Generalized Fuzzy Relations

John N. Mordeson, Sunil Mathew, Davender S. Malik

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Fuzzy relations are fundamental in applications of fuzzy set theory and fuzzy logic. The entire literature on fuzzy relations as applied to fuzzy graph theory are based on Rosenfeld's relations. Rosenfeld used minimum and maximum as the norm and conorm in his study of compositions of fuzzy relations. In this paper, we generalize fuzzy relations using arbitrary t-norms and t-conorms. Many of the results do not hold when minimum and maximum are replaced by an arbitrary norm and an arbitrary conorm. Reflexive, symmetric and transitive generalized fuzzy relations are also discussed and an application to human trafficking and illegal immigration is presented.

Original languageEnglish (US)
Pages (from-to)187-202
Number of pages16
JournalNew Mathematics and Natural Computation
Volume14
Issue number2
DOIs
StatePublished - Jul 1 2018

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Fuzzy Relation
Fuzzy set theory
Graph theory
Fuzzy logic
Arbitrary
Fuzzy Graph
T-conorms
Norm
Chemical analysis
Immigration
T-norm
Fuzzy Set Theory
Fuzzy Logic
Entire
Generalise

All Science Journal Classification (ASJC) codes

  • Human-Computer Interaction
  • Computer Science Applications
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

Generalized Fuzzy Relations. / Mordeson, John N.; Mathew, Sunil; Malik, Davender S.

In: New Mathematics and Natural Computation, Vol. 14, No. 2, 01.07.2018, p. 187-202.

Research output: Contribution to journalArticle

Mordeson, John N. ; Mathew, Sunil ; Malik, Davender S. / Generalized Fuzzy Relations. In: New Mathematics and Natural Computation. 2018 ; Vol. 14, No. 2. pp. 187-202.
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