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.

Keywords

• Interval-valued q-rung dual hesitant fuzzy
• Muirhead mean
• interval-valued q-rung dual hesitant fuzzy Muirhead mean
• multi-attribute decision-making