arXiv subjects

Xue-ping Wang

Publications and source records attributed to Xue-ping Wang.

At least 19 recordsLinked to original sources

arXiv2026

Bounds of triangular subnorms and their algorithms

This article deals with the upper and lower bounds of triangular subnorms generated by continuous, strictly decreasing additive generators. It first establishes necessary and sufficient conditions for the comparability of such triangular subnorms. It then explores the existence of strict (resp. nilpotent) bounds of a finite family of strict (resp. nilpotent) triangular subnorms generated by continuous, strictly decreasing additive generators. By duality, completely analogous results are derived for triangular superconorms generated by continuous, strictly increasing additive generators. In particular, it supplies the corresponding algorithms for computing those bounds, which are illustrated by several examples.

math.GM↗

arXiv2026

Further results on fuzzy negations and implications induced by fuzzy conjunctions and disjunctions

In this article, we deeply investigate some properties of fuzzy negations induced from fuzzy conjunctions (resp. disjunctions), which are then applied to characterizing the fuzzy negations. We further use the obtained characterization of fuzzy negations to explore some properties of $(D,N)$-implications generated from fuzzy disjunctions and negations. We finally describe $(D,N)$-implications (resp. continuous $(D,N)$-implications) generated from fuzzy disjunctions and negations.

math.RT↗

arXiv2026

Monotone functions that generate conditionally cancellative triangular subnorms

Let a function $F: [0,1]^2\rightarrow [0,1]$ be given by $F(x,y)= f^{(-1)}(T(f(x), f(y)))$ where $f :[0,1]\rightarrow [0,1]$ is a monotone function, $f^{(-1)}$ is the pseudo-inverse of $f$ and $T$ is a triangular norm. This article characterizes the monotone function $f$ satisfying that the function $F$ is a conditionally cancellative triangular subnorm completely. It finally answers an open problem posed by Mesiarov\'{a}.

math.GM↗

arXiv2026

Constructing left-continuous triangular norms on complete lattices

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 applied to establish the following key results: weak $\mathfrak{f}$-mappings are used to induce left-continuous t-subnorms; $\mathfrak{f}$-mappings are used to generate left-continuous t-norms whenever the top element $1$ of the complete lattice is a completely join-irreducible element. Finally, some necessary and sufficient conditions are provided for an operator constructed by the ordinal sum of a series of annihilating binary operators being a left-continuous t-norm on a complete lattice.

math.GM↗

arXiv2025

Additive generator pairs of overlap functions

Let $\theta:[0,1]\rightarrow[-\infty,+\infty]$ be a function with both $\theta(x^{-})$ and $\theta(x^{+})$ existing for every $x\in [0,1]$ and $\vartheta:[-\infty,+\infty]\rightarrow[-\infty,+\infty]$ be a function. In this article we completely characterize the pair $(\theta,\vartheta)$ for the bivariate function $O_{\theta,\vartheta}: [0,1]^{2}\rightarrow[0,1]$ given by $$O_{\theta,\vartheta}(x,y)=\vartheta(\theta(x)+\theta(y))$$ being an overlap function. In particular, we give analytical expressions of some transformations for the pair $(\theta,\vartheta)$.

math.GM↗

arXiv2025

Characterizations of monotone right continuous functions which generate associative functions

Associativity of a two-place function $T: [0,1]^2\rightarrow [0,1]$ defined by $T(x,y)=f^{(-1)}(T^*(f(x),f(y)))$ where $T^*:[0,1]^2\rightarrow[0,1]$ is an associative function with neutral element in $[0,1]$, $f: [0,1]\rightarrow [0,1]$ is a monotone right continuous function and $f^{(-1)}:[0,1]\rightarrow[0,1]$ is the pseudo-inverse of $f$ depends only on properties of the range of $f$. The necessary and sufficient conditions for the $T$ to be associative are presented by applying the properties of the monotone right continuous function $f$.

math.FA↗

arXiv2025

The characterizations of monotone functions which generate associative functions

Associativity of a two-place function $T: [0,1]^2\rightarrow [0,1]$ defined by $T(x,y)=f^{(-1)}(F(f(x),f(y)))$ where $F:[0,\infty]^2\rightarrow[0,\infty]$ is an associative function, $f: [0,1]\rightarrow [0,\infty]$ is a monotone function which satisfies either $f(x)=f(x^{+})$ when $f(x^{+})\in \mbox{Ran}(f)$ or $f(x)\neq f(y)$ for any $y\neq x$ when $f(x^{+})\notin \mbox{Ran}(f)$ for all $x\in[0,1]$ and $f^{(-1)}:[0,\infty]\rightarrow[0,1]$ is a pseudo-inverse of $f$ depends only on properties of the range of $f$. The necessary and sufficient conditions for the $T$ to be associative are presented by applying the properties of the monotone function $f$.

math.GM↗

arXiv2025

A characterization of a class of border continuous triangular conorms

Let $T^*:[0,1]^2\rightarrow[0,1]$ be a continuous, non-decreasing and associative function with neutral element, $f: [0,1]\rightarrow [0,1]$ be a strictly monotone function and $f^{(-1)}:[0,1]\rightarrow[0,1]$ be the pseudo-inverse of $f$. This article characterizes the function $T: [0,1]^2 \rightarrow [0,1]$ defined by $T(x,y)=f^{(-1)}(T^*(f(x),f(y)))$ when it is a border continuous triangular conorm.

