Complex Atanassov's intuitionistic fuzzy relation
type: Item
instance of: scholarly article
title: Complex Atanassov's intuitionistic fuzzy relation
zbMATH Open document ID: 1448.03040
DOI: 10.1155/2013/287382
author: Abd Ulazeez M. Alkouri
author: Abdul Razak Salleh
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: This paper presents distance measure between two complex Atanassov's intuitionistic fuzzy sets (CAIFSs). This distance measure is used to illustrate an application of CAIFSs in solving one of the most core application areas of fuzzy set theory, which is multiattributes decision-making (MADM) problems, in complex Atanassov's intuitionistic fuzzy realm. A new structure of relation between two CAIFSs, called complex Atanassov's intuitionistic fuzzy relation (CAIFR), is obtained. This relation is formally generalised from a conventional Atanassov's intuitionistic fuzzy relation, based on complex Atanassov's intuitionistic fuzzy sets, in which the ranges of values of CAIFR are extended to the unit circle in complex plane for both membership and nonmembership functions instead of \([0, 1]\) as in the conventional Atanassov's intuitionistic fuzzy functions. Definition and some mathematical concepts of CAIFS, which serve as a foundation for the creation of complex Atanassov's intuitionistic fuzzy relation, are recalled. We also introduce the Cartesian product of CAIFSs and derive two properties of the product space. The concept of projection and cylindric extension of CAIFRs are also introduced. An example of CAIFR in real-life situation is illustrated in this paper. Finally, we introduce the concept of composition of CAIFRs.
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 6306611
describes a project that uses: ANCFIS
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/287382
OpenAlex ID: W1997294134
Wikidata QID: Q58915830
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description: scientific article; zbMATH DE number 6306611