## 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 σ_{μ}, 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 language | English (US) |
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Pages (from-to) | 117-123 |

Number of pages | 7 |

Journal | Fuzzy Sets and Systems |

Volume | 43 |

Issue number | 1 |

DOIs | |

State | Published - Sep 5 1991 |

## All Science Journal Classification (ASJC) codes

- Logic
- Artificial Intelligence