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http://dx.doi.org/10.7468/jksmeb.2013.20.2.117

A GENERALIZATION OF FUZZY SUBSEMIGROUPS IN SEMIGROUPS  

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)
Publication Information
The Pure and Applied Mathematics / v.20, no.2, 2013 , pp. 117-127 More about this Journal
Abstract
As a generalization of fuzzy subsemigroups, the notion of ${\varepsilon}$-generalized fuzzy subsemigroups is introduced, and several properties are investigated. A condition for an ${\varepsilon}$-generalized fuzzy subsemigroup to be a fuzzy subsemigroup is considered. Characterizations of ${\varepsilon}$-generalized fuzzy subsemigroups are established, and we show that the intersection of two ${\varepsilon}$-generalized fuzzy subsemigroups is also an ${\varepsilon}$-generalized fuzzy subsemigroup. A condition for an ${\varepsilon}$-generalized fuzzy subsemigroup to be ${\varepsilon}$-fuzzy idempotent is discussed. Using a given ${\varepsilon}$-generalized fuzzy subsemigroup, a new ${\varepsilon}$-generalized fuzzy subsemigroup is constructed. Finally, the fuzzy extension of an ${\varepsilon}$-generalized fuzzy subsemigroup is considered.
Keywords
${\varepsilon}$-generalized fuzzy subsemigroup; ${\varepsilon}$-product; ${\varepsilon}$-Cartesian product; fuzzy ${\alpha}$-translation; (${\varepsilon}_1$, ${\varepsilon}_2$)-fuzzy extension;
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