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ARTICLE INFO ABSTRACT

Article history:

Received XX Month 2024

Revised XX Month 2024

Accepted XX Month 2024

Online first

Published 1 September 2024

 Supplier selection is a critical factor in the success of fertigation systems, which integrate irrigation and fertilization to enhance agricultural productivity. This process's inherent uncertainty and complexity necessitate decision-making methodologies considering human judgment and risk preference factors. This study proposes the fuzzy Decision-Making Trial and Evaluation Laboratory (DEMATEL) method with a ranking based on the degree of optimism to evaluate and prioritise supplier selection criteria in fertigation systems. Six experts were involved in evaluating the influence of criteria such as price, quality, delivery, public procurement policy, technical, and managerial. The proposed method consists of eleven steps, including developing a fuzzy direct-relation matrix, average matrix, normalised fuzzy direct-relation matrix, fuzzy total relation matrix, ranking based on integral value and centroid defuzzification. The findings reveal that technical and quality criteria are paramount, though their relative importance shifts depending on the decision-maker’s degree of optimism. Specifically, technical criteria are prioritised by neutral and optimistic decision-makers, while quality criteria are regarded as most important by pessimistic decision-makers. Furthermore, the study identifies public procurement policy and technical criteria as part of the causal group, significantly influencing other criteria such as price, delivery, and managerial factors. Enhancing these causal criteria can lead to concurrent improvements in the effect criteria, optimising supplier selection processes. The results align with previous research, confirming the effectiveness and robustness of the fuzzy Dematel method with a degree of optimism-based ranking. This approach provides a comprehensive framework for agricultural decision-makers, facilitating more greater knowledge and reliable supplier selection decisions.

Keywords:

Fuzzy Dematel

Ranking Fuzzy Numbers

Degree of Optimism

Supplier Selection

Fertigation System

DOI:

