Fuzziness in L-algebras

Abstract

The aim of this paper is to introduce fuzzy ideals and fuzzy (weak) congruence relations of L-algebras. We give a sufficient and necessary condition for a fuzzy set to be a fuzzy ideal of an L-algebra. After obtaining a necessary condition for a fuzzy set to be a fuzzy ideal of L-algebras, we construct an example to show that the condition is not sufficient. For CKL-algebras, however, we prove that it is both necessary and sufficient. Then we give a process to generate a fuzzy ideal by a fuzzy set of CKL-algebras. Finally, we establish a correspondence between fuzzy ideals and fuzzy weak congruence relations of L-algebras, and get homomorphism theorems induced by fuzzy congruence relations.