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 (IV-IFS). IVPFS can be reduced to IVIFS satisfying the condition µ + + ν + ≤ 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 (♢, , ♠, ♣, , →, $) 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-criteria decision making (MCDM) problem based on proposed ♠ operator. Finally, the effectiveness and feasibility of proposed algorithm is demonstrated by mine emergency decision making example.
The tourism mobile e-commerce service quality evaluation (TMESQE) is of great concern to enterprises for enriching the service content of the enterprise and improving its market competitiveness. The key issue arises tremendous vagueness and reciprocity for TMESQE. The Maclaurin symmetric mean (MSM), as a vital fusion approach, can capture the reciprocity between multiple given argument more effectually. Amount of weighted MSM (WMSM) has been presented for dealing various neutrosophic information integration issues because the arguments are hourly interoperable. However, these kinds of WMSM operators are out of the reducibility or idempotency. To handle two problems above, we introduce single-valued neutrosophic linguistic reducible WMSM (SVNLRWMSM) operator and single-valued neutrosophic linguistic reducible weighted dual MSM (SVNLRWDMSM) operator. In the meantime, the diverting properties and certain peculiar cases of developed operators are discussed. Whereafter, we explore two multi-criteria decision making (MCDM) algorithms based on SVNLRWMSM and SVNLRWDMSM for dealing the TMESQE issue, along with the sensitivity analysis of various values on final ordering. Conclusively, the comparison with some existing algorithms has been conducted for showing their availability.
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