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Pythagorean fuzzy Bonferroni means based on T‐norm and its dual T‐conorm
Author(s) -
Yang Yi,
Chin KwaiSang,
Ding Heng,
Lv HongXia,
Li YanLai
Publication year - 2019
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.22097
Subject(s) - pythagorean theorem , operator (biology) , mathematics , bonferroni correction , fuzzy logic , norm (philosophy) , dual (grammatical number) , fuzzy set , algebra over a field , computer science , mathematical optimization , artificial intelligence , discrete mathematics , pure mathematics , statistics , law , biochemistry , chemistry , geometry , literature , repressor , transcription factor , political science , gene , art
For multiple‐attribute decision making problems in Pythagorean fuzzy environment, few existing aggregation operators consider interrelationships among the attributes. To deal with this issue, this article extends the Bonferroni means to Pythagorean fuzzy sets (PFSs) to provide Pythagorean Fuzzy Bonferroni means. We first extend t‐norm and its dual t‐conorm to propose the generalized operational laws for PFSs, which can be considered as the extensions of the known ones. Based on these new laws, Pythagorean fuzzy weighted Bonferroni mean operator and Pythagorean fuzzy weighted geometric Bonferroni mean operator are developed, both of them can capture the correlations among Pythagorean fuzzy input arguments and their desired properties and special cases are also investigated in detail. At last, a novel approach is proposed based on the developed operators with its effectiveness being proved by an investment selection problem.