Abstract
This paper focuses on multi-attribute group decision-making (MAGDM) course in which attributes are evaluated in terms of interval-valued intuitionistic fuzzy (IVIF) information. More explicitly, this paper introduces new aggregation operators for IVIF information and further proposes a new IVIF MAGDM method. The power average (PA) operator and the Muirhead mean (MM) are two powerful and effective information aggregation technologies. The most attractive advantage of the PA operator is its power to combat the adverse effects of ultra-evaluation values on the information aggregation results. The prominent characteristic of the MM operator is that it is flexible to capture the interrelationship among any numbers of arguments, making it more powerful than Bonferroni mean (BM), Heronian mean (HM), and Maclaurin symmetric mean (MSM). To absorb the virtues of both PA and MM, it is necessary to combine them to aggregate IVIF information and propose IVIF power Muirhead mean (IVIFPMM) operator and the IVIF weighted power Muirhead mean (IVIFWPMM) operator. We investigate their properties to show the strongness and flexibility. Furthermore, a novel approach to MAGDM problems with IVIF decision-making information is introduced. Finally, a numerical example is provided to show the performance of the proposed method.
Highlights
There are quite a few decision-making (DM) activities in real life
Quite a few intuitionistic fuzzy aggregation operators have been proposed based on Bonferroni mean (BM), Heronian mean (HM), and Maclaurin symmetric mean (MSM) [13,14,15], as scholars started to realize the relationship among attributes
If Sup αi, α j = t for all i 6= j, nv j = 1, the IVIF power Muirhead mean (IVIFPMM) operator reduces to the interval-valued intuitionistic fuzzy geometric (IVIFG) operator [22], that is, IV IFPMM(1,1,...,1) or (1/n,1/n,...,1/n) (α1, α2, . . . , αn ) =
Summary
There are quite a few decision-making (DM) activities in real life. For example, when buying a car, we usually have to comprehensively take into consideration the various indicators of the alternatives of potential candidates. When using MAGDM theory framework to solve practical DM problems, we always need to consider four basic elements, all possible alternatives, multiple attributes, evaluation information, and best choice determining methods, among which the latter two are the most important and complicated. Quite a few intuitionistic fuzzy aggregation operators have been proposed based on Bonferroni mean (BM), Heronian mean (HM), and Maclaurin symmetric mean (MSM) [13,14,15], as scholars started to realize the relationship among attributes. Atanassov and Gargov [21] generalized the traditional IFSs and proposed the interval-valued intuitionistic fuzzy (IVIF) sets (IVIFSs). More and more scholars started to investigate aggregation operators for IVIF information. We utilize the proposed operators to propose a new method to handle IVIF MAGDM problems.
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