A GENERALIZATION OF FUZZY SUBSEMIGROUPS IN SEMIGROUPS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2013, v.20 no.2, pp.117-127

https://doi.org/10.7468/jksmeb.2013.20.2.117

Kang, Mee Kwang (Department of Mathematics, Dongeui University)
Ban, Hee Young (Department of Mathematics Education, Gyeongsang National University)
Yun, Sang Wook (Department of Mathematics Education, Gyeongsang National University)

Kang, Mee Kwang, Ban, Hee Young, & Yun, Sang Wook. (2013). A GENERALIZATION OF FUZZY SUBSEMIGROUPS IN SEMIGROUPS. 한국수학교육학회지시리즈B:순수및응용수학, 20(2), 117-127, https://doi.org/10.7468/jksmeb.2013.20.2.117

복사

Abstract

As a generalization of fuzzy subsemigroups, the notion of <TEX>${\varepsilon}$</TEX>-generalized fuzzy subsemigroups is introduced, and several properties are investigated. A condition for an <TEX>${\varepsilon}$</TEX>-generalized fuzzy subsemigroup to be a fuzzy subsemigroup is considered. Characterizations of <TEX>${\varepsilon}$</TEX>-generalized fuzzy subsemigroups are established, and we show that the intersection of two <TEX>${\varepsilon}$</TEX>-generalized fuzzy subsemigroups is also an <TEX>${\varepsilon}$</TEX>-generalized fuzzy subsemigroup. A condition for an <TEX>${\varepsilon}$</TEX>-generalized fuzzy subsemigroup to be <TEX>${\varepsilon}$</TEX>-fuzzy idempotent is discussed. Using a given <TEX>${\varepsilon}$</TEX>-generalized fuzzy subsemigroup, a new <TEX>${\varepsilon}$</TEX>-generalized fuzzy subsemigroup is constructed. Finally, the fuzzy extension of an <TEX>${\varepsilon}$</TEX>-generalized fuzzy subsemigroup is considered.

keywords: <tex> ${\varepsilon}$</tex>-generalized fuzzy subsemigroup, <tex> ${\varepsilon}$</tex>-product, <tex> ${\varepsilon}$</tex>-Cartesian product, fuzzy <tex> ${\alpha}$</tex>-translation, (<tex> ${\varepsilon}_1$</tex>, <tex> ${\varepsilon}_2$</tex>)-fuzzy extension

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Vol.20 No.2

A GENERALIZATION OF FUZZY SUBSEMIGROUPS IN SEMIGROUPS

A GENERALIZATION OF FUZZY SUBSEMIGROUPS IN SEMIGROUPS

Abstract

참고문헌

한국수학교육학회지시리즈B:순수및응용수학