The Study Of Fuzzy Aggregation Operators

Selecting a proper t-norm plays an important role in fuzzy sets theory, up to now without a set of methods to deal with the problem. We propose a neural network fitting a t-norm to the empirical data, and give its algorithms. If high accuracy needs, this network may involve more parameters. This paper gives another method to adjust a t-norm approximately by less parameter. These methods are beneficial to find out a suitable t-norm in fuzzy logic theory and fuzzy neural networks.We investigate the properties and representation of uninorms. The concept of uninorm was introduced by Yager to unify and generalize the t-norms and t-conorms. We prove that uninorms continuous on [0,1]2 must be t-norms or t-conorms, and each of uninorm continuous in (0,1)2 can be represented by an one-variable continuous strictly increasing function and a t-norm or t-conorm.Last, we study the structures of S implication and R implication based on uninorms, give out their axiomatic definitions, and obtain a necessary and sufficient condition of an implication which being S implication and R implication simultaneously.