is derived from ideal and anti-ideal solutions given in Equations (10) and (11) [26]: In this x ij indicates the performance measure of the i th alternative concerning criterion j and r ij is the normalized value of the x ij .
The pairwise calculation is done to get the difference in criteria value (d j ). Equation (12) is used to calculate the preference function to measure the extent to which the alternative i dominate over the alternative i / for the j th criteria.
Here x ij (i = 1, 2, . . . , m; j = 1, 2, . . . , n) is the value of j th criteria and i th alternative. To get the weights by the entropy technique, the normalized decision matrix P ij is estimated by Equation (13) given by Gowda and Jayaramaiah [27].
Equation (14) is used to calculate the weak preference index WP ij i, i / .
In Equation (14), the w j is the weight of the j th criterion derived from the compromised weighting method.
The definition of the strict preference function is given by Equations (15) and (16).
In this, dm j is the difference between the ideal and anti-ideal value of the j th criterion and the L j is the limit of the preference.
The total preference index is given by Equation (17).
The positive flow for the i th alternative is calculated by Equation (18).
Agronomy 2020, 10, 536 6 of 15 The negative flow for the i th alternative is calculated by the by Equation (19).
Here m is the number of the alternatives. The total outranking flow for each alternative is calculated by Equation (20).
The best alternative is chosen based on the highest value of ϕ(i).
The technique for order of preference by similarity to ideal solution method (TOPSIS) The steps followed in the TOPSIS method are: 1. The decision matrix x ij mxn with dimension, mxn is formed by n criteria and m alternatives with the interaction of each criterion and alternative given by x ij .
2. The weight of each criterion is computed by comparing the relative importance of one attribute with the other (Saaty 1980) [24].
3. The matrix x ij mxn is now normalized (Equation (21)): Using the normalization method (Equation (22)): 4. Calculate the weighted normalized decision matrix from Equations (23) and (24) in which, T is the resultant of matrix operation, t ij is the matrix element corresponding to the i th row and j th column: where n j=1 w j = 1, W j is the original weight given to the indicator r ij , j = 1, 2, . . . , n. 5. Determine the worst alternative (A w ) (Equation (25)) and the best alternative (A b ) (Equation (26)): In which, J + = j = 1, 2, . . . , n j has a positive impact, and J − = j = 1, 2, . . . , n j has a negative impact.
Equation (27) is used to calculate the distance between the target alternative i and the worst condition A w .
The alternative i and the best condition A b (Equation (28)): where, i = 1, 2, . . . , m and; j = 1, 2, . . . , n and d iw and d ib are the distances from the target option i to the best and worst conditions, respectively.
6. Euclidean distance S iw is calculated by Equation (29) to determine the similarity to the worst condition: S iw = 1 for the best condition, and; S iw = 0 for the worst condition. 7. Ranking of S iw (i = 1, 2, . . . , m) by prioritization.

VIKOR Technique
The VIKOR method gives a compromised solution. The main steps of the VIKOR technique [28] are: The decision matrix is used to obtain the best i.e., (x ij ) max and the worst i.e., (x ij ) min values of all the criteria., The following equations are used to determine the standard parameters of the VIKOR method: E i , F i , and P i respectively.
The values of P i are calculated by Equation (32).
Here ϑ is the weight of the policy of the majority of the criteria, the range of this can be any value between 0 and 1 and the most common value is 0.5. The maximum and minimum values of E i and F i are designated by E i-max , E i-min , F i-max , and F -min respectively.
The criteria weighting and the MADM techniques have been explicitly given in the preceding section and Figure 2 presents a summary in a flow chart. The abbreviations, mathematical operators, and symbols have been given at the end of the article for quick reference. where, = 1,2, … , ; = 1,2, … , and and are the distances from the target option to the best and worst conditions, respectively.
6. Euclidean distance is calculated by Equation (29) to determine the similarity to the worst condition: = 1 for the best condition, and; = 0 for the worst condition. 7. Ranking of ( = 1,2, … , ) by prioritization.

VIKOR Technique
The VIKOR method gives a compromised solution. The main steps of the VIKOR technique [28] are: The decision matrix is used to obtain the best i.e., (xij)max and the worst i.e., (xij)min values of all the criteria., The following equations are used to determine the standard parameters of the VIKOR method: Ei, Fi, and Pi respectively.
The values of Pi are calculated by Equation (32).
Here is the weight of the policy of the majority of the criteria, the range of this can be any value between 0 and 1 and the most common value is 0.5. The maximum and minimum values of Ei and Fi are designated by Ei-max, Ei-min, Fi-max, and F-min respectively.
The criteria weighting and the MADM techniques have been explicitly given in the preceding section and Figure 2 presents a summary in a flow chart. The abbreviations, mathematical operators, and symbols have been given at the end of the article for quick reference.  of each criterion is interchanged with another. To validate the criteria weighting and compare the results obtained from the MADM techniques, sensitivity analysis was done. A similar methodology has been adopted by Ahmed et al. [17,18]. The criteria weights were obtained from a survey among the stakeholders and the recent data obtained from the government sources [21,22].

