On fuzzy semigroups

Kuroki, Nobutaka

doi:10.1016/0020-0255(91)90037-u

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2013

2023

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Cited by 138 publications

(66 citation statements)

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“…The notion of fuzzy subgroup was introduced by A. Rosenfeld et.al [5], [10] in his pioneering paper. Many authors [2], [3], [6], [7], [8] applied the concept of fuzzy sets for studies in fuzzy semigroups, fuzzy groups, fuzzy rings, fuzzy ideals, fuzzy semirings and fuzzy near-rings and so on. In fact many basic properties in group theory are found to be carried over to fuzzy groups.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy subgroups on direct product of groups over a $t$-norm

Rasuli¹

2017

Journal of Fuzzy Set Valued Analysis

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Section: Introductionmentioning

confidence: 99%

Fuzzy subgroups on direct product of groups over a $t$-norm

Rasuli¹

2017

Journal of Fuzzy Set Valued Analysis

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“…The ideal of fuzzy subsemigroup was also introduced by Kuroki [7], [9]. In [8], Kuroki characterized several classes of semigroups in terms of fuzzy left, fuzzy right and fuzzy bi-ideals. Xie [12] introduced the idea of extensions of fuzzy ideals in semigroups.…”

Section: Introductionmentioning

confidence: 99%

On $Q$-Fuzzy Ideals in Ordered Semigroups

Lekkoksung¹

2014

Int. J. of Pure and Appl. Math.

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In this paper we shows that in ordered groupoids the Q-fuzzy right (resp. Q-fuzzy left) ideals are Q-fuzzy quasi-ideals, in ordered semigroups the Q-fuzzy quasi-ideals are Q-fuzzy bi-ideals, and in regular ordered semigroups the Q-fuzzy quasi-ideals and the Q-fuzzy bi-ideals coincide and show that if S is an ordered semigroup, then a Q-fuzzy subset f is a Q-fuzzy quasi-ideal of S if and only if there exist a Q-fuzzy right ideal g and a Q-fuzzy left ideal h of S such that f = g ∩ h.

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“…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%