Some characterizations of ternary semigroups by the properties of their $\left( \in _{\gamma },\in _{\gamma }\vee q_{\delta }\right)$-fuzzy ideals

Abstract

This paper is the continuation of our previous work “Some kinds of $\left( \in _{\gamma },\in _{\gamma }\vee q_{\delta }\right)$-fuzzy ideals of ternary semigroups” (N. Rehman and M. Shabir, Some kinds of $\left( \in _{\gamma },\in _{\gamma }\vee q_{\delta }\right)$-fuzzy ideals of ternary semigroups, Iranian Journal of Science and Technology Trans A 37(A4) (2013)), where, we have generalized the concepts of $\left( \in ,\in \vee q\right)$-fuzzy (left, right, lateral) ideals, $\left( \in ,\in \vee q\right)$-fuzzy quasi-ideals and $\left( \in ,\in \vee q\right)$-fuzzy bi (generalized bi-) ideals in ternary semigroups, by introducing the notions of $\left( \in _{\gamma },\in _{\gamma }\vee q_{\delta }\right)$-fuzzy (left, right, lateral) ideals, $\left( \in _{\gamma },\in _{\gamma }\vee q_{\delta }\right)$-fuzzy quasi-ideals and $\left( \in _{\gamma },\in _{\gamma }\vee q_{\delta }\right)$-fuzzy bi (generalized bi-) ideals in ternary semigroups. In this paper we give several characterizations of different classes of ternary semigroups by using these notions.