# New operations for interval-valued Pythagorean fuzzy set

Document Type: Article

Author

School of Information Science and Engineering, Shaoguan University, Shaoguan, China

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 close
relationship with interval-valued intuitionistic fuzzy set (IVIFS). IVPFS can be reduced to IVIFS satisfying the
condition $\mu^++\nu^+ \leq 1$. 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 ($\diamondsuit, \Box, \spadesuit, \clubsuit, \maltese, \rightarrow, \$ $) and discuss their properties in relation with some existing operators$(\cup, \cap, \oplus, \otimes)$in detail. It will promote the development of interval-valued Pythagorean fuzzy operators. Later, we propose an algorithm to deal with multi-attribute decision making (MADM) problem based on proposed$\spadesuit\$ operator. Finally, the effectiveness and feasibility of approach is
demonstrated by mine emergency decision making example.

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