M.Sc. Tezi Görüntüleme

      In this thesis, we consider a relationship between fuzzy sets and hyperlattices. We first introduce the concept of “belongingness” (∈) and “k-quasi-coincidence” (q_k) of a fuzzy point within a fuzzy set. This concept is a generalized concept of quasi-coincidence of a fuzzy point within a fuzzy set. By using this new idea, we consider algebraic structure (∈,∈∨q_k)-fuzzy sub-hyperlattice (hyperideal) of a hyperlattice, and hence, a generalization of a fuzzy sub-hyperlattice (hyperideal) is given. Some related properties of fuzzy sub-hyperlattices (hyperideals) are described.

      The second section of this thesis consist of two part. In the first part, using the notions belongingness (∈) and k-quasi-coincidence (q_k) of fuzzy points within fuzzy sets, the concept of an (∈,∈∨q_k)-fuzzy sub-hyperlattice (hyperideal) generalization of the concept a fuzzy sub-hyperlattice (hyperideal) is given. In the second part, we consider the concept of implication-based fuzzy sub-hyperlattice (hyperideal) of hyperlattices and research the implication operators in Lukasiewicz system of continuous-valued logic.