Some Interval-Valued q-Rung Dual Hesitant Fuzzy Muirhead Mean Operators With Their Application to Multi-Attribute Decision-Making

Abstract

Considering decision makers (DMs) maybe hesitant among a set of values when determining the membership and non-membership degrees in a q-rung orthopair fuzzy environment, the q-rung dual hesitant fuzzy sets (q-RDHFS) were proposed. However, in practical multi-attribute decision-making (MADM) problems, instated of crisp numbers, DMs prefer to use interval values to represent the membership and non-membership degrees. Motivated by the interval-valued dual hesitant fuzzy sets (IVDHFS), this paper proposes the concept of interval-valued q-rung dual hesitant fuzzy sets (IVq-RDHFSs). First, the definition of IVq-RDHFS, operations and comparison method of interval-valued q-rung dual hesitant fuzzy elements (IVq-RDHFEs) are presented. Second, to effectively aggregate IVq-RDHFEs, a set of new aggregation operators are proposed, namely, the interval-valued q-rung dual hesitant fuzzy Muirhead mean (IVq-RDHFMM) operator, the interval-valued q-rung dual hesitant fuzzy weighted Muirhead mean (IVq-RDHFWMM) operator, the interval-valued q-rung dual hesitant fuzzy dual Muirhead mean (IVq-RDHFDMM) operator and the interval-valued q-rung dual hesitant fuzzy dual weighted Muirhead mean (IVq-RDHFDWMM) operator. Third, a new MADM approach is proposed based on the proposed operators. We verify the new method through an illustrative example. The superiority and advantages of the proposed method are also discussed.