10.24191/jcrinn.v9i2
# INTRODUCTION Fertigation systems, which integrate irrigation and fertilisation, are essential in contemporary agriculture for increasing yields of crops and optimising resource use. A thorough assessment procedure is necessary to ensure the success of such systems, as the selection of appropriate suppliers is crucial, and the criteria for suppliers are complex and extensive. Choosing proper suppliers significantly influences these systems' overall efficiency, durability, and cost-efficiency. Over the years, numerous techniques have been developed and utilised to address the complex and varied aspects of supplier selection in fertigation systems (Hendiani et al., 2020). However, especially in the unpredictable and dynamic agriculture sector, traditional decision-making techniques frequently cannot address the inherent ambiguity and uncertainty in supplier selection (Govindan et al., 2015). Fuzzy approaches have successfully addressed the inherent ambiguity and vagueness in decision-making processes for selecting supplier criteria in fertigation systems. One such method is the fuzzy AHP, which extends the traditional AHP by incorporating fuzzy theory to handle imprecise pairwise comparisons, which enables decision-makers to employ linguistic variables to appropriately prioritise criteria (Buyukozkan & Cifci, 2012; Chang, 1996). While fuzzy TOPSIS ranks suppliers based on their distance from an ideal solution, it considers the best and worst scenarios and uses fuzzy numbers to represent uncertainty (Modibbo et al., 2022). Fuzzy Data Envelopment Analysis (DEA) is also utilised to evaluate the relative efficiency of suppliers by incorporating fuzzy theory into the DEA framework, which benchmarks suppliers based on their performance. At the same time, the uncertainty in measurements is considered (Azadi et al., 2015; Mansour et al., 2022). Furthermore, the Fuzzy Decision-Making Trial and Evaluation Laboratory (DEMATEL) analyses and visualises causal relationships among criteria under uncertainty, enabling a greater understanding of the interdependencies between criteria (Nassir et al., 2021; Abadi et al., 2021; Keskin, 2015). These fuzzy methods collectively offer robust tools for selecting suppliers with knowledge and reliability in the context of fertigation systems and improving sustainability and overall performance. However, the current fuzzy DEMATEL method does not consider the decision-makers attitudes towards uncertainty, which can significantly influence the evaluation and ranking process. Incorporating the degree of optimism, which reflects the decision-makers risk preference, into the fuzzy DEMATEL can yield more realistic supplier rankings. This improved method enables a comprehensive assessment that balances optimistic and pessimistic options, leading to more resilient decision-making. In this paper, we propose an improved methodology that combines fuzzy DEMATEL with ranking based on the degree of optimism to evaluate and prioritise supplier selection criteria in fertigation systems. The proposed method aims to provide a more adaptable and flexible decision-support tool, enhancing the reliability of supplier selection in the context of fertigation systems. By applying this method, agricultural practitioners can make informed decisions that align with their risk preferences and operational objectives, ultimately contributing to the sustainability and efficiency of fertigation practices. The structure of this paper is as follows: Section 2 reviews the preliminaries of the concept used in the proposed method. Section 3 describes the methodology, including the incorporation of the degree of optimism into the fuzzy DEMATEL framework. Section 4 presents a numerical example to demonstrate the practical application of the proposed method. Finally, Section 5 discusses the results and implications, while Section 6 concludes the paper. # PRELIMINARIES In this section, some basic definitions of fuzzy numbers are reviewed. The ranking of fuzzy numbers based on the total integral value from Liou and Wang (1992) and the defuzzification method using centroid by Wang et al. (2006) are also presented. ## Definition 2.1 (Cheng, 1998) A fuzzy number *T* is a fuzzy set in the universe of discourse *X* that is both convex and normal, has bounded support, and all α-cuts of *T* are closed intervals of *X*. 1. 2. 