ON $(ALPHA ,BETA)$-FUZZY IDEALS OF TERNARY SEMIGROUPS
Abstract
In this paper, we introduce the concept of generalized
fuzzy ideals in ternary semigroups, which is a generalization of the fuzzy
ideals of semigroups. In this regard, we define ($\alpha ,\beta $)-fuzzy
left (right, lateral) ideals, ($\alpha ,\beta $)-fuzzy quasi-ideals and ($
\alpha ,\beta $)-fuzzy bi-ideals and invetigate some related properties of
ternary semigroups. Special concentration is paid to ($\in ,\in \vee q$
)-fuzzy left (right, lateral) ideals, ($\in ,\in \vee q$)-fuzzy quasi-ideals
and ($\in ,\in \vee q$)-fuzzy bi-ideals. Finally, we
characterize regular ternary semigroups in terms of these notions.
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