Classification of ordered semigroups in terms of generalized interval-valued fuzzy interior ideals

Abstract

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 (α, β)-fuzzy interior ideal. This new concept is called interval-valued (∈, ∈ V qk)-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 (∈, ∈ V qk)-fuzzy ideals and interval-valued (∈, ∈ V qk)-fuzzy interior ideals coincide. It is also shown that the intersection of non-empty class of interval-valued (∈, ∈ V qk)-fuzzy interior ideals of an ordered semigroup is also an interval-valued (∈, ∈ V qk)-fuzzy interior ideal.