This paper is devoted to classify all idempotent uninorms defined on the finite scale Ln = {0, 1, . . . , n}, called discrete idempotent uninorms. It is proved that any discrete idempotent uninorm with neutral element e ∈ Ln is uniquely determined by a decreasing function g : [0, e]→ [e, n] and vice versa. Based on this correspondence, the number of all possible discrete idempotent uninorms on ...

This paper presents a continuation of the study on a mathematical morphology based on left-continuous conjunctive uninorms given in [1]. Experimental results are displayed using the morphological Top-Hat transformation, used to highlight certain components of the image, and on the reduction and elimination of noise using alternate filters that are generated with the operators of opening and clo...

In this paper, we introduce the concept of interval pseudo-homegeneous uninorms. We extend the concept of pseudo-homogeneity of specific functions for interval pseudo-homogeneous functions. It is studied two cases of interval pseudo-homogeneous uninorms, that is, interval pseudo-homogeneous tnorms and interval pseudo-homogeneous t-conorms. It is proved a form of interval pseudo-homogeneous t-no...

In this work, by Zadeh’s extension principle, we extend representable uninorms and their fuzzy implications (coimplications) to type-2 fuzzy sets. Emphatically, we investigate in which algebras of fuzzy truth values the extended operations are type-2 uninorms and type-2 fuzzy implications (coimplications), respectively.

In this article, we present two methods to construct uninorms on bounded lattices by using additive generators. We also provide some examples for illustrating the constructing of uninorms.

In this paper we provide two axiomatizations of the class of idempotent discrete uninorms as conservative binary operations, where an operation is conservative if it always outputs one of its input values. More precisely we first show that the idempotent discrete uninorms are exactly those operations that are conservative, symmetric, and nondecreasing in each variable. Then we show that, in thi...

This work deals with strong implications (S-implications in short) derived from uninorms continuous at ]0, 1[2. The general expression of such implications is found and several properties are studied. In particular, the distributivity of the Simplications over conjunctive and disjunctive uninorms is investigated.