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ON FUZZY PRIME IDEALS OF LATTICE

In this paper, We study the notion of fuzzy prime ideal and highlight the difference between fuzzy prime ideal and prime fuzzy ideal. Using the characterization of fuzzy ideal induced by a fuzzy set, we show that a fuzzy ideal μ of a lattice is a fuzzy prime ideal if and only if any nonempty α−cut set of μ is a prime ideal. We show that if a fuzzy ideal μ is proper and maximal then μ is a fuzzy prime ideal. By an example, we show that the converse is not true. At the end we give a fuzzy prime ideal theorem.