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.

中文翻译：

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基于新的模糊加权零不一致方法确定多目标优化竞争算法评估标准的重要性

随着过去几十年大量 MaOO 算法的发展，MaOO 算法的性能相互比较也是非常必要的。许多研究试图操纵这种比较来分析 MaOO 的性能质量。在这种情况下，重要性权重对于评估 MaOO 算法的性能至关重要。所有 MaOO 算法的评估研究都忽略了在评估过程中为目标标准分配这样的权重，这对最终的决策结果起着关键作用。因此，必须确定每个标准的权重值，以保证评估过程中结果的准确性。多准则决策（MCDM）方法在解决 MaOO 算法评估过程中的权重问题时非常受欢迎。MCDM 中的几项研究提出了竞争性加权方法。然而，这些方法存在由成对比较的高度主观性引起的不一致问题。当标准数量增加时，不一致率会以过高的方式增加，并影响最终结果。本研究的主要目的是提出一种新方法，称为新型模糊加权零不一致性 (FWZIC) 方法，该方法可以确定具有零一致性的标准的权重系数。该方法依赖于专家对每个标准的偏好差异来计算其在决策过程中的显着性水平。所提出的 FWZIC 方法包括确定评估标准权重的五个阶段：（1）探索和定义评估标准集，（2）使用结构化专家判断（SEJ），（3）专家决策矩阵（EDM）建立在标准和SEJ交叉的基础上，（4）模糊隶属函数应用于结果EDM 和 (5) 计算评估标准的权重系数的最终值。将该方法应用于MaOO竞争算法的评价标准。案例研究包括分布在主要标准、子标准和指标中的 50 多个项目。确定每个项目对算法评估的重要贡献。结果表明，标准、子标准及其相关指标的权重没有不一致。研究结果清楚地表明，FWZIC 方法可以处理不一致问题并为每个标准提供准确的权重值。