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 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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