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http://dx.doi.org/10.5831/HMJ.2017.39.4.527

MORE GENERALIZED FUZZY SUBSEMIGROUPS/IDEALS IN SEMIGROUPS  

Khan, Muhammad Sajjad Ali (Department of Mathematics, Hazara University)
Abdullah, Saleem (Department of Mathematics, Abdul Wali Khan University)
Jun, Young Bi (Department of Mathematics Education, Gyeongsang National University)
Rahman, Khaista (Department of Mathematics, Hazara University)
Publication Information
Honam Mathematical Journal / v.39, no.4, 2017 , pp. 527-559 More about this Journal
Abstract
The main motivation of this article is to generalized the concept of fuzzy ideals, (${\alpha},{\beta}$)-fuzzy ideals, (${\in},{\in}{\vee}q_k$)-fuzzy ideals of semigroups. By using the concept of $q^{\delta}_K$-quasi-coincident of a fuzzy point with a fuzzy set, we introduce the notions of (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy left ideal, (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy right ideal of a semigroup. Special sets, so called $Q^{\delta}_k$-set and $[{\lambda}^{\delta}_k]_t$-set, condition for the $Q^{\delta}_k$-set and $[{\lambda}^{\delta}_k]_t$-set-set to be left (resp. right) ideals are considered. We finally characterize different classes of semigroups (regular, left weakly regular, right weakly regular) in term of (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy left ideal, (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy right ideal and (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy ideal of semigroup S.
Keywords
$q^{\delta}_k$-quasi-coincident; (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy subsemigroup; (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy left ideal; (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy right ideal;
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Times Cited By KSCI : 1  (Citation Analysis)
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