Classification of Ordered Semigroups in Terms of Generalized Interval-Valued Fuzzy Interior Ideals

Several applied fields dealing with decision-making process may not be successfully modeled by ordinary fuzzy sets. In such a situation, the interval-valued fuzzy set theory is more applicable than the fuzzy set theory. Using a new approach of "quasi-coincident with relation", which is a central focused idea for several researchers, we introduced the more general form of the notion of (alpha, beta)-fuzzy interior ideal. This new concept is called interval-valued (is an element of,is an element of boolean OR q((k) over tilde)) -fuzzy interior ideal of ordered semigroup. As an attempt to investigate the relationships between ordered semigroups and fuzzy ordered semigroups, it is proved that in regular ordered semigroups, the interval-valued (is an element of,is an element of boolean OR q((k) over tilde)) -fuzzy ideals and interval-valued (is an element of,is an element of boolean OR q((k) over tilde)) -fuzzy interior ideals coincide. It is also shown that the intersection of non-empty class of interval-valued (is an element of,is an element of boolean OR q((k) over tilde)) -fuzzy interior ideals of an ordered semigroup is also an interval-valued (is an element of,is an element of boolean OR q((k) over tilde)) -fuzzy interior ideal.