## 1. Introduction

As one of the earliest domesticated grain legumes, the roots of cultivated chickpea (

Cicer arietinum L.) dates back to nearly 7500 years ago [

1]. Chickpea cultivars are believed to have originated in the Old World, where south eastern part of Turkey and adjoining Syria lie today [

2]. Archeological explorations at this region provided evidence that chickpea cultivars already existed in the early times of Neolithic revolution [

3]. Today, cultivation of chickpea has global interest with numerous variants to satisfy distinct dietary habits. According to 2018 data by Food and Agriculture Organization of the United Nations (FAO) [

4], India is the top producer by far over the world with a volume of over 11 million tons a year. India is followed by Australia with nearly 1 million tons. By ascending on the list year by year, Turkey is the third global producer with 630,000 tons.

Domesticated plants may be confronted by many biotic and abiotic stress elements. Remarkable yield loss is observed globally due to external impacts. Specific to chickpea cultivation, biotic stress includes pathogens and pests such as

Ascochyta rabiei,

Fusarium oxysporum,

Liriomyza cicerina, and

Callosobruchus chinensis L., where cold (both chilling and freezing) and drought stresses are prominent types of abiotic stresses that delimitate both nutritional value and development of plant, particularly in semiarid regions [

5,

6]. Kashiwagi et al. [

7] determined the variability of root length and its contribution to crop productivity under drought stress. Molina et al. [

8] applied Super Serial Analysis of Gene Expression (SuperSAGE) technology in order to observe the response of chickpea seeds to drought stress by analyzing gene expression. Mafakheri et al. [

9] researched the results of drought stress on 3 types of chickpea cultivars concerning selected characteristics, where Çiçek et al. [

5] screened 21 cultivars by chlorophyll

$\alpha $ fluorescence measurement at 3 different severity levels of drought. Arslan et al. [

6] focused on biochemical and molecular changes of three chickpea cultivars at freezing temperatures. Nayyar and Chander [

10] observed the protection response of polyamines in case of oxidative stress that is arisen in consequence of water and cold stress. Nayyar et al. [

11] exposed chickpea cultivars to chilling stress, assisted the plants by injecting glycine betaine additive, and observed the recovery with respect to control cultivar. Gao et al. [

12] created two cDNA libraries, selected random clones from the libraries, performed sequencing analysis on expressed sequence tags (ESTs) and revealed gene regulations against dehydration stress. Unlike many studies on this topic, Croser et al. [

13] tried to determine the effects of low temperature by fusing findings of a wide range of study in the literature, nevertheless the study is lacking in a generic mathematical model.

There are many distinct studies in the literature that have their own focus. Rather than having a specific and focused conceptual research on chickpeas, this study concentrates on developing an analytical decision-making approach by comparing different cultivars in terms of key characteristics that are changed during stress conditions. The aim of constructing such an analytical model is to provide an efficient decision making process for breeders to select cultivars to achieve the best results under abiotic stress conditions, to compare efficiency of crop cultivars with regard to their traits, and to encourage agricultural policy makers to revise their cultivation strategies by generalizing this approach for crops of interest. This study handles the cultivation of chickpea under cold and drought stress conditions with a holistic perspective. These abiotic stresses have an aggregated effect of nearly 65–70% on crop loss. Hence, a vital portion of agents that engender yield loss is covered for a more accurate ranking. The proposed multi criteria decision making (MCDM) model provides a ranking sequence for chickpea cultivars with regard to their durability under cold and drought stress conditions to enhance optimum results.

Many statistical approaches are applied to agricultural data to culminate in intended solution, conclusion, or inference. These models implicitly reveal patterns with pure numerical methods without intervention and should be interpreted with a defined hypothesis. Analysis of variance (ANOVA) is a very common example that is widely used in agricultural studies. MCDM methods deal with suggesting an order or ranking of alternatives. Many MCDM algorithms were developed to overcome various types of real-world decision-making problems. In contradistinction to statistical methods, MCDM methods encourage decision makers to contribute to the solution methodology for achieving more accurate and preferable results. MCDM methods may be reinforced with fuzzy theory to adjoin linguistic evaluations of decision makers with regard to selection criteria and handle uncertainties of decision makers on concluding judgments. Analytical hierarchy process (AHP) is widely implemented to determine weights of the criteria of decision model by pairwise comparisons of expert decision makers. As an extension, intuitionistic fuzzy-AHP (IF-AHP) can be administered for decision models where decision makers have suspicion on comparing criteria. IF-AHP can manage linguistic judgments or comparisons without disregarding the uncertainties of decision makers. Goal programming (GP) has been used in many studies to rank alternatives according to the closeness to the goal values with regard to weighted criteria.

