Determining Importance of Many-Objective Optimisation Competitive Algorithms Evaluation Criteria Based on a Novel Fuzzy-Weighted Zero-Inconsistency Method

Abstract

Along with the developments of numerous MaOO algorithms in the last decades, comparing the performance of MaOO algorithms with one another is also highly needed. Many studies have attempted to manipulate such comparison to analyze the performance quality of MaOO. In such cases, the weight of importance is critical for evaluating the performance of MaOO algorithms. All evaluation studies for MaOO algorithms have ignored to assign such weight for the target criteria during evaluation process, which plays a key role in the final decision results. Therefore, the weight value of each criterion must be determined to guarantee the accuracy of results in the evaluation process. Multicriteria decision-making (MCDM) methods are extremely preferred in solving weighting issues in the evaluation process of MaOO algorithms. Several studies in MCDM have proposed competitive weighting methods. However, these methods suffer from inconsistency issues arising from the high subjectivity of pairwise comparison. The inconsistency rate increases in an exorbitant manner when the number of criteria increases, and the final results are affected. The primary objective of this study is to propose a new method, called a Novel Fuzzy-Weighted Zero-Inconsistency (FWZIC) Method which can determine the weight coefficients of criteria with zero consistency. This method depends on differences in the preference of experts per criterion to compute its significance level in the decision-making process. The proposed FWZIC method comprises five phases for determining the weights of the evaluation criteria: (1) the set of evaluation criteria is explored and defined, (2) the structured expert judgement (SEJ) is used, (3) the expert decision matrix (EDM) is built on the basis of the crossover of criteria and SEJ, (4) a fuzzy membership function is applied to the result of the EDM and (5) the final values of the weight coefficients of the evaluation criteria are computed. The proposed method is applied to the evaluation criteria of MaOO competitive algorithms. The case study consists of more than 50 items distributed amongst the major criteria, subcriteria and indicators. The significant contribution of each item to the algorithm evaluation is determined. Results show that the criteria, subcriteria and their related indicators are weighted without inconsistency. The findings clearly show that the FWZIC method can deal with the inconsistency issue and provide accurate weight values to each criterion.

Novel dynamic fuzzy Decision-Making framework for COVID-19 vaccine dose recipients

“…Define the level of importance scale : In this step, the selected group of three experts were asked to define the level of importance/significance of each criterion by using a five-point Likert scale. In general, no theoretical reason is considered in ruling out the different lengths of the response scale [61] . The options usually reflect an underlying continuum rather than a finite number of possible attitudes.…”

“…In view of resolving this issue, a method should be able to assign weights to the criteria without entailing a pairwise comparison amongst the set of criteria, which was the basis of developing the FDOSM [50] . According to the literature review, the latest method proposed by [61] is called the fuzzy-weighted zero-inconsistency (FWZIC), which can provide weights for criteria with zero inconstancy. The FWZIC method could solve the following limitations of the best worst method, AHP and analytic network process: (i) inability of the procedure to offer the decision maker an instant feedback on the consistency of pairwise comparisons, (ii) absence of accounting for ordinary consistency and (iii) shortage of the consistency threshold value for evaluating the reliability of results [61] , [62] .…”

Integration of fuzzy-weighted zero-inconsistency and fuzzy decision by opinion score methods under a q-rung orthopair environment: A distribution case study of COVID-19 vaccine doses

“… Define the level of importance scale: In this step, the selected group of experts can define the level of importance or significance of each criterion with a five-point Likert scale. No theoretical reason exists to rule out different lengths of a response scale [69] . The options reflect an underlying continuum rather than a finite number of possible attitudes.…”

“…To resolve this issue, a method explicitly assigning weights to criteria without pairwise comparison among the sets of criteria is needed. According to the literature review, the latest method was proposed in [69] , namely, fuzzy-weighted zero-inconsistency (FWZIC) method, which can provide weights for criteria with zero inconstancy. The FWZIC method solves the following limitations of the best worst method and analytic hierarchy process: (i) the inability of the procedure to offer decision maker instant feedback on the consistency of pairwise comparisons, (ii) absence of accounting for ordinary consistency and (iii) shortage of consistency threshold value for evaluating the reliability of results [69] .…”

Interval type 2 trapezoidal‐fuzzy weighted with zero inconsistency combined with VIKOR for evaluating smart e‐tourism applications

“…In the case of using FDOSM, the variation of the ideal value of each criterion will be limited given that the discussed key concepts require evaluation based on the values of zero and one in each application. Nevertheless, the technique for order of preference by similarity to ideal solution (TOPSIS) 76 and Vlsekriterijumska Optimizcija I Kaompromisno Resenje (VIKOR) 77 are the most commonly used methods, which employ quantitative or qualitative data to identify the appropriate alternative 78 . Unlike the TOPSIS, VIKOR considers the relative importance of distances 67 .…”