The main aim of this paper is to summarize recent advances on some new classes of associative operations (uninorms, nullnorms, t-operators) used in fuzzy set theory.

A characterization of all pairs (U,S) where is U left-continuous uninorms with neutral element e from (0,1] and S countinuous t-conorms satisfying distributivity of U over S ( socalled conditional distributivity) is given.

In this paper we characterize those uninorms which are rational functions (i.e., quotients of two polynomials). These are closely related to the wellknown parametric families of t-norms and t-conorms studied and characterized by Hamacher [8].

Modus Ponens is a key property for fuzzy implication functions that are going to be used in fuzzy inference processes. In this paper it is investigated when fuzzy implication functions derived from uninorms via residuation, usually called RU implications, satisfy the modus ponens with respect to a continuous t-norm T , or equivalently, when they are T -conditionals. For RU -implications it is p...

This paper deals with the construction of RET (relevancy transformation) operators for fuzzy systems. The notion of pseudo-duality is introduced to obtain new RET operators from old ones and, t-norms, tconorms, nullnorms and uninorms are used to construct this kind of operators.

Based on the definitions and theorems for lattice ordered monoids and left continuous uninorms and t-norms, certain parameter dependent distance-based operators are focused on, with the help of which the uninorm-residuum based and sinilarity measures based approximate reasoning system becomes possible in Fuzzy Logic Control (FLC) systems. 1