Abstract
Pythagorean hesitant fuzzy sets are widely watched because of their excellent ability to deal with uncertainty, imprecise and vague information. This paper extends Pythagorean hesitant fuzzy environments to interval-valued Pythagorean hesitant fuzzy environments and proposes the concept of interval-valued Pythagorean hesitant fuzzy set (IVPHFS), which allows the membership of each object to be a set of several pairs of possible interval-valued Pythagorean fuzzy elements. Furthermore, we develop a series of aggregation operators for interval-valued Pythagorean hesitant fuzzy information and apply them to multiattribute group decision-making (MAGDM) problems. Then, some desired operational laws and properties of IVPHFSs are studied. Especially, considering an interval-valued Pythagorean fuzzy element (IVPHFE) is formed by several pairs of interval values, this paper proposes the concepts of score function and accuracy function in the form of two interval numbers which can retain interval-valued Pythagorean fuzzy information as much as possible. Then, the relationship among these operators is discussed by comparing the interval numbers. Eventually, an illustrative example fully shows the feasibility, practicality, and effectiveness of the proposed approach.
Highlights
Complexity [35, 36], Zhang and Xu [37], Ren et al [38], Liu et al [39], and Teng et al [39] have studied several kinds of Pythagorean fuzzy aggregation operators and applied them to decision-making problems
For real multiattribute group decision-making (MAGDM) problems, it is difficult for decision makers to provide some exact and crisp fuzzy values to depict uncertain or insufficient alternatives because of the increasing complexity of social and economic life. e aim of this paper is to extend PHFSs to interval-valued Pythagorean hesitant fuzzy sets (IVPHFSs) and develop MAGDM approaches to intervalvalued Pythagorean hesitant fuzzy environments based on newly constructed aggregation operators
Considering an interval-valued Pythagorean fuzzy element (IVPHFE) is regarded as the extension of an IVHFE, interval-valued Pythagorean fuzzy element (IVPFE), or PHFE, we propose a series of aggregation operators for intervalvalued Pythagorean hesitant fuzzy information based on the discussion of aggregation operators in [27, 45, 50, 51] and deduce some desirable properties
Summary
Complexity [35, 36], Zhang and Xu [37], Ren et al [38], Liu et al [39], and Teng et al [39] have studied several kinds of Pythagorean fuzzy aggregation operators and applied them to decision-making problems. An interval-valued Pythagorean hesitant fuzzy set (IVPHFS) P on U is described as 4. Aggregation Operators for Interval-Valued Pythagorean Hesitant Fuzzy Information
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