Abstract
The Hamy mean (HM) operator, as a useful aggregation tool, can capture the correlation between multiple integration parameters, and the 2-tuple linguistic Pythagorean fuzzy numbers (2TLPFNs) are a special kind of Pythagorean fuzzy numbers (PFNs), which can easily describe the fuzziness in actual decision making by 2-tuple linguistic terms (2TLTs). In this paper, to consider both Hamy mean (HM) operator and 2TLPFNs, we combine the HM operator, weighted HM (WHM) operator, dual HM (DHM) operator, and dual WHM (DWHM) operator with 2TLPFNs to propose the 2-tuple linguistic Pythagorean fuzzy HM (2TLPFHM) operator, 2-tuple linguistic Pythagorean fuzzy WHM (2TLPFWHM) operator, 2-tuple linguistic Pythagorean fuzzy DHM (2TLPFDHM) operator and 2-tuple linguistic Pythagorean fuzzy DWHM (2TLPFDWHM) operator. Then some multiple attribute decision making (MADM) procedures are developed based on these operators. At last, an applicable example for green supplier selection is given.
Highlights
Pythagorean fuzzy set (PFS) [1,2] is the generalization of the intuitionistic fuzzy set (IFS), in which the membership degree (MD) and the non-membership degree (NMD) satisfy the condition that their square sum is equal or less than 1
Some multiple attribute decision making (MADM) procedures are developed based on these operators
In order to overcome this issue, we develop the definition of 2-tuple linguistic Pythagorean fuzzy sets (2TLPFSs) based on the PFS [1,2] and 2-tuple linguistic terms (2TLTs) [68,69,70,71]
Summary
Pythagorean fuzzy set (PFS) [1,2] is the generalization of the intuitionistic fuzzy set (IFS), in which the membership degree (MD) and the non-membership degree (NMD) satisfy the condition that their square sum is equal or less than 1. PFSs theory has been broadly applied to many domains, all the above approaches are unsuitable to depict the MD and NMD of an element to a set by 2TLSs. In order to overcome this issue, we develop the definition of 2-tuple linguistic Pythagorean fuzzy sets (2TLPFSs) based on the PFS [1,2] and 2-tuple linguistic terms (2TLTs) [68,69,70,71]. Because 2-tuple linguistic Pythagorean fuzzy numbers (2TLPFNs) can describe the fuzzy information, and the HM and DHM operators can capture interrelationships among any number of arguments assigned by a variable vector, it is necessary to extend the HM and DHM operators to deal with the 2TLPFNs. The aim of this paper is to combine the HM operator, weighted HM (WHM) operator, dual.
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