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 µ⁺ +v⁺ < l. 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 (◊, d, ., 4', �, -, $) and discuss their properties in relation with some existing operators (u, n, eb, ®) 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.