1. ## Definition 2.2 (Cheng, 1998) A trapezoidal fuzzy number, represented as *T* = (*t*1, *t*2, *t*3, *t*4), has its membership function defined as follows: For *t*2 = *t*3, *T* becomes a triangular fuzzy number represented as *T* = (*t*1, *t*2, *t*4), and has its membership function defined as follows: ## Definition 2.3 (Liou & Wang, 1992) For a trapezoidal fuzzy number *T* = (*t*1, *t*2, *t*3, *t*4), for the total integral value is given in Eq. (1). (1) The higher the value of , the higher the rank of the fuzzy number. ## Definition 2.4 (Wang et al, 2006) For a trapezoidal fuzzy number *T* = (*t*1, *t*2, *t*3, *t*4), the centroid point *x* can be expressed as indicated in Eq. (2). (2) # **FUZZY DEMATEL WITH RANKING BASED ON DEGREE OF OPTIMISM** Equations and formulas This section describes the procedure of the proposed fuzzy Dematel with a ranking based on the degree of optimism. The procedure consists of 11 steps as follows: **Step 1:** Define the evaluation criteria, *B*1, *B*2, … *Bn*, where *Bi* represents the *i*-th criteria and *n* is the total number of criteria. **Step 2:** Choose a group of *K* experts with knowledge and competence in evaluating the effect between criteria through pairwise comparison. **Step 3:** Establish a fuzzy linguistic scale to address the uncertainty inherent in human judgement. The group decision-making process utilises a five-level linguistic concept called “influence”. The scale consists of five levels of impact: no influence (NO), very low influence (VL), low influence (L), high influence (H), and very high influence (VH). Table 1 displays the fuzzy numbers for these linguistic terms. | Table 1. The fuzzy linguistic scale for experts’ evaluation | | | ----------------------------------------------------------- | -------------------- | | **Linguistic Terms** | **Fuzzy numbers** | | No influence (NO) | (0, 0, 0, 0.25) | | Very low influence (VL) | (0, 0, 0.25, 0.5) | | Low influence (L) | (0, 0.25, 0.5, 0.75) | | High influence (H) | (0.25, 0.5, 0.75, 1) | | Very high influence (VH) | (0.5, 0.75, 1, 1) | **Step 4:** Build a fuzzy direct-relation matrix where decision-makers gather judgements on a linguistic scale based on Table 1. The fuzzy initial direct-relation matrix , which contains fuzzy numbers represented as , can be expressed as indicated in Eq. (3), which reflects the subjective assessment made by decision maker *k* regarding the degree of influence of element *i* on element *j*. (3) **Step 5:** Aggregate the assessments of *K* decision-makers for each of the k experts. These form the average matrix, as indicated by Eq. (4). (4) **Step 6:** Using Eq. (5), calculate the normalised fuzzy direct-relation matrix as follows: (5) where ; for all criteria of **Step 7:** Let and , , and . The elements in these matrices are derived from *F* as presented in Eq. (6): (6) **Step 8:** Using Eq. (7) and Eq. (8), construct the fuzzy total relation matrix in which the matrix has trapezoidal fuzzy numbers. > (7) , , , and (8) whereby *I* is the matrix identity *n* x *n*. Compute the summation of rows (*ri*) and columns (*cj*) for each row *i* and column *j* from matrix respectively. > (9) > > (10) **Step 9:** Calculate the sum of 𝑟i and 𝑐j using the fuzzy arithmetic operation described in Eq. (11), and calculate the difference between 𝑟i and 𝑐j using the fuzzy arithmetic operation described in Eq. (12). The expressions 𝑟i + 𝑐j and 𝑟i − 𝑐j are in the form of trapezoidal fuzzy numbers. The sum of 𝑟i and 𝑐j represents the strength of each criterion. Meanwhile, 𝑟i − 𝑐j denotes the group of criteria. For two trapezoidal fuzzy numbers, *A* = (*a*1, *a*2, *a*3, *a*4) and *B* = (*b*1, *b*2, *b*3, *b*4), the addition and subtraction operations are as in Eq. (11) and Eq. (12) relatively. (11) (12) **Step 10:** Rank the 𝑟i + 𝑐i using the integral value and degree of optimism approaches from Liou and Wang’s (1992) study as indicated in Eq. (1) **Step 11:** Compute the defuzzification of 𝑟*i* − 𝑐*j* using the centroid method in point-wise form, as proposed by Wang et al. (2006) in Eq. (2). # NUMERICAL EXAMPLE This section applies the proposed fuzzy DEMATEL method in the selection of criteria for suppliers in the fertigation system. The selection process occurs at one branch of RISDA (Rubber Industry Smallholders Development Authority) located on the East Coast of Malaysia. The procedure for implementing the fuzzy DEMATEL with ranking based on the degree of optimism is illustrated in the subsequent steps. **Step 1:** The six criteria for supplier selection in the fertigation system employed in this study were taken from Etraj and Jayaprakash (2017). The criteria include price (*B*1), quality (*B*2), delivery (*B*3), public procurement policy (*B*4), technical (*B*5), and managerial (*B*6). **Step 2:** Six experts in the field of fertigation systems were engaged in the selection process. All experts possess over five years of expertise in managing the fertigation system. **Step 3:** As stated in Table 1, the five fuzzy language terms used in this study were no influence (NO), very low influence (VL), low influence (L), high influence (H), and very high influence (VH). **Step 4:** Table 2 displays the linguistic fuzzy scale direct-relation matrix *S*1 for Expert 1 based on Table 1 and Eq. (3). | Table 2. The linguistic scale direct-relation matrix for Expert 1, *S*1 | | | | | | | | ---------------------------------------------------------------------------------- | ------------------------ | ------------------------ | ------------------------ | --------------------- | ------------------------ | ------------------------ | | ** ** | ***B*1** | ***B*2** | ***B*3** | ***B*4** | ***B*5** | ***B*6** | | ***B*1** | (0, 0, 0, 0) | (0.5, 0.75, 1.00, 1.00) | (0, 0.25, 0.50, 0.75) | (0, 0.25, 0.50, 0.75) | (0, 0, 0.25, 0.50) | (0, 0, 0.25, 0.50) | | ***B*2** | (0.25, 0.50, 0.75, 1.00) | (0, 0, 0, 0) | (0, 0, 0.25) | (0, 0, 0, 0.25) | (0, 0.25, 0.50) | (0, 0, 0.25, 0.50) | | ***B*3** | (0, 0.25, 0.50, 0.75) | (0, 0, 0.25, 0.50) | (0, 0, 0, 0) | (0, 0.25, 0.50, 0.75) | (0, 0.25, 0.50, 0.75) | (0.25, 0.50, 0.75, 1.00) | | ***B*4** | (0, 0.25, 0.50, 0.75) | (0, 0, 0.25, 0.50) | (0, 0.25, 0.50) | (0, 0, 0, 0) | (0.25, 0.50, 0.75, 1.00) | (0.50, 0.75, 1.00, 1.00) | | ***B*5** | (0, 0.25, 0.50, 0.75) | (0.50, 0.75, 1.00, 1.00) | (0.25, 0.50, 0.75, 1.00) | (0, 0, 0.25, 0.50) | (0, 0, 0, 0) | (0.50, 0.75, 1.00, 1.00) | | ***B*6** | (0, 0, 0.25, 0.50) | (0.25, 0.50, 0.75, 1.00) | (0.25, 0.50, 0.75, 1.00) | (0, 0, 0.25, 0.50) | (0.25, 0.50, 0.75, 1.00) | (0, 0, 0, 0) | **Steps 5-6:** Based on Eq. (4) and Eq. (5), and all experts' linguistic scale direct-relation matrix, the normalised fuzzy direct-relation matrix *F* is shown in Table 3. | Table 3. The normalised fuzzy direct relation matrix F | | | | | | | | ------------------------------------------------------ | --------------------- | --------------------- | --------------------- | --------------------- | --------------------- | --------------------- | | | ***B*1** | ***B*2** | ***B*3** | ***B*4** | ***B*5** | ***B*6** | | ***B*1** | (0,0,0,0) | (0.33,0.58,0.83,1.0) | (0.08,0.29,0.54,0.79) | (0.17,0.42,0.67,0.88) | (0.17,0.33,0.54,0.75) | (0.08,0.29,0.54,0.75) | | ***B*2** | (0.33,0.5830.83,0.96) | (0,0,0,0) | (0.04,0.25,0.46,0.71) | (0.21,0.42,0.62,0.83) | (0.25,0.42,0.62,0.79) | (0.25,0.46,0.71,0.88) | | ***B*3** | (0,0.25,0.50,0.75) | (0.08,0.29,0.54,0.79) | (0,0,0,0) | (0,0.25,0.50,0.75) | (0.08,0.33,0.58,0.83) | (0.08,0.33,0.58,0.83) | | ***B*4** | (0.17,0.42,0.67,0.92) | (0.25,0.46,0.71,0.88) | (0.25,0.46,0.71,0.88) | (0,0,0,0) | (0.21,0.46,0.71,0.96) | (0.25,0.46,0.71,0.88) | | ***B*5** | (0.29,0.54,0.79,0.92) | (0.33,0.58,0.83,1.0) | (0.21,0.46,0.71,0.92) | (0.12,0.33,0.58,0.79) | (0,0,0,0) | (0.29,0.54,0.79,1.0) | | ***B*6** | (0.29,0.42,0.66,0.88) | (0.12,0.38,0.62,0.88) | (0.12,0.37,0.62,0.83) | (0,0.17,0.38,0.62) | (0.17,0.42,0.67,0.92) | (0,0,0,0) | | TTable 4. The values of 𝑟i + 𝑐j and 𝑟i − 𝑐j | | | | | | ------------------------------------------- | -------------------------------- | ----------------------------------- | --------------------------------- | --------------------------------- | | | **Sum of rows, *ri*** | **Sum of columns, *cj*** | **𝑟i + 𝑐j** | **𝑟i − 𝑐j** | | ***B*1** | (0.228,0.737,2.212,11.262) | (0.292,0.837,2.421,11.845) | (0.520,1.574,4.632,23.107) | (-11.616,-1.684, 1.374, 10.971) | | ***B*2** | (0.293,0.808,2.290,11.269) | (0.299,0.863,2.467,12.130) | (0.592,1.671,4.756,23.399) | (-11.837,-1.659, 1.426, 10.970) | | ***B*3** | (0.069,0.566,1.943,10.787) | (0.186,0.695,2.140,11.146) | (0.255,1.261,4.083,21.934) | (-11.078,-1.574, 1.248, 10.601) | | ***B*4** | (0.296,0.846,2.437,12.034) | (0.138,0.615,1.974,10.602) | (0.434,1.461,4.411,22.635) | (-10.305,-1.128, 4.822, 11.895) | | ***B*5** | (0.329,0.915,2.557,12.279) | (0.235,0.744,2.201,11.429) | (0.563,1.659,4.757,23.708) | (-11.100,-1.285, 1.813, 12.045) | | ***B*6** | (0.189,0.669,2.096,11.158) | (0.254,0.787,2.331,11.638) | (0.443,1.456,4.427,22.797) | (-11.449,-1.662,1.309,10.904) | **Steps 7-9:** Table 4 displays the values of 𝑟i + 𝑐j and 𝑟i − 𝑐j based on Eq. (6) to Eq. (12). **Step 10:** Based on Eq. (1), the ranking of 𝑟i + 𝑐j is shown in Table 5, with represent pessimistic, neutral and optimistic decision maker relatively. | **Table 5. The ranking** of 𝑟i + 𝑐j | | | | | | | | --------------------------------------------------------- | ------------------------------- | ----------- | --------------------------- | ----------- | ------------------------------ | ----------- | | | **Pessimistic decision maker,** | **Ranking** | **Neutral decision maker,** | **Ranking** | **Optimistic decision maker,** | **Ranking** | | ***B*1** | 1.047 | 3 | 7.458 | 3 | 13.870 | 3 | | ***B*2** | 1.132 | 1 | 7.605 | 2 | 14.077 | 2 | | ***B*3** | 0.758 | 6 | 6.883 | 6 | 13.008 | 6 | | ***B*4** | 0.948 | 5 | 7.236 | 5 | 13.523 | 5 | | ***B*5** | 1.111 | 2 | 7.672 | 1 | 14.233 | 1 | | ***B*6** | 0.950 | 4 | 7.281 | 4 | 13.612 | 4 | ** ** **Step 11:** Based on Eq. (2), the defuzzified value of 𝑟i - 𝑐j is shown in Table 6. | **Table 6. The defuzzified value of 𝑟i - 𝑐j ** | | | | -------------------------------------------------------------------- | ------------------------ | --------- | | **Criteria** | **Defuzzified value of** | **Group** | | ***B1*** | \-0.260 | Effect | | ***B2*** | \-0.315 | Effect | | ***B3*** | \-0.210 | Effect | | ***B4*** | 0.628 | Cause | | ***B5*** | 0.395 | Cause | | ***B6*** | \-0.237 | Effect | # RESULT AND DISCUSSION \[CHART\]Based on Table 5, for an optimistic decision-maker , the ranking result is , which indicate that the technical criterion is ranked the highest, followed by quality, price, managerial factor, public procurement policy, and delivery. The neutral decision-maker also has the same ranking as the optimistic decision-maker. However, for the pessimistic decision-maker , the ranking results differ slightly , that indicate quality is ranked the highest, followed by technical, while the remaining criteria have similar rankings. These results indicate that the technical criterion is the most important for both neutral and optimistic decision-makers, followed by quality. Conversely, for pessimistic decision-makers, the quality criterion takes precedence, followed by technical. Thus, both technical and quality criteria are crucial in the selection of suppliers in fertigation systems. The ranking result for pessimistic decision-makers aligns with the study by Mohd et al. (2020), which utilised the CFC defuzzification approach. Meanwhile, the ranking results for optimistic and neutral decision-makers are consistent with the findings of Nassir et al. (2021) using the simplified centroid defuzzification method. Fig. 1. The causal diagram Based on Table 6 and the causal diagram in Fig. 1, the criteria public procurement policy (*B*4) and technical (*B*5) are categorised into the causal group, while the effect group consists of the criteria price (*B*1), quality (*B*2), delivery (*B*3), and managerial (*B*6). The most significant causal criterion for supplier selection in this study is public procurement policy (*B*4), followed by technical (*B*5). These two criteria require greater consideration than the others, as the causal group influences the effect group criteria. By improving the causal criteria, the effect criteria are concurrently enhanced (Seker & Zavadskas, 2017). The public procurement policy (*B*4) and technical (*B*5) criteria can directly or indirectly influence the other criteria. These results provide valuable guidance for improving supplier selection in fertigation systems by focusing on these critical criteria. # CONCLUSION In this study, the fuzzy Dematel method with a ranking based on degree of optimism is proposed to evaluate and prioritise supplier selection criteria in fertigation systems. The proposed approach effectively addresses the inherent uncertainty and vagueness in decision-making by analysing causal relationships among criteria under uncertainty, enabling a deeper understanding of the interdependencies between criteria and evaluating the strength of criteria based on decision-makers risk preferences. The results indicate that the technical and quality criteria are crucial in the supplier selection process, with their importance varying based on the decision-maker's degree of optimism. For neutral and optimistic decision-makers, the technical criterion emerged as the most crucial, while pessimistic decision-makers prioritised the quality criterion. This highlights the need to consider different perspectives in supplier evaluation to achieve a comprehensive and balanced selection process. Furthermore, our analysis revealed that public procurement policy (*B*4) and technical (*B*5) criteria belong to the causal group, significantly influencing other criteria such as price, quality, delivery, and managerial aspects. Improving these causal criteria can lead to concurrent enhancements in the effect criteria, thereby optimising the overall supplier selection process in fertigation systems. Our findings align with previous studies and demonstrate the robustness and applicability of the fuzzy DEMATEL method with degree of optimism-based ranking. This approach provides a valuable framework for decision-makers in the agricultural sector to make more informed and reliable supplier selection decisions, ultimately enhancing the performance, sustainability, and cost-effectiveness of fertigation systems. In conclusion, the integration of fuzzy DEMATEL with degree of optimism-based ranking offers a comprehensive and flexible tool for addressing the complexities and uncertainties in supplier selection based on decision-makers risk preferences. Future research could further refine this method by exploring additional criteria and incorporating other fuzzy multi-criteria decision-making techniques to support continuous improvement in supplier evaluation practices within fertigation systems. # **ACKNOWLEDGEMENT** (DOUBLE-BLIND reviewing. Leave the section as is. Only include Acknowledgements text in the final submission paper) # Conflict of interest statement (DOUBLE-BLIND reviewing. Leave the section as is. Only include CONFLICT OF INTERESTS text in the final submission paper) # # Authors’ contributions # References Abadi, S.K.G., Bathaei, A., Awang, S,R., & Ahmad, T. (2021). 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