New Notions for Fuzzy Equivalence Using α-cut Relation

S. R. Kannan, Rajesh Kumar Mohapatra

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


This paper introduces a new notion to define equivalence to the non-reflexive fuzzy relation equation. The most important condition for the fuzzy equivalence relations is reflexive, but the condition of reflexive is unsuccessful in many cases of fuzzy relation in real life problems that creates problem to form partition tree. Therefore, this paper defines the equivalence for the cases of fuzzy relation that satisfies the symmetry, and transitive. That is, it proves the reflexive to non-reflexive fuzzy relations through alpha-cut relations. Further, this paper defines tolerance to the non-reflexive fuzzy relation equation through alpha-cut relations and it proves the entire upper left, lower right and centre sub matrices of every weakly-similarity relation matrix are weaklysimilarity relation matrices.

Original languageEnglish
Article number012040
JournalJournal of Physics: Conference Series
Issue number1
StatePublished - 31 Oct 2019
Externally publishedYes
EventInternational Conference on Recent Inventions and Innovations in Mathematical Sciences, ICRIIMS 2019 - Visakhapatnam, Andhra Pradesh, India
Duration: 28 Feb 20191 Mar 2019


  • Constant e-reflexivity
  • Fuzzy Equivalence
  • Weakly-Similarity
  • α-cut Relation

ASJC Scopus subject areas

  • General Physics and Astronomy


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