Similarity L-logics

The main goal of this paper is to present similarity l - algebra and consider the properties of this new algebras. A similarity L - algebra is an L - algebra endowed with a binary operation S that verifies certain additional properties. Also, we study their properties and obtain that the class of all similarity triangle algebras form a variety. Next , we give some properties of the similarity L – algebras. For any L – algebra X , we define X – fuzzy subset and consider the relationship between similarity L – algebras and X – fuzzy subsets.In addition, we introduce and investigate similarity ideals in similarity L - algebras. We consider the properties of similarity ideals by some propositions , theorem and examples . The notion of representable similarity L – algebras and prove (X, S) is representable if and only if any minimal prime ideal is an S-ideal of X. Moreover, we present similarity L -logic (SL), a system of many valued logic. For introduce the notion of similarity L- logics, firstly give some introduction, the formulas, the axioms and the inference rules. The notion of the logic of the similarity L - algebras were introduced to prove their soundness and completeness.