Archimedean Muirhead Aggregation Operators of q‐Rung Orthopair Fuzzy Numbers for Multicriteria Group Decision Making

Abstract

q-Rung orthopair fuzzy number (qROFN) is a flexible and superior fuzzy information description tool which can provide stronger expressiveness than intuitionistic fuzzy number and Pythagorean fuzzy number. Muirhead mean (MM) operator and its dual form geometric MM (GMM) operator are two all-in-one aggregation operators for capturing the interrelationships of the aggregated arguments because they are applicable in the cases in which all arguments are independent of each other, there are interrelationships between any two arguments, and there are interrelationships among any three or more arguments. Archimedean T-norm and T-conorm (ATT) are superior operations that can generate general and versatile operational rules to aggregate arguments. To take advantage of qROFN, MM operator, GMM operator, and ATT in multicriteria group decision making (MCGDM), an Archimedean MM operator, a weighted Archimedean MM operator, an Archimedean GMM operator, and a weighted Archimedean GMM operator for aggregating qROFNs are presented to solve the MCGDM problems based on qROFNs in this paper. The properties of these operators are explored and their specific cases are discussed. On the basis of the presented operators, a method for solving the MCGDM problems based on qROFNs is proposed. The effectiveness of the proposed method is demonstrated via a numerical example, a set of experiments, and qualitative and quantitative comparisons. The demonstration results suggest that the proposed method has satisfying generality and flexibility at aggregating q-rung orthopair fuzzy information and capturing the interrelationships of criteria and the attitudes of decision makers and is feasible and effective for solving the MCGDM problems based on qROFNs.

Digital Twin Driven Green Performance Evaluation Methodology of Intelligent Manufacturing: Hybrid Model Based on Fuzzy Rough-Sets AHP, Multistage Weight Synthesis, and PROMETHEE II

“…Multicriteria decision-making (MCDM) [23,24] by using the experience and wisdom of experts is a feasible method to comprehensively consider the multidimensional influencing factors and their coupling relationship that affect the green performance evaluation. In the existing similar evaluation problem and its solution, the value or importance of a factor is usually evaluated by one expert in numerical number form, which is unreasonable due to the preferences 2 Complexity of individual expert and the fuzziness of expert judgment [25,26].…”

q ‐Rung orthopair fuzzy decision‐making framework for integrating mobile edge caching scheme preferences

“…The existing methods used to solve MCDM problems have counterintuitive situations (caused by parameter selection 43 and caused by score function 42 and caused by AOs [12][13][14][15][16][17]19,[21][22][23][24][25][26][27]29,30 ), antilogarithm by negative and zero issue 33 and DBZ issue. 28 The DM's selection of the best option may not be worthwhile, or it may be impractical. The TAOV method, originally proposed by Hajiagha et al, 1 is an adaptive algorithm that processes information in a logical and feasible way.…”

“…For better comparison, we set parameter q = 3 in all existing methods. In addition, the settings for the other parameters are given as follows: p k t λ = 1, = 1, = 3, = 0.5 k in Reference [33]; h s = = 2 in Reference [27]; λ = 0.5 in Reference [40]; ϕ φ = = 1 in Reference [26]; λ δ = 1, = (1, 0, 0, 0, 0, 0, 0) in Reference [28]; ℘ = 1 in Reference [17]; x = 1 in Reference [29]; k = 2 in Reference [22];…”

Linguistic Interval-Valued Intuitionistic Fuzzy Archimedean Power Muirhead Mean Operators for Multiattribute Group Decision-Making

“…(2) To make the AO have the capability to capture the interrelationships among attributes, the Muirhead mean (MM) operator [63], which is suitable for the situations where all aggregated arguments are independent of each other, where there are interrelationships between any two arguments, and 2 Complexity where there are interrelationships among any multiple arguments [64,65], is selected as the core component of the AO (3) To make the AO capable to reduce the negative influence of biased attribute values on the aggregation result, the power average (PA) operator [66], which has the capability to reduce the negative effect of unreasonable argument values, is combined with the MM operator Based on the analysis above, this paper aims to present a linguistic interval-valued intuitionistic fuzzy weighted Archimedean power MM operator for MAGDM. is aim is achieved via combining the ATNTC operations, the MM operator, and the PA operator with weights in the context of LIVIFSs.…”