Operations on complex multi-fuzzy sets

Yousef Al-Qudah, Nasruddin Hassan

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

In this paper, we introduce the concept of complex multi-fuzzy sets (CMkFSs) as a generalization of the concept of multi-fuzzy sets by adding the phase term to the definition of multi-fuzzy sets. In other words, we extend the range of multi-membership function from the interval [0,1] to unit circle in the complex plane. The novelty of CMkFSs lies in the ability of complex multi-membership functions to achieve more range of values while handling uncertainty of data that is periodic in nature. The basic operations on CMkFSs, namely complement, union, intersection, product and Cartesian product are studied along with accompanying examples. Properties of these operations are derived. Finally, we introduce the intuitive definition of the distance measure between two complex multi-fuzzy sets which are used to define δ-equalities of complex multi-fuzzy sets.

Original languageEnglish
Pages (from-to)1527-1540
Number of pages14
JournalJournal of Intelligent and Fuzzy Systems
Volume33
Issue number3
DOIs
Publication statusPublished - 2017

Fingerprint

Fuzzy sets
Fuzzy Sets
Membership functions
Membership Function
Cartesian product
Distance Measure
Unit circle
Argand diagram
Range of data
Intuitive
Equality
Union
Complement
Intersection
Uncertainty
Interval
Term
Concepts

Keywords

  • Complex multi-fuzzy set
  • distance measure
  • fuzzy set
  • multi-fuzzy sets

ASJC Scopus subject areas

  • Statistics and Probability
  • Engineering(all)
  • Artificial Intelligence

Cite this

Operations on complex multi-fuzzy sets. / Al-Qudah, Yousef; Hassan, Nasruddin.

In: Journal of Intelligent and Fuzzy Systems, Vol. 33, No. 3, 2017, p. 1527-1540.

Research output: Contribution to journalArticle

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