Table 1 summarizes preceding studies that are similar to our methodology. The methodologies of these studies will be compared in the discussion and conclusion sections.

Aydemir and Akçakaya [

23] pioneered the implementation of the MCDM approach on chickpea cultivars and applied the technique for order preference by similarity to ideal solution (TOPSIS) method to rank cultivars according to their growth on regular fields. Sudha and Jeba [

24] proposed a TOPSIS model for evaluating five different crops versus five criteria.

The MCDM methodology, instead of statistical methods, is preferred for this study since subjective evaluations of decision makers were paramount to overcome the ambiguity of the stress conditions. For instance, drought stress plays a more important role on the growth of chickpea cultivars according to the judgments by decision makers. It would be hard to reveal this sophisticated decision tree with statistical methods.

From this standpoint, this study proposes an integrated IF-AHP and GP approach for development of a systematic procedure for agricultural decision-making processes. Multiple decision makers may judge the evaluation criteria with imprecise linguistic terms from which the weights of the criteria are derived. The integrated GP model analytically suggests the ranks and scores of the alternatives concerning their closeness to the goal values. The distinguishing feature of this methodology in comparison to statistical methods is the capability of comprising the judgements of decision makers considering uncertainties.

To the best of the author’s knowledge, the proposed methodology, which integrates IF-AHP and GP, is the first intelligent MCDM methodology for the field of agriculture that is empowered by a sensitivity analysis to determine bounds of weights. The MCDM studies on agricultural data in the literature have not yet handled sensitivity analysis.

The rest of this study is organized as follows:

Section 2 explains the materials and methods in detail. Case study and results are given in

Section 3. Discussion, conclusions, and recommendations are emphasized in

Section 4.

## 3. Case Study and Results

Proposed methodology is applied step by step to evaluate durability of chickpea cultivars.

Step-1: To establish the MCDM problem, 18 chickpea cultivars are defined as alternatives. Alternatives are evaluated in line with a three-layer structure. Cold stress and drought stress are described as categories. Each state of both stress experiments that has calculated values for variables are introduced as subcategories. Hence, the number of subcategories under cold stress and drought stress are five and six, respectively. Finally, each calculated variable in the experiment is counted as criterion linked to subcategories. As a result, each subcategory has five criteria. The resulting MCDM model is represented in

Figure 4.

Step-2: The scale in

Table 2 by Abdullah and Najib [

31] is assigned to be utilized in pairwise comparisons.

Step-3: To achieve group decision making, three decision makers expressed their judgments. The scale in

Table 3 by Boran et al. [

32] is used to resolve weights of decision makers. The weights of decision makers are determined as VI, I, and M for DM1, DM2, and DM3 according to their experience and relevance to the subject, respectively. Transforming linguistic weights by suggested formulation ensues crisp values as 0.413, 0.344, and 0.242, which can be seen in

Table 4.

Step-4: Decision makers are requested to compare 2 categories, 11 subcategories, and 5 criteria mutually.

Table 5 and

Table 6 demonstrate sample pairwise comparison matrices by decision makers concerning criteria of cold stress and drought stress states, respectively. These matrices express the preference or importance level of a criterion in the rows versus a criterion on the columns.

Step-5: The linguistic expressions in the decision matrices are converted into IF values referenced to scale defined in the methodology.

Table 7 and

Table 8 show converted values for IF decision matrices demonstrated in

Table 5 and

Table 6.

Step-6: Each row of the decision matrices is aggregated into one single IF value, so that evaluations of decision makers regarding each criterion can be expressed with a single IF value. IFWA operator is applied for this operation. Applying IFWA operator to

Table 7 results in the aggregated IF decision matrices in

Table 9.

Table 10 shows the aggregated results after applying IFWA operator to

Table 8.

