Related papers: Ordinal sum of two binary operations being a t-nor…
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…
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…
This paper constructs a $t_{r}$-norm and a $t_{r}$-conorm on the set of all normal and convex functions from ${[0, 1]}$ to ${[0, 1]}$, which are not obtained by using the following two formulas on binary operations ${\curlywedge}$ and…
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 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…
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…
We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…
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…
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 consider ordinal sums of combinatorial games where each summand is a number, not necessarily in canonical form. In doing so we give formulas for the value of an ordinal sum of numbers where the literal form of the base has…
In this paper, we further investigate new construction methods for uninorms on bounded lattices via given uninorms. More specifically, we first construct new uninorms on arbitrary bounded lattices by extending a given uninorm on a…
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 introduce the notion of pseudo-triangular norm (pseudo-t-norm, for short) as a classes of weakly associative operations on trellises and as a generalization of triangular norm (t-norm, for short) on bounded trellises and…
In this paper we give and prove a criterion for the normality of unbounded closed operators, which is a sort of a maximality result which will be called "double maximality". As applications, we show, under some assumptions, that the sum of…
This paper proves that a binary operation ${\star}$ on ${[0, 1]}$, ensuring that the binary operation ${\curlywedge}$ is a ${t}$-norm or ${\curlyvee}$ is a ${t}$-conorm, is a ${t}$-norm, where ${\curlywedge}$ and ${\curlyvee}$ are special…
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.
We motivate and study an infinite sequence of binary operations on the ordinal numbers, extending the standard arithmetic on the ordinals to higher degrees of iteration. Connections to the hyperoperations on the natural numbers are…
In the present paper we give results on the closedness and the self-adjointness of the sum of two unbounded operators. We present a new approach to these fundamental questions in operator theory. We also prove a new version of the Fuglede…
Given a suitable arithmetic function h, we investigate the average order of h as it ranges over the values taken by an integral binary form F. A general upper bound is obtained for this quantity, in which the dependence upon the…
We investigate properties of an ordinal sum of uninorms introduced in [8] in the case that the summands are proper representable uninorms. We show sufficient and necessary conditions for a uninorm to be an ordinal sum of representable…