arXiv subjects

Yao Ouyang

Publications and source records attributed to Yao Ouyang.

6 recordsLinked to original sources

arXiv2026

On weak dominance of t-conorms over t-norms

The weak dominance of aggregation operators, particularly between triangular norms (t-norms) and triangular conorms (t-conorms), has attracted considerable attention in aggregation operator theory. While several characterizations have been obtained for Archimedean and continuous cases, a general criterion for continuous t-conorms over continuous t-norms remains to be fully clarified. In this paper, we provide a complete characterization of a continuous t-conorm weakly dominating a continuous t-norm. We first reduce the problem for ordinal sum operators to that for their single Archimedean components, and then express the weak dominance condition entirely in terms of the additive generators of these components. Our approach covers both strict and nilