New operations for interval-valued Pythagorean fuzzy set

Abstract

Interval-Valued Pythagorean Fuzzy Set (IVPFS), originally proposed by Peng and Yang, is a novel tool to deal with vagueness and incertitude. As a generalized set, IVPFS has a close relationship with Interval-Valued Intuitionistic Fuzzy Set (IVIFS). IVPFS can be reduced to IVIFS, satisfying the condition +++ 1. However, the related operations of IVPFS do not take different conditions into consideration. In this paper, we initiate some new interval-valued Pythagorean fuzzy operators (}; 2; |; z; !; $) and discuss their properties in relation with some existing operators ([; \;) in detail. It will promote the development of interval-valued Pythagorean fuzzy operators. Later, an algorithm is proposed to deal with Multi-Criteria Decision-Making (MCDM) problem based on the proposed operator. Finally, the effectiveness and feasibility of the proposed algorithm is demonstrated by mine emergency decision-making example.