Fuzzy relations on rings and groups

Davender S. Malik, John N. Mordeson

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Let S be any nonempty set. A fuzzy relation on S is a fuzzy subset of S × S. In this paper we study fuzzy relations on rings and groups. In particular we show that if μ and σ are fuzzy left (right) ideals of a ring R, then μ × σ is a fuzzy left (right) ideal of R × R and conversely if μ × σ is a fuzzy left (right) ideal of R × R, then either μ or σ is a fuzzy left (right) ideal of R. An example is given to show that if μ × σ is a fuzzy left (right) ideal of R × R, then μ and σ both need not be fuzzy left (right) ideals of R. An example is also given to show that if μ is a fuzzy left (right) ideal of R × R, then σμ, the weakest fuzzy subset of R on which μ is a fuzzy relation, need not be a fuzzy left (right) ideal of R. We obtain similar results for groups. We also show that certain results of Bhattacharya and Mukherjee (1985) are not true.

Original languageEnglish
Pages (from-to)117-123
Number of pages7
JournalFuzzy Sets and Systems
Volume43
Issue number1
DOIs
StatePublished - Sep 5 1991

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Fuzzy Relation
Ring
Fuzzy Subset

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Computer Science Applications
  • Computer Vision and Pattern Recognition
  • Information Systems and Management
  • Statistics, Probability and Uncertainty
  • Electrical and Electronic Engineering
  • Statistics and Probability

Cite this

Fuzzy relations on rings and groups. / Malik, Davender S.; Mordeson, John N.

In: Fuzzy Sets and Systems, Vol. 43, No. 1, 05.09.1991, p. 117-123.

Research output: Contribution to journalArticle

Malik, Davender S. ; Mordeson, John N. / Fuzzy relations on rings and groups. In: Fuzzy Sets and Systems. 1991 ; Vol. 43, No. 1. pp. 117-123.
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