Related papers: Some further construction methods for uninorms via…
In this article, we study new methods for constructing uninorms on bounded lattices. First, we present new methods for constructing uninorms on bounded lattices under the additional constraints and prove that some of these constraints are…
In this paper, we provide some structures of uninorms on bounded lattices via t-conorms, closure operators and t-subnorms, subject to certain constraints on the closure operators and t-subnorms. Importantly, these constraints are shown to…
In this paper, we propose novel methods for constructing uninorms using two comparable closure operators or, alternatively, two comparable interior operators on bounded lattices. These methods are developed under the necessary and…
In this paper, we study the construction methods for uninorms on bounded lattices via functions with the given uninorms and $q\in \mathbb{L_{B}}$ (or $p\in \mathbb{L_{B}}$). Specifically, we investigate the conditions under which these…
In this article, we present two methods to construct 2-uninorms on bounded lattices by using additive generators, which are further used for inducing uninorms, nullnorms, uni-nullnorms and null-uninorms, respectively. We also provide some…
This paper establishes some equivalent conditions of a uninorm, extending an arbitrary triangular norm on [0, e] or an arbitrary triangular conorm on [e, 1] to the whole lattice.
The uninorms with continuous underlying t-norm and t-conorm are characterized via an extended ordinal sum construction. Using the results of [18], where each uninorm with continuous underlying operations was characterized by properties of…
This article focuses on the construction of left-continuous t-norms on complete lattices. The concepts of $\mathfrak{f}$-mappings and weak $\mathfrak{f}$-mappings on complete lattices are first introduced, respectively. They are then…
In this paper, we introduce the notion of a t-norm on bounded pseudo-ordered sets and in particular on bounded trellises (also known as weakly associative lattices), and provide some basic examples. The impact of abandoning transitivity is…
In this paper, we introduce the notion of nullnorms on bounded trellises and study some basic properties. Based on the existence of $t$-norms and $t$-conorms on arbitrary bounded trellises, we propose some construction methods of nullnorms…
This article focuses on the relationship between pseudo-t-norms and the structure of lattices. First, we establish a necessary and sufficient condition for the existence of a left-continuous t-norm on the ordinal sum of two disjoint…
The ordinal sum construction provides a very effective way to generate a new triangular norm on the real unit interval from existing ones. One of the most prominent theorems concerning the ordinal sum of triangular norms on the real unit…
The ordinal sum of t-norms on a bounded lattice has been used to construct other t-norms. However, an ordinal sum of binary operations (not necessarily t-norms) defined on the fixed subintervals of a bounded lattice may not be a t-norm.…
Uninorms with continuous underlying t-norm and t-conorm are discussed and properties of the set of discontinuity points of such a uninorm are shown. This set is proved to be a subset of the graph of a special symmetric, surjective,…
Uninorms play a prominent role both in the theory and the applications of Aggregations and Fuzzy Logic. In this paper the class of group-like uninorms is introduced and characterized. First, two variants of a general construction -- called…
Unbounded convergences have been applied successfully to locally solid topologies on vector lattices. In the present paper, we first expose several properties of various classes of Riesz pseudonorms on vector lattices. We accomplish this by…
We present in this paper a universal method of constructing left-continuous triangular norms (l.-c. t-norms). The starting point is an arbitrary, possibly finite, totally ordered monoid fulfilling the conditions that are characteristic for…
It is pointed out that despite of the non-linearity of the underlying equations, there do exist rather general methods that allow to generate new minimal surfaces from known ones.
I discuss a new approach to constructing lattices for gauge theories with extended supersymmetry. The lattice theories themselves respect certain supersymmetries, which in many cases allows the target theory to be obtained in the continuum…
In this paper we investigate measures over bounded lattices, extending and giving a unifying treatment to previous works. In particular, we prove that the measures of an arbitrary bounded lattice can be represented as measures over a…