On fuzzy ideals and fuzzy bi-ideals in semigroups

Kuroki, Nobutaka

doi:10.1016/0165-0114(81)90018-x

Cited by 232 publications

(135 citation statements)

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“…In order to generalize the concepts of fuzzy subsemigroup and various fuzzy ideals of S defined in [3], we introduced the followings.…”

Section: (λ µ)−Fuzzy Ideal Fuzzy Quasi-ideal and Fuzzy Bi-idealmentioning

confidence: 99%

“…Since then, many scholars have been engaged in the fuzzification of some algebraic structures. Kuruki [3,4] initiated the theory of fuzzy semigroups, and introduced the concepts of fuzzy ideal and fuzzy bi-ideal. A systemtic exposition of fuzzy semigroup by Mordeson et al appeared in [5] , where one can find the theoretical results of fuzzy semigroup and their use in fuzzy coding, fuzzy finite state machines and fuzzy languages.…”

Section: Introductionmentioning

confidence: 99%

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Characterizations of Regular Semigroups

Bing-xue¹

2014

Appl. Math. Inf. Sci.

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“…In order to generalize the concepts of fuzzy subsemigroup and various fuzzy ideals of S defined in [3], we introduced the followings.…”

Section: (λ µ)−Fuzzy Ideal Fuzzy Quasi-ideal and Fuzzy Bi-idealmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Characterizations of Regular Semigroups

Bing-xue¹

2014

Appl. Math. Inf. Sci.

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“…Since then the literature of various fuzzy algebraic concepts has been growing very rapidly. In the literature, the relationships between the fuzzy sets and semigroups have been considered by many authors (see [1,2,3,4,5,6,7,8,9,10,11,13,15]). …”

Section: Introductionmentioning

confidence: 99%

“…Based on this pioneering work, Kuroki [6,7,8,9, 10] introduced fuzzy semigroups and various kinds of fuzzy ideals in semigroups and characterized certain semigroups using those fuzzy ideals. Since then the literature of various fuzzy algebraic concepts has been growing very rapidly.…”

Section: Introductionmentioning

confidence: 99%

A Generalization of Fuzzy Subsemigroups in Semigroups

Kang¹,

Ban²,

Yun³

2013

The Pure and Applied Mathematics

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Abstract. As a generalization of fuzzy subsemigroups, the notion of ε-generalized fuzzy subsemigroups is introduced, and several properties are investigated. A condition for an ε-generalized fuzzy subsemigroup to be a fuzzy subsemigroup is considered. Characterizations of ε-generalized fuzzy subsemigroups are established, and we show that the intersection of two ε-generalized fuzzy subsemigroups is also an ε-generalized fuzzy subsemigroup. A condition for an ε-generalized fuzzy subsemigroup to be ε-fuzzy idempotent is discussed. Using a given ε-generalized fuzzy subsemigroup, a new ε-generalized fuzzy subsemigroup is constructed. Finally, the fuzzy extension of an ε-generalized fuzzy subsemigroup is considered.

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“…Kuroki [10,11,12] presented the notion of fuzzy ideals and fuzzy bi-ideals in semigroups. He characterized several classes of semigroups in the terms of fuzzy ideals.…”

Section: Introductionmentioning

confidence: 99%