Some Remarks Regarding MTL and Divisible Residuated Algebras

Divisible residuated lattices and MTL-algebras are algebraic structures connected with algebras in t-norm based fuzzy logics, being examples of BLalgebras. They are an important significance in the study of fuzzy logic. The purpose of this paper is to investigate and give classifications of these types of algebras. From computational considerations, we analyze the structure of these residuated lattices of small size n (2 ≤ n ≤ 5) and we give summarizing statistics. To extend these results for higer size, we used computer and a constructive algorithm for generating all residuated lattices.