Fuzzy congruence pairs of inverse semigroups

Al-Thukair, Fawzi

doi:10.1016/0165-0114(93)90192-k

Cited by 8 publications

(2 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In 1993, Samhan [ 3 ] studied the modularity condition in the fuzzy congruence lattice of a semigroup and derived that the fuzzy congruence lattice of a group is modular. In the same year, Al-Thukair [ 4 ] described the fuzzy congruences of an inverse semigroup and obtained a one-one correspondence between fuzzy congruence pairs and fuzzy congruences on an inverse semigroup. Moreover, Kuroki also studied the fuzzy congruences on inverse semigroups in [ 5 ] in which the notion of group congruences of a semigroup is provided.…”

Section: Introductionmentioning

confidence: 99%

The Lattices of Group Fuzzy Congruences and Normal Fuzzy Subsemigroups onE-Inversive Semigroups

Wang

2014

The Scientific World Journal

View full text Add to dashboard Cite

The aim of this paper is to investigate the lattices of group fuzzy congruences and normal fuzzy subsemigroups on E-inversive semigroups. We prove that group fuzzy congruences and normal fuzzy subsemigroups determined each other in E-inversive semigroups. Moreover, we show that the set of group t-fuzzy congruences and the set of normal subsemigroups with tip t in a given E-inversive semigroup form two mutually isomorphic modular lattices for every t∈ [0,1].

show abstract

Section: Introductionmentioning

confidence: 99%

The Lattices of Group Fuzzy Congruences and Normal Fuzzy Subsemigroups onE-Inversive Semigroups

Wang

2014

The Scientific World Journal

View full text Add to dashboard Cite

show abstract

“…In 1965, Zadeh [33] introduced the concept of fuzzy sets as the generalization of ordinary subsets. After that time,several researchers [1,23,[24][25][26][27]29,31] have applied the notion of fuzzy sets to congruence. In particular, Das [10] and Yijia [32] investigated the set of all fuzzy congruences in the view of lattice theory.…”

Section: Introductionmentioning

confidence: 99%

The lattice of intuitionistic fuzzy congruences

Hur

Jang²,

Statistic

et al. 2006

imf

View full text Add to dashboard Cite

First, we prove that the set of intuitionistic fuzzy congruences on a semigroup satisfying the particular condition is a modular lattice [Theorem 2.9]. Secondly, we prove that the set of all intuitionistic fuzzy congruences on a regular semigroup contained in (χ H , χ H c) forms a modular lattice [Proposition 3.5]. And also we show that the set of all intuitionistic fuzzy idempotent separating congruences on a regular semigroup forms a modular lattice[Theorem 3.6]. Moreover, we prove that the lattice of intuitionistic fuzzy congruences on a regular semigroup is a disjoint union of some modular sublattices of the lattice[Corollary 3.15]. Finally, we show that the lattice of intuitionistic fuzzy congruences on a group and the lattice of intuitionistic fuzzy normal subgroups satisfying the particular condition are lattice isomorphic[Theorem 4.6].

show abstract