Step-7: Weights of the decision makers and aggregated decision matrices are combined into weighted aggregated IF decision matrices by IFWA operator. Weighted aggregated IF decision matrix for criteria of cold subcategories and drought subcategories is shown in

Table 11 and

Table 12, respectively.

Step-8: Each weighted aggregated IF decision matrix is checked for consistency. Sample calculation for the matrix in

Table 11 and

Table 12 is formulated in Equation (8). Because the CR value is 0.098 for cold subcategories and 0.099 for drought subcategories, which is below 0.10, the matrix is accepted to be consistent. The matrices with a CR value higher than 0.10 should be evaluated again by DMs.

Step-9: Relative weights for each category, subcategory, and criterion are calculated using Equation (9). Results are shown in

Table 13.

Step-10: Crisp weights are added to the GP model and the GP model is solved. Cultivars are ranked according to their difference scores from the goal values in ascending order. That is, a lower score grants a cultivar a better rank. Ranking results are shown in

Table 14.

The solution steps only cover sample calculations and tables because of space limitations. The resulting order presents the cumulative performance against cold and drought stress conditions. The scores of the cultivars also provides evidence for the degree of performance distinction. With this focus, Diyar 95 shows a prominent performance against remaining cultivars, while Işık 05 performs worst with the lowest value.

#### Sensitivity Analysis

Final ranks of alternatives are sensitive to the weights of the criteria. As a result of this assumption, relative changes of criteria may lead to a completely different ranking of alternatives. The weights are acquired from the subjective judgments of decision makers. Any perturbation on ranking may bias rational solution of any MCDM problem. Because the judgments of decision makers change according to knowledge, experience, and relativeness, a sensitivity analysis should be added to the methodology to evaluate boundaries of the solution rather than having a point solution.

A set of scenarios with changing weights were considered for sensitivity analysis. In Scenario 1, the weight of each criterion was accepted as equal. In Scenario 2, the effect of drought stress is assessed solely, thus weight of drought stress was 1.00 where the weight of cold stress was 0. Scenario 3 was the opposite case of Scenario 2 where weight of drought stress was 0 and the weight of cold stress was 1.00. Results for these scenarios are demonstrated in

Figure 5. The scenarios have given rise to significant results. The most significant result is Diyar 95 remains as best alternative except in Scenario 3 where the weight of the drought stress is 0. This result advises that the performance of Diyar 95 under cold stress avoids it to remain as best alternative. Another significant result is Işık 05 remains as worst alternative in all scenarios. Damla 89 presents a highly varying performance, which keeps it as best alternative in Scenario 3 where cold stress is considered and 16th alternative in Scenario 2 where drought stress is considered. Çağatay presents an opposing performance to the Damla 89, thus it becomes 2nd in Scenario 2 and 17th in Scenario 3.

In addition to scenarios, limits regarding the best three alternatives are evaluated. The results are shown in

Table 15.

## 4. Discussion and Conclusions

In this paper, a MCDM methodology is proposed to rank chickpea cultivars with respect to their cumulative tolerance to cold and drought stress conditions. The methodology integrates two important algorithms, namely AHP and goal programming. AHP is applied to determine the weights of the categories, subcategories, and criteria. Goal programming is handled to rank the alternatives with regard to their distances from their target values. AHP is widely used in literature to determine weights since it eases the process by pairwise comparisons. It enables GDM, in which the evaluations of multiple experts are aggregated to achieve a more concrete decision. However, classical AHP forces DMs to compare the criteria with crisp values. Thus, the comparison should be conducted numerically without any regret. However, in some cases DMs may be required to avoid definitive judgments. That is, they may need to express their uncertainties. Fuzzy sets are integrated to MCDM methodology to overcome this deficiency in the literature. Fuzzy numbers allow DMs to express the degree of membership and the degree of nonmembership to a set. Nevertheless, by expressing their evaluation with fuzzy numbers, DMs are still required to express exact levels of membership and nonmembership. As an extension of fuzzy theory, IF theory has been preferred to allow DMs to express their hesitancy while declaring their judgments. Various similar methodologies are surveyed and listed in

Table 1. Studies [

14] through [

17] propose an IF-GP, in which the “performances” of alternatives may be evaluated with hesitancies. However, they lack evaluation of criteria by GDM experts and also a sensitivity analysis. The studies [

