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 a close relationship with Interval-Valued Intuitionistic Fuzzy Set (IVIFS). IVPFS can be reduced to IVIFS, satisfying the condition However, the related operations of IVPFS do not take dierent conditions into 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, an algorithm is proposed to deal with Multi-Criteria Decision-Making (MCDM) problem based on the proposed  operator. Finally, the eectiveness and feasibility of the proposed algorithm is demonstrated by mine emergency decision-making example.