On Fuzzy Ideals of BL-Algebras

الملخص EN

In this paper we investigate further properties of fuzzy ideals of a BL-algebra.

The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated.

We give a procedure to generate a fuzzy ideal by a fuzzy set.

We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal may not be a fuzzy irreducible ideal and prove that a fuzzy prime ideal ω is a fuzzy irreducible ideal if and only if ω 0 = 1 and | Im ( ω ) | = 2 .

We give the Krull-Stone representation theorem of fuzzy ideals in BL-algebras.

Furthermore, we prove that the lattice of all fuzzy ideals of a BL-algebra is a complete distributive lattice.

Finally, it is proved that every fuzzy Boolean ideal is a fuzzy Gödel ideal, but the converse implication is not true.