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Fuzzy normal congruences of inverse semigroups

성열욱|B.G. SON
장전수학회 (Jangjeon Mathematical Society)|2017.04|Advanced Studies in Contemporary Mathematics|제27권 제2호|pp. 181-188|DOI 10.17777/ascm2017.27.2.181

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참고문헌

키워드

inverse semigroupfuzzy kernelfuzzy tracefuzzy difunctional congruencefuzzy normal congruence
주제분류수학

초록

In this paper we introduce the notions of fuzzy kernel, fuzzy trace of a fuzzy congruence on an inverse semigroup, give some of their properties in connection with fuzzy normal congruences. As a continuation of these works, we define a fuzzy normal congruence as a fuzzy relation and characterize fuzzy normal congruences in the framework of fuzzy relations.

Abstract

In this paper we introduce the notions of fuzzy kernel, fuzzy trace of a fuzzy congruence on an inverse semigroup, give some of their properties in connection with fuzzy normal congruences. As a continuation of these works, we define a fuzzy normal congruence as a fuzzy relation and characterize fuzzy normal congruences in the framework of fuzzy relations.

참고문헌 (9)

  1. F. Al-Thukair, "Fuzzy congruence pairs of inverse semigroups", Fuzzy sets and systems, 56, pp.117~122 (1993)
  2. N. Kuroki, "Fuzzy congruences and fuzzy normal subgroups", Information sciences, 60, pp.247~259 (1992)
  3. V. Murali, "Fuzzy equivalence relations", Fuzzy Sets and Systems, 30, pp.155~163 (1989)
  4. W.C. Nemitz, "Fuzzy relations and fuzzy functions", Fuzzy sets and Systems, 19, pp.177~191 (1986)
  5. H. Ounalli, "On fuzzy difunctional relations", Information sciences, 95, pp.219~232 (1996)
  6. M. Samhan, "Fuzzy congruences on semigroups", Information sciences, 74, pp.165~175 (1993)
  7. E. Sanchez, "Resolution of composite fuzzy relation equations", Inform and control, 30, pp.38~48 (1976)
  8. C.H. Seo, "On the relationships between fuzzy equiv-alence relations and fuzzy difunctional relation, and their properties", Fuzzy Sets and Systems, 109, pp.459~462 (2000)
  9. Y.O. Sung, "Fuzzy congruences on groups", Far East J. Math, 89(2), pp.227~237 (2014)

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