Premium
On generalized similarity measures for Pythagorean fuzzy sets and their applications to multiple attribute decision‐making
Author(s) -
Verma Rajkumar,
Merigó José M.
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.22160
Subject(s) - pythagorean theorem , cosine similarity , similarity (geometry) , pythagorean trigonometric identity , mathematics , similarity measure , trigonometry , measure (data warehouse) , fuzzy logic , trigonometric functions , artificial intelligence , computer science , data mining , pattern recognition (psychology) , geometry , image (mathematics) , linear interpolation , bicubic interpolation
In this paper, we develop a new and flexible method for Pythagorean fuzzy decision‐making using some trigonometric similarity measures. We first introduce two new generalized similarity measures between Pythagorean fuzzy sets based on cosine and cotangent functions and prove their validity. These similarity measures include some well‐known Pythagorean fuzzy similarity measures as their particular and limiting cases. The measures are demonstrated to satisfy some very elegant properties which prepare the ground for applications in different areas. Further, the work defines a generalized hybrid trigonometric Pythagorean fuzzy similarity measure and discuss its properties with particular cases. Then, based on the generalized hybrid trigonometric Pythagorean fuzzy similarity measure, a method for dealing with multiple attribute decision‐making problems under Pythagorean fuzzy environment is developed. Finally, a numerical example is given to demonstrate the flexibility and effectiveness of the developed approach in solving real‐life problems.