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Pythagorean Membership Grades, Complex Numbers, and Decision Making
Author(s) -
Yager Ronald R.,
Abbasov Ali M.
Publication year - 2013
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.21584
Subject(s) - pythagorean theorem , pythagorean triple , mathematics , pythagorean trigonometric identity , negation , set (abstract data type) , algebra over a field , discrete mathematics , combinatorics , computer science , artificial intelligence , pure mathematics , pattern recognition (psychology) , linear interpolation , bicubic interpolation , programming language , geometry
We describe the idea of Pythagorean membership grades and the related idea of Pythagorean fuzzy subsets. We focus on the negation and its relationship to the Pythagorean theorem. We look at the basic set operations for the case of Pythagorean fuzzy subsets. A relationship is shown between Pythagorean membership grades and complex numbers. We specifically show that Pythagorean membership grades are a subclass of complex numbers called Π‐i numbers. We investigate operations that are closed under Π‐i numbers. We consider the problem of multicriteria decision making with satisfactions expressed as Pythagorean membership grades, Π‐i numbers. We look at the use of the geometric mean and ordered weighted geometric operator for aggregating criteria satisfaction.