Characterizations of Ordered Semigroups by New Type of Interval Valued Fuzzy Quasi-Ideals

Abstract

The concept of non-$k$-quasi-coincidence of an interval valued ordered fuzzy point with an interval valued fuzzy set is considered. In fact, this concept is a generalized concept of the non-$k$-quasi-coincidence of a fuzzy point with a fuzzy set. By using this new concept, we introduce the notion of interval valued $(\overline{\in },\overline{\in }\vee \overline{q_{\tilde{k}}})$-fuzzy quasi-ideals of ordered semigroups and study their related properties. In addition, we also introduce the concepts of prime and completely semiprime interval valued $(\overline{\in },\overline{\in }\vee \overline{q_{\tilde{k}}})$-fuzzy quasi-ideals of ordered semigroups and characterize bi-regular ordered semigroups in terms of completely semiprime interval valued $(\overline{\in },\overline{\in }\vee \overline{q_{\tilde{k}}})$-fuzzy quasi-ideals. Furthermore, some new characterizations of regular and intra-regular ordered semigroups by the properties of interval valued $(\overline{\in },\overline{\in }\vee \overline{q_{\tilde{k}}})$-fuzzy quasi-ideals are given.