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

Abstract

Two important tasks in multiattribute group decision-making (MAGDM) are to describe the attribute values and to generate a ranking of all alternatives. A superior tool for the first task is linguistic interval-valued intuitionistic fuzzy number (LIVIFN), and an effective tool for the second task is aggregation operator (AO). To date, nearly ten AOs of LIVIFNs have been presented. Each AO has its own features and can work well in its specific context. But there is not yet an AO of LIVIFNs that can offer desirable generality and flexibility in aggregating attribute values and capturing attribute interrelationships and concurrently reduce the influence of unreasonable attribute values. To this end, a linguistic interval-valued intuitionistic fuzzy Archimedean power Muirhead mean operator and its weighted form, which have such capabilities, are presented in this paper. Firstly, the generalised expressions of the AOs are established by a combination of the Muirhead mean operator and the power average operator under the Archimedean T-norm and T-conorm operations of LIVIFNs. Then the properties of the AOs are explored and proved, their specific expressions are constructed, and the special cases of the specific expressions are discussed. After that, a new method for solving the MAGDM problems based on LIVIFNs is designed on the basis of the weighted AO. Finally, the designed method is illustrated via a practical example, and the presented AOs are evaluated via experiments and comparisons.

Linguistic Interval-Valued Intuitionistic Fuzzy Copula Heronian Mean Operators for Multiattribute Group Decision-Making

“…In the comparison, the WA operator in [12] and PWA operator in [13] were chosen which ignored the interaction between attributes. However, the YWMSM operator in [14] and WPMM operator in [15] considered the interaction between attributes. As can be seen from Table 9, the ranking order of the proposed method is exactly the same with Liu and Qin [14] and Qin [15].…”

“…However, the YWMSM operator in [14] and WPMM operator in [15] considered the interaction between attributes. As can be seen from Table 9, the ranking order of the proposed method is exactly the same with Liu and Qin [14] and Qin [15]. erefore, it can be concluded that the method proposed in this paper is feasible and effective for dealing with MAGDM problems based on LIVIFNs.…”

“…e reason is that the former methods assume that all attributes are independent. Furthermore, compared with the YWMSM operator in [14] and WPMM operator in [15], the proposed method is based on ECs and ECCs, which have 5 different generator functions, so it can provide DMs more options. erefore, this method is more flexible.…”

“…When the upper and lower bounds of ILVs are equal, the LIVIFS degenerates to the LIFS. Based on the LIVIFS, scholars have proposed some aggregation operators (AOs), such as a prioritised weighted averaging operator by Kumar and Garg [13], a weighted Maclaurin symmetric mean operator (LIVIFWMSM) by Liu and Qin [14], and a weighted aggregation operator (LIVI-FAWPMM) by Qin [15].…”

“…In order to address some of the aforementioned limitations, some improved linguistic intervalvalued intuitionistic fuzzy AOs are developed to solve some DMPs. For example, Xu et al proposed the interval-valued intuitionistic fuzzy (IVIF) weighted power Muirhead mean (IVIFWPMM) operator [16]; a LIVIF-based Archimedean power Muirhead mean operator by Qin [15], which can tackle DMPs more generally and flexibly; entropic combined weighted averaging operator by Xian et al [17]; LIVIFSbased Maclaurin symmetric mean (MSM) operator by Liu and Qin [14]; interval-valued intuitionistic 2-tuple linguistic setting and Bonferroni mean by Du and Yuan [18]; Pythagorean fuzzy linguistic (dual) Muirhead mean (PFLMM) operators and their weighted form by Liu [19]; Dombi Heronian mean operators by Wu et al [20]; and Hamy mean operators by Wu et al [21]. Besides, some DMP approaches have been built [22][23][24][25][26][27][28][29][30][31][32].…”