Results and Discussion
An effort is made to develop a MADM model using a systems approach to rank the five kharif crops (given in Table 1) in Rajasthan-India. The four major criteria considered are; area of crop field (ACF) in Ha, production of crop field (PCF) in kg/Ha, production cost (PC) USD/Ha, and sales price (SP) in USD/kg. The pairwise comparison is made by summarizing the survey from the stakeholders and the results are reported in Table 2. The higher digit indicates a higher relevance in the pairwise comparison.  Table 3 summarizes the weight of each criterion using AHP, entropy and the compound weight methods. The highest weight is obtained for the ACF among the three methods.  Table 4 gives the normalized decision matrix for the four criteria and five alternatives. The digits obtained from the matrix are used as inputs in the MADM techniques.  Table 5 shows the results obtained from the Exprom2 method and the value of the positive flow for the i th alternative, the negative flow of the i th alternative, and the total flow is given in the table after calculation. The best alternative is chosen based on the highest value of ϕ(i). The positive and negative flow indicates extremes. The ranking is based on the resultant of the positive and negative flow. The first rank is of Pennisetum glaucum, followed by Vigna radiate, Zea mays, Vigna mungo, and Sorghum. The first rank hence determines the most favorable crop under the selected criteria. Tables 6 and 7 show the general matrix outcomes used as inputs in the MADM techniques. Table 8 shows the result obtained from the TOPSIS method. Here, an alternative with the highest value of C i is ranked first, and so on. On comparing the ranks of the crops obtained by the Exprom2 (Table 5), one may observe 100% consistency. This validates the results obtained under the selected criteria for the selected crops. Crop A2 (Pennisetum glaucum) emerges as the most suitable one.  Table 9 shows the results obtained for the VIKOR method where the ranking is based on the value of P i . The lower the value of P i , the higher will be the rank. The first ranked alternative is Pennisetum glaucum, followed by others. The ranks of the crops obtained by the Exprom2, TOPSIS, and VIKOR are in 100% conformation.  Figure 3 presents a comparative picture of the results obtained from the three methods. There is a perfect match between the ranks obtained from all the three techniques and Pennisetum glaucum has emerged as the first ranked crop.
For sensitivity analysis, nine conditions were taken into account, given in Table 10. For each condition, the rank is computed by all three methods i.e., the Exprom2, the TOPSIS, and the VIKOR respectively. In Table 10, the criteria weights are represented by w1 (ACF), w2 (PCF), w3 (PC), and w4 (PS) respectively. After fixing one criterion weight and interchanging the others, nine unique combinations (conditions) have been considered.
Agronomy 2020, 10, x FOR PEER REVIEW 8 of 16 Figure 3 presents a comparative picture of the results obtained from the three methods. There is a perfect match between the ranks obtained from all the three techniques and Pennisetum glaucum has emerged as the first ranked crop. For sensitivity analysis, nine conditions were taken into account, given in Table 10. For each condition, the rank is computed by all three methods i.e., the Exprom2, the TOPSIS, and the VIKOR respectively. In Table 10, the criteria weights are represented by w1 (ACF), w2 (PCF), w3 (PC), and w4 (PS) respectively. After fixing one criterion weight and interchanging the others, nine unique combinations (conditions) have been considered. Table 10. Different conditions for the sensitivity analysis.
The sensitivity analysis of the TOPSIS and the VIKOR methods are given in Figures 5 and 6 respectively. In both the Figures, conditions 2 and 3 emerge as most sensitive. The rank of crop A2 is at the first rank in four conditions in each method, consolidating and validating the ranking results given in Table 9 and Figure 3. In all three methods, the weights w2 (PCF) and w3 (PC) are the dominant criteria, conforming with the results obtained from AHP ( Table 3).
The process of selecting kharif crops in the arid region of Rajasthan state in India for sustainable agriculture is complex. Especially when it is derived under the influence of a large number of criteria that influence sustainability, it poses many challenges. Without sufficient kharif crop production resources, the problem of kharif crop harvest becomes more complicated. The present methodology will, therefore, be of great help to stakeholders in agriculture in these environments. For future research, the MADM-based methodology will have more advantage, as comparison depends on experts' subjective judgment. By using MADM-based methods, biases and vagueness in decision-making can be largely overcome. The MADM methods will help farmers and agricultural policymakers to formulate a comprehensive policy for sustainable agricultural practices, which has a potential and immediate solution to address the ongoing urgent requirement worldwide. Prospects of the research may include adaptation and mitigation options for better sustainable agricultural practices resulting from climate change problems to improve the decision-making process. Agronomy 2020, 10, x FOR PEER REVIEW 9 of 16  Table 9 and Figure 3. In all three methods, the weights w2 (PCF) and w3 (PC) are the dominant criteria, conforming with the results obtained from AHP (Table 3).   Table 9 and Figure 3. In all three methods, the weights w2 (PCF) and w3 (PC) are the dominant criteria, conforming with the results obtained from AHP (Table 3).  The process of selecting kharif crops in the arid region of Rajasthan state in India for sustainable agriculture is complex. Especially when it is derived under the influence of a large number of criteria that influence sustainability, it poses many challenges. Without sufficient kharif crop production resources, the problem of kharif crop harvest becomes more complicated. The present methodology will, therefore, be of great help to stakeholders in agriculture in these environments. For future research, the MADM-based methodology will have more advantage, as comparison depends on experts' subjective judgment. By using MADM-based methods, biases and vagueness in decisionmaking can be largely overcome. The MADM methods will help farmers and agricultural policymakers to formulate a comprehensive policy for sustainable agricultural practices, which has a potential and immediate solution to address the ongoing urgent requirement worldwide. Prospects of the research may include adaptation and mitigation options for better sustainable agricultural practices resulting from climate change problems to improve the decision-making process.