math.RT↗

arXiv2025

Orders of continuous cancellative triangular subnorms

The order relations of continuous cancellative t-subnorms are discussed. First, we present some necessary and sufficient conditions along with several interesting sufficient criteria for the comparability of continuous cancellative t-subnorms. Then we characterize the growth and boundedness of additive generators, which are used for the comparison of continuous cancellative t-subnorms.

math.RT↗

arXiv2025

Associativity of two-place functions generated by left continuous monotone functions and other properties

This article introduces a weak pseudo-inverse of a monotone function, which is applied to characterize the associativity of a two-place function $T: [0,1]^2\rightarrow [0,1]$ defined by $T(x,y)=t^{[-1]}(F(t(x),t(y)))$ where $F:[0,\infty]^2\rightarrow[0,\infty]$ is an associative function with neutral element in $[0,\infty]$, $t: [0,1]\rightarrow [0,\infty]$ is a left continuous monotone function and $t^{[-1]}:[0,\infty]\rightarrow[0,1]$ is the weak pseudo-inverse of $t$. It shows that the associativity of the function $T$ depends only on properties of the range of $t$. Moreover, it investigates the idempotence, the limit property, the conditional cancellation law and the continuity of the function $T$, respectively.

math.GM↗

arXiv2025

Left-continuous pseudo-t-norms on modular lattices

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 complete lattices. Then, we define the $1$-distributivity of a lattice, which is applied for characterizing a complete atomistic lattice that has a left-continuous pseudo-t-norm. We also describe the forbidden structures of a finite modular lattice that is a $1$-distributive lattice, which is used for representing a kind of finite planar modular lattices that have left-continuous pseudo-t-norms.

math.RT↗

arXiv2025

Note on additive generator pairs of overlap and grouping functions

In this article, we deeply reveal the relationship between functions $θ$ and $\vartheta$ in an overlap function additively generated by an additive generator pair ($θ$,$\vartheta$). Then we characterize the conditions for an overlap function additively generated by the pair being a triangular norm by terms of functions $θ$ and $\vartheta$. We also establish the conditions that an overlap function additively generated by the additive generator pair can be obtained by a distortion of a triangular norm and a (pseudo) automorphism. Finally, we dually give the related results concerned grouping functions.

math.RT↗

arXiv2024

Associativity of a class of two-place functions and its consequences for classes of triangular norms

This article characterizes the associativity of two-place functions $T: [0,1]^2\rightarrow [0,1]$ defined by $T(x,y)=f^{(-1)}(F(f(x),f(y)))$ where $F:[0,1]^2\rightarrow[0,1]$ is a triangular norm (even a triangular subnorm), $f: [0,1]\rightarrow [0,1]$ is a strictly increasing function and $f^{(-1)}:[0,1]\rightarrow[0,1]$ is the pseudo-inverse of $f$. We prove that the associativity of functions $T$ only depends on the range of $f$, which is used to give a sufficient and necessary condition for the function $T$ being associative when the triangular norm $F$ is an ordinal sum of triangular norms and an ordinal sum of triangular subnorms in the sense of A. H. Clifford, respectively. These results finally are applied for describing classes of triangular norms generated by strictly increasing functions.

math.GM↗

arXiv2024

New characterizations of migrative 2-uninorms

This article pays attention to the $α$-migrativity of 2-uninorms with $α\in [0,1]$ deeply. It describes the $α$-migrativity of 2-uninorms completely, which generalizes and unifies some current existing characterizations for $α$-migrativity of triangular norm, triangular conorm, uninorms, nullnorms, uni-nullnorms and null-uninorms, respectively.

math.GM↗

arXiv2024

Characterizations of quasi-homogeneous aggregation functions

In this article, we first give the characterizations of quasi-homogeneous aggregation functions, which show us that quasi-homogeneous aggregation functions are classified into three classes. We then introduce the concept of triple generator of quasi-homogeneous aggregation function, which is applied to construct a quasi-homogeneous aggregation function.

math.GM↗

arXiv2023

Eigenproblems in addition-min algebra

In order to guarantee the downloading quality requirements of users and improve the stability of data transmission in a BitTorrent-like peer-to-peer file sharing system, this article deals with eigenproblems of addition-min algebras. First, it provides a sufficient and necessary condition for a vector being an eigenvector of a given matrix, and then presents an algorithm for finding all eigenvalues and eigenvectors of a given matrix. It further proposes a sufficient and necessary condition for a vector being a constrained eigenvector of a given matrix and supplies an algorithm for computing all the constrained eigenvectors and eigenvalues of a given matrix. This article finally discusses the supereigenproblem of a given matrix and presents an algorithm for obtaining the maximum constrained supereigenvalue and depicting the feasible region of all the constrained supereigenvectors for a given matrix. It also gives some examples for illustrating the algorithms, respectively.

math.GM↗

arXiv2023

The pseudocomplementedness of modular lattices described by two 0-sublattices

In this article, we first characterize pseudocomplemented inductive modular lattices by using their two 0-sublattices. Then we use two 0-sublattices of a subgroup lattice to describe all locally cyclic abelian groups. In particular, we show that a locally cyclic abelian group can be characterized by its three subgroups.

math.GR↗

arXiv2022

Constructing 2-uninorms on bounded lattices by using additive generators

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 examples for illustrating the constructing methods of 2-uninorms.

math.RA↗