Uninorms as binary operations on the unit interval have been widely applied in the fuzzy set theory. This paper presents some 7 properties of uninorm-like operations for which the underlying operations are given by ordinal sums. If the underlying operations of a uninorm are given by ordinal sums, then the Cartesian product of the union of two arbitrary intervals (one in [0, e] and the other in ...

In this paper, a set of axioms is given that characterizes those functions I : [0, 1] → [0, 1] for which a left-continuous uninorm U exists in such a way that I is the residual implication derived from U . A characterization for the particular case when U is representable is also given. Keywords— Implication function, left-continuity, residual implication, uninorm.

A new fuzzy edge detector based on uninorms is proposed and deeply studied. The behaviour of different classes of uninorms is discussed. The obtained results suggest that the best uninorm in order to improve the edge detection process is the uninorm Umin, with underlying Lukasiewicz operators. This algorithm gets statistically substantial better results than the others obtained by well known ed...

The paper deals with binary operations in the unit interval. We investigate connections between families of triangular norms, triangular conorms, uninorms and some decreasing functions. It is well known, that every uninorm is build by using some triangular norm and some triangular conorm. If we assume, that uninorm fulfils additional assumptions, then this triangular norm and this triangular co...

The paper introduces novel residuum-based reasoning systems in a pseudo— analysis based uninorm environment. Based on the definitions and theorems for lattice ordered monoids and left continuous uninorms and t-norms, certain distance-based operators are focused on, with the help of which the uninorm-residuum based approximate reasoning system becomes possible in Fuzzy Logic Control (FLC) system...

This is an investigation of weakening-free fuzzy logics expanded by the delta connective D; which can be interpreted by Baaz’s projection and its generalizations. First, logical systems obtained from weakeningfree uninorm (based) logics by adding D to be interpreted by the Baaz projection are introduced. Next, expansions of the weakening-free uninorm logics with D to be interpreted by its gener...

A novel social network based group decision making (SN-GDM) model with experts’ weights not provided beforehand and with the following four tuple information: trust; distrust; hesitancy; and inconsistency, is introduced. The concepts of trust score (TS) and knowledge degree (KD) are defined and combined into a trust order space. Then, a strict trust ranking order relation of trust function valu...

In this paper the equation I(U1(x,y),z) = U2(I(x,z), I(y,z)) for all x,y,z ∈ [0,1] is solved where I is a residual implication defined from a uninorm U , and U1,U2 are a conjunctive and a disjunctive uninorm, respectively. Three cases are considered: i) when U is a t-norm, ii) when U1 is a t-norm and/or U2 is a t-conorm, and iii) the general case when the neutral elements of U,U1 and U2 are in ...