Cartesian product of interval-valued fuzzy ideals in ordered semigroup

Abstract

Interval-valued fuzzy set theory is a more generalized theory that can deal with real world problems more precisely than ordinary fuzzy set theory. In this paper, the concepts of interval-valued fuzzy (prime, semiprime) ideal and the Cartesian product of interval-valued fuzzy subsets have been introduced. Some interesting results about Cartesian product of interval-valued fuzzy ideals, interval-valued fuzzy prime ideals, interval- valued fuzzy semiprime ideals, interval-valued fuzzy bi-ideals and interval- valued fuzzy interior ideals in ordered semigroups are obtained. The pur- port of this paper is to link ordinary ideals with interval-valued fuzzy ideals by means of level subset of Cartesian product of interval-valued fuzzy sub- sets.