New Operations for Interval-valued Pythagorean Fuzzy Set

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 closerelationship with interval-valued intuitionistic fuzzy set (IVIFS). IVPFS can be reduced to IVIFS satisfying thecondition μ⁺+ν⁺ ≤ 1. However, the related operations of IVPFS do not take different conditionsinto consideration. In this paper, we initiate some new interval-valued Pythagorean fuzzy operators (, , , , , →, \ $) and discuss their properties in relation with some existing operators $(∪, ∩, ⊕, ⊗)$ 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 operator. Finally, the effectiveness and feasibility of approach isdemonstrated by mine emergency decision making example.