Abstract
Interval-valued Pythagorean fuzzy numbers (IVPFNs) can easily describe the incomplete and indeterminate information by degrees of membership and non-membership, and the Hamy mean (HM) operator and dual HM (DHM) operators are a good tool for dealing with multiple attribute decision making (MADM) problems because it can capture the interrelationship among the multi-input arguments. Motivated by the studies regarding the HM operator and dual HM operator, we expand the HM operator and dual HM (DMM) operator to process the interval-valued Pythagorean fuzzy numbers (IVPFNs) and then to solve the MADM problems. Firstly, we propose some HM and DHM operators with IVPFNs. Moreover, we present some new methods to solve MADM problems with the IVPFNs. Finally, an applicable example is given.
Highlights
Atanassov [1] gave the intuitionistic fuzzy set (IFS) based on the fuzzy set [2] such that their sum is not greater than one
The purpose of this paper is to propose some Hamy mean (HM) and dual Hamy mean (DHM) operators with interval-valued Pythagorean fuzzy numbers (IVPFNs), to study some properties of these operators, and apply them to solve multiple attribute decision making (MADM) problems with IVPFNs
From the aggregation result above, we prove the result of interval-valued Pythagorean fuzzy DHM (IVPFDHM) aggregation is an IVPFN
Summary
Atanassov [1] gave the intuitionistic fuzzy set (IFS) based on the fuzzy set [2] such that their sum is not greater than one. In order to resolve this, Pythagorean fuzzy set (PFS) [18,19], an extension of IFSs, has emerged as a good tool for describing the indeterminacy in uncertain multiple attribute decision making (MADM) For this set, the condition of the sum of the degrees that is replaced with their sum of squares is less than one; the PFS is more general than the IFS. Other scholars studied the MADM under the PFS or IVPFS [24,27,30,31,33,34,35,36,37,38,39,40,41] Both Bonferroni mean (BM) operators [42,43,44,45,46,47] and the Heronian mean (HM) [48,49,50,51,52,53] operators consider the interrelationships of aggregated arguments.
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