The conditional distributivity, that is distributivity equation with additional restriction imposed on the domain of aggregation operations, an issue interest for many different theoretical and practical areas, special integration theory utility theory. This paper presents new results this specific form semi-t-operators over conjunctive uninorms. Since observed class uninorms rather wide includ...

In this paper, we further investigate the constructions of fuzzy connectives on a complete lattice. We firstly illustrate the concepts of left (right) semi-uninorms and implications satisfying the order property by means of some examples. Then we give out the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation.

Uninorms are a generalization of t-norms and tconorms for which the neutral element is an element of [0,1] which is not necessarily equal to 0 (as for t-norms) or 1 (as for t-conorms). Uninorms on the unit interval are either conjunctive or disjunctive, i.e. they aggregate the pair (0,1) to either 0 or 1. In reallife applications, this kind of aggregation may be counter-intuitive. Atanassov’s i...

Uninorms are a generalization of t-norms and t-conorms for which the neutral element is an element of [0, 1] which is not necessarily equal to 0 (as for t-norms) or 1 (as for t-conorms). Uninorms on the unit interval are either conjunctive or disjunctive, i.e. they aggregate the pair (0, 1) to either 0 or 1. In real-life applications, this kind of aggregation may be counter-intuitive. Interval-...

In this paper a method to extend discrete uninorms and nullnorms on the finite chain L = {0, . . . , n}, to uninorms and nullnorms defined on the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers contained in L is presented. Some basic properties of discrete uninorms and nullnorms are preserved by this extension method and the structure of these kinds of aggreg...

U,N)-implications and RU-implications are the generalizations of (S,N)and R-implications to the framework of uninorms, where the t-norms and t-conorms are replaced by appropriate uninorms. In this work, we present the intersections that exist between (U,N)-implications and the different families of RU-implications obtainable from the well-established families of uninorms.

In this paper we introduce the semi-uninorm based ordered weighted averaging (SUOWA) operators, a new class of aggregation functions that, as WOWA operators, simultaneously generalize weighted means and OWA operators. To do this we take into account that weighted means and OWA operators are particular cases of Choquet integral. So, SUOWA operators are Choquet integral-based operators where thei...

In this paper, an approach to fuzzy mathematical morphology based on conjunctive uninorms is studied. It is proved that the most suitable conjunctive uninorms to be used in this framework are two special kinds of both, representable and idempotent uninorms. For these operators, it is proved that the most usual algebraic and morphological properties are preserved, such as, duality, monotonicity,...

. By using special group of fuzzy operators like distance based operators or uninorms a novel reasoning method appears, which is based on residual operators of uninorms. The 3-dimensional representation of the compositional rule of inference will be given.