Conclusions
The multi-attribute decision making (MADM) has been successfully applied for the best selection of the output under the given inputs and constraints (criteria). The applications of MADM techniques in agricultural engineering are still emerging. India is an agricultural-based and fastestgrowing economy in the world. In an agriculture-dependent economy like India, precision agriculture is extremely important for an increase in productivity. These techniques may provide better decision-making rather than deciding intuitively. The study employed two criteria (subjective and objective) weighting methods and then obtained the criteria weights by normalizing, to standardize the results. The ranking of the crops has been done by three MADM methods, namely, the Exprom2, the TOPSIS, and the VIKOR to rank the crops to facilitate the farmers and the policymakers to decide on inclusion or exclusion of an attribute according to the significance of the criteria concerning the objective. Three methods were used to validate the accuracy of the results and avoid the inherent deficiency of a single MADM technique. A sensitivity analysis was done for each

Conclusions
The multi-attribute decision making (MADM) has been successfully applied for the best selection of the output under the given inputs and constraints (criteria). The applications of MADM techniques in agricultural engineering are still emerging. India is an agricultural-based and fastest-growing economy in the world. In an agriculture-dependent economy like India, precision agriculture is extremely important for an increase in productivity. These techniques may provide better decision-making rather than deciding intuitively. The study employed two criteria (subjective and objective) weighting methods and then obtained the criteria weights by normalizing, to standardize the results. The ranking of the crops has been done by three MADM methods, namely, the Exprom2, the TOPSIS, and the VIKOR to rank the crops to facilitate the farmers and the policymakers to decide on inclusion or exclusion of an attribute according to the significance of the criteria concerning the objective. Three methods were used to validate the accuracy of the results and avoid the inherent deficiency of a single MADM technique. A sensitivity analysis was done for each method to determine its impact. The government hence spends a considerable percentage of the annual GDP for supporting farmers. This study gives a scientific approach to decision making, which affects the livelihood of a large section of the society (farmer) and the overall economy of the state and the country, suggesting a replacement of conventional, preferential, or intuitive decision-making approaches.
The attributes and the criteria were kept in mind while formulating and modeling the problems. The results obtained by TOPSIS, Exprom2, and VIKOR were in good agreement for prioritizing the kharif crops. The first ranked crop is Pennisetum glaucum, the second is Vigna radiate, the third is Zea mays, the fourth is Vigna mungo, and the last one (fifth) is Sorghum. Results from the three MADM techniques are in exact confirmation indicating that any one of them may be used to rank the crops. The scope of the study may be global and the selected criteria may be increased as suitable. The outcome of the research work will help the policymakers and the farmers to implement sustainable farming practices, increase profit, and minimize losses due to poor decision making. Similar studies may be done changing the criteria, depending on the region and the best productive crop may be suggested to the farmers. The sensitivity analysis of the three methods validates that the PCF and PC are dominant criteria and Pennisetum glaucum emerged as the first ranked crop on maximum counts in the sensitivity analysis of each method. If the government of India motivates the farmers to cultivate this crop in Rajasthan, the productivity is expected to increase.
The future recommendations are to use the MADM-based advanced techniques to handle decision-making problems for the farmers and state agriculture departments to formulate better guidelines for sustainable agricultural practices, globally. The prospects of the research may also include adaptation and mitigation options for better sustainable agricultural practices resulting from climate change problems to improve the decision-making process. w j Weight of the j th criterion SP j i, i / Strict preference function dm j Difference of ideal and anti-ideal value of j th criterion L j Limit of the preference TP i, i / Total preference index ϕ + (i) Positive flow for the i th alternative ϕ − (i) Negative flow for the i th alternative ϕ(i) Total outranking flow x ij mxn Matrix formed by n criteria and m alternatives with the intersection of each alternative and criteria given by x i j R Normalized matrix T

Resultant of matrix operation t ij
Matrix element corresponding to i th row and j th column W j Original weight is given to the indicator v j Standard value of indicator A b Best alternative A w Worst alternative J + Positive impact (benefit criteria) J − Negative impact (cost criteria) d ib Distance between target alternative and best condition d iw Distance between target alternative and worst condition S iw Similarity to the worst condition E i , F i , and P i Standard parameters of the VIKOR method ϑ Weight of the strategy of the majority of the criteria (decision mechanism index) ranging between 0 and 1