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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.20 No.2

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A GENERALIZATION OF FUZZY SUBSEMIGROUPS IN SEMIGROUPS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
Ban, Hee Young
Yun, Sang Wook
Kang,, M. K. , Ban,, H. Y. , & Yun,, S. W. (2013). A GENERALIZATION OF FUZZY SUBSEMIGROUPS IN SEMIGROUPS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 20(2), 117-127, https://doi.org/10.7468/jksmeb.2013.20.2.117

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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