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Multicriteria decision‐making using Archimedean aggregation operators in Pythagorean hesitant fuzzy environment
Author(s) -
Sarkar Arun,
Biswas Animesh
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.22099
Subject(s) - pythagorean theorem , t norm , operator (biology) , algebraic number , mathematics , fuzzy logic , algebra over a field , norm (philosophy) , computer science , discrete mathematics , fuzzy number , fuzzy set , pure mathematics , artificial intelligence , law , geometry , mathematical analysis , biochemistry , chemistry , repressor , transcription factor , political science , gene
In multicriteria decision‐making (MCDM), the existing aggregation operators are mostly based on algebraic t ‐conorm and t ‐norm. But, Archimedean t ‐conorms and t ‐norms are the generalized forms of t ‐conorms and t ‐norms which include algebraic, Einstein, Hamacher, Frank, and other types of t ‐conorms and t ‐norms. From that view point, in this paper the concepts of Archimedean t ‐conorm and t ‐norm are introduced to aggregate Pythagorean hesitant fuzzy information. Some new operational laws for Pythagorean hesitant fuzzy numbers based on Archimedean t ‐conorm and t ‐norm have been proposed. Using those operational laws, Archimedean t ‐conorm and t ‐norm‐based Pythagorean hesitant fuzzy weighted averaging operator and weighted geometric operator are developed. Some of their desirable properties have also been investigated. Afterwards, these operators are applied to solve MCDM problems in Pythagorean hesitant fuzzy environment. The developed Archimedean aggregation operators are also applicable in Pythagorean fuzzy contexts also. To demonstrate the validity, practicality, and effectiveness of the proposed method, a practical problem is considered, solved, and compared with other existing method.