18] and [

19] suggest a fuzzy AHP-GP integration without GDM and sensitivity. The common deficit of studies from [

18] to [

21] is their integration with classical fuzzy sets that avoids DMs expressing their uncertainties. The methodology by Alegoz and Yapicioglu [

22] is reinforced by type 2 fuzzy set that supports hesitancy with similar fashion to IF Set. However, GP methodology in this methodology cannot be applied to rank alternatives. Aggregating all these aspects, to the best of the author’s knowledge, this is the first study in this field that suggests a MCDM methodology for ranking alternatives that encourages a GDM process in which DMs also express their hesitancies by proposing an integration IF-AHP with GDM and GP followed by a sensitivity analysis. The distinguishing features of the methodology are the generic structure that allows the application to any other selection process, GDM where IF theory is applied to help DMs to evaluate the criteria by also indicating their uncertainties, and sensitivity analysis that helps to determine the limit values that change the result. The methodology may be applied to any MCDM problem without any change, where expert DMs exist to express their linguistic evaluations for criteria and alternatives have crisp performance values for each criterion.

The MCDM model of the case study has been built on chickpea cultivars as alternatives and stress conditions as categories, states of the stress experiments as subcategories, and critical parameters of chickpea cultivars as criteria. The experimental data consist of critical numerical parameters that decrease or increase under stress conditions. F_{V}/F_{M}, PI_{ABS}, and PI_{TOTAL} keep a decreasing trend whereas ABS/RC, DIo/RC, MDA, and H_{2}O_{2} have an increase under stress conditions. Goal programming of the proposed methodology penalizes these deviations with respect to control cultivars to calculate cumulative capability of durability, since an increase or decrease in the values indicates sensitivity to stress conditions. In other words, cultivars are qualified as more tolerant to stress conditions provided that they have as little difference as possible from control cultivar parameter values. As a result, Diyar 95 outperforms with a highly separated score. Sensitivity analysis shows that Diyar 95 has the best capability to protect itself under drought stress. However, Damla 89 performs slightly well if the weight of cold stress is adjusted over 75%, since Damla 89 has better durability under cold stress conditions. The worst performing cultivar is Işık 05 with a distinctly low score.

Evaluating the final weights of categories, subcategories, and criteria, it can be inferred that real-life conditions of the geography are effective on evaluations by DMs. Drought stress condition is counted as more important than cold stress condition, in line with the conditions in Turkey. Discussing the subcategories, it can be recognized that the states followed by adaptation in cold stress and recovery state for drought stress are more important. The reason behind these preferences may be considered as also the similarities of these states to cultivations in Turkey. Among the criteria, PI_{ABS} and PI_{TOTAL} have the highest importance levels after comparisons. This result should not be surprising since these indicators collectively show the vitality level of the cultivars. All these deductions are consistent with the conditions in Turkey and may result in differences after evaluations by DMs in different regions.

The results in this study may be compared to the experimental studies by Turan [

25] for cold stress and Çiçek et al. [

5] for drought stress. Rather than having totally mathematical formulations, both studies have heuristic scoring approaches. Turan [

25] partitioned the cultivars into three sets, namely tolerant, moderately tolerant, and sensitive. The proposed algorithm in this study has been run with weight values “0” for drought category and “1” for cold category to have the same scale with the study by Turan [

25]. Dividing the ranking list of this study into same sets yields to have exactly the same cultivars within the same clusters. With the same manner, the algorithm has been run with weight values “1” for drought category and “0” for cold category to compare with the study by Çiçek et al. [

5]. Both studies perform similar results. Four out of five cultivars at the top of both lists are the same cultivars. Hence, the comparisons with both studies suggest that the proposed methodology and results are consistent with experimental deductions.

This study aims to support decision makers on agriculture to select best alternatives for cultivation planning. For future research directions, new decision categories like cost, availability, etc. may be included to enhance the decision-making process for cultivar ranking. More parameters would enrich the quality of the decision process. Furthermore, integrated Z-Score AHP, neutrosophic sets, or Pythagorean fuzzy AHP may be applied to enhance the capability of handling uncertainties of the decision processes. Because the alternatives have numerical parameters, the model cannot be applied to data that include linguistic parameters. Instead of pure GP, IF-GP may be applied to transform linguistic terms into numerical values to involve them in calculations.