Multiple‐attribute group decision‐making method of linguisticq‐rung orthopair fuzzy power Muirhead mean operators based on entropy weight

Abstract

Linguistic q-rung orthopair fuzzy numbers (Lq-ROFNs) are a qualitative form of q-rung orthopair fuzzy numbers (q-ROFNs) where the membership and nonmembership degrees are represented by linguistic variables. The Lq-ROFNs can describe a broader range of linguistic assessment information flexibly by adjusting the parameter q based on different situations, so they are more superior to the linguistic intuitionistic fuzzy numbers and linguistic Pythagorean fuzzy numbers in real application. Based on the Lq-ROFNs, we introduce the entropy measure which can be used to determine the indefiniteness of the assessment information. Then, based on the linguistic entropy measure, we further propose a method to obtain the attribute weights when the weight information is incomplete known. For aggregating the assessment information, the power average (PA) operator can reduce the influence of extreme data caused by the biased decision-makers by considering the support degree of different evaluation individuals, and the Muirhead mean (MM) operator can take the interrelationship of different numbers of attributes into account by adjusting the parameter vector based on the real situations. In this paper, based on these two operators, we firstly propose the linguistic q-rung orthopair fuzzy PA operator and linguistic q-rung orthopair fuzzy weighted PA operator. Further, for combing the advantages of the MM operator and PA operator, we propose the linguistic q-rung orthopair fuzzy power MM (PMM) operator and linguistic q-rung orthopair fuzzy weighted PMM operator, and then investigate some properties of them. Finally, a new multiple-attribute group decision-making (MAGDM) method is proposed to process the Lq-ROFNs, and some practical examples are given to illustrate the effectiveness and superiority of this new method in comparison with other existing MAGDM methods.