Pseudo-addition and fuzzy ideals in BL-algebras
نویسندگان
چکیده
A pseudo-addition in BL-algebras is a binary operation that is associative and non commutative. The aim of this paper is to use the notion of pseudo-addition to study the notion of ideal and fuzzy ideal as a natural generalization of that of ideal and fuzzy ideal in MV-algebras. Using a pseudo-addition, we characterize fuzzy ideals and also obtain a concrete description of the fuzzy ideals generated by a fuzzy subset. Among other things, we establish the extension property of fuzzy prime ideal, prove the fuzzy prime ideal Theorem and show that the set of cosets of a fuzzy ideal is a linearly ordered MV-algebra. Finally, we use the operators N and D to make a link between fuzzy ideals and fuzzy filters. 2010 AMS Classification: 06D99, 08A30
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