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

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.