Complex atanassov's intuitionistic fuzzy relation

Abd Ulazeez M Alkouri, Abdul Razak Salleh

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number287382
JournalAbstract and Applied Analysis
Volume2013
DOIs
Publication statusPublished - 2013

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Fuzzy Relation
Fuzzy sets
Intuitionistic Fuzzy Set
Fuzzy set theory
Distance Measure
Decision making
Multi-attribute Decision Making
Fuzzy Function
Product Space
Cartesian product
Fuzzy Set Theory
Unit circle
Argand diagram
Chemical analysis
Projection

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Complex atanassov's intuitionistic fuzzy relation. / Alkouri, Abd Ulazeez M; Salleh, Abdul Razak.

In: Abstract and Applied Analysis, Vol. 2013, 287382, 2013.

Research output: Contribution to journalArticle

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