Some New Kinds Of Solutions To The Iterative Boolean-like Functional Equation

In this paper, in the fuzzy logic framework we study the iterative boolean-like law I(x,I(x,y))= I(x,y) involved fuzzy implications operations, and then obtain the full characterizations of thisfunction equation based on a Dishkant operation (D-operation in short), where the D-operationis generated by a continuous t-norm T, a continuous t-conorm S and a strong negation N, also wedisscuss the solution of above functional equation based on S-, R-and QL-fuzzy operation gener-ated by a uninorm U. Together with the [39], this work gives out the complete characterizationsof this equation for the usual implications known presently.In Chapter 1. Definition and properties of t-norms, t-conorms and fuzzy implication op-erators are reviewed. Variety and construction of t-norms and t-conorms are introduced. Inparticular, the relations of continuous t-norms, continuous t-conorms and related operators aregiven. Finally, several kinds of fuzzy implication operators and their basic properties are recalled.In Chapter 2. Firstly, we introduce the concepts of uninorm , and the general constructionuninorm is given. At the same time , we review the implications generated by a uninorm as well.In Chapter 3. Firstly, we make use of all possible combinations of continuous S and Tto investigate all solution of the functional equation (1) based on a continutous D-implication.Then fully characterization of equation (1) is given about S-, R-and QL-operation generated bya uninorm .