Fuzzy relations on rings and groups

D. S. Malik, John N. Mordeson

Research output: Contribution to journalArticle

10 Scopus citations

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

All Science Journal Classification (ASJC) codes

  • Logic
  • Artificial Intelligence

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