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Minkowski‐type distance measures for generalized orthopair fuzzy sets
Author(s) -
Du Wen Sheng
Publication year - 2018
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.21968
Subject(s) - mathematics , fuzzy set , minkowski space , fuzzy number , fuzzy logic , fuzzy set operations , discrete mathematics , computer science , artificial intelligence , geometry
Abstract The generalized orthopair fuzzy set inherits the virtues of intuitionistic fuzzy set and Pythagorean fuzzy set in relaxing the restriction on the support for and support against. The very lax requirement provides decision makers great freedom in expressing their beliefs about membership grades, which makes generalized orthopair fuzzy sets having a wide scope of application in practice. In this paper, we present the Minkowski‐type distance measures, including Hamming, Euclidean, and Chebyshev distances, for q ‐rung orthopair fuzzy sets. First, we introduce the Minkowski‐type distances of q ‐rung orthopair membership grades, based on which we can rank orthopairs. Second, we propose several distances over q ‐rung orthopair fuzzy sets on a finite discrete universe and subsequently discuss their applications to multiattribute decision‐making problems. Then we extend these results to a continuous universe, both bounded and unbounded cases are considered. Some illustrative examples are employed to substantiate the conceptual arguments.