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Research on arithmetic operations over generalized orthopair fuzzy sets
Author(s) -
Du Wen Sheng
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.22073
Subject(s) - multiplication (music) , arithmetic , infimum and supremum , division (mathematics) , mathematics , subtraction , fuzzy logic , arbitrary precision arithmetic , pointwise , algebra over a field , computer science , discrete mathematics , pure mathematics , artificial intelligence , mathematical analysis , combinatorics
The four fundamental operations of arithmetic for real (and complex) numbers are well known to everybody and quite often used in our daily life. And they have been extended to classical and generalized fuzzy environments with the demand of practical applications. In this paper, we present the arithmetic operations, including addition, subtraction, multiplication, and division operations, over q ‐rung orthopair membership grades, where subtraction and division operations are both defined in two different ways. One is by solving the equation involving addition or multiplication operations, whereas the other is by determining the infimum or supremum of solutions of the corresponding inequality. Not all of q ‐rung orthopairs can be performed by the former method but by the latter method, and it is proved that the former is a special case of the latter. Moreover, the elementary properties of arithmetic operations as well as mixed operations are extensively investigated. Finally, these arithmetic operations are pointwise defined on q ‐rung orthopair fuzzy sets in which the membership degree of each element is a q ‐rung orthopair.