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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, intervalvalued fuzzy semiprime ideals, interval-valued fuzzy bi-ideals and intervalvalued fuzzy interior ideals in ordered semigroups are obtained. The purport 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 subsets.