Several New Interval-Valued Intuitionistic Fuzzy Hamacher Hybrid Operators and Their Application to Multi-Criteria Group Decision Making

Abstract

Interval-valued intuitionistic fuzzy sets (IVIFSs) contain three ranges, namely the membership degree range, the non-membership degree range, and the hesitancy degree range, and they are very suitable for depicting uncertain or fuzzy information. In the course of decision making with IVIFSs, interval-valued intuitionistic fuzzy aggregation operators play a very important role and have received considerable attention in recent years. In this paper, we note the drawbacks of existing aggregation operators for IVIFNs. Some new interval-valued intuitionistic fuzzy Hamacher hybrid aggregation operators, such as the interval-valued intuitionistic fuzzy Hamacher hybrid arithmetical averaging operator and the interval-valued intuitionistic fuzzy Hamacher hybrid arithmetical geometric operator, are introduced to overcome the drawbacks of the existing operators. All of these newly developed operators can weigh both the interval-valued intuitionistic fuzzy arguments and their ordered positions simultaneously, and they have several desirable properties, such as idempotency, boundedness, and monotonicity. To show the applications of our proposed hybrid aggregation operators, we propose a simple procedure for multi-criteria group decision making with interval-valued intuitionistic fuzzy information and then use a numerical example to illustrate the validity and applicability of the proposed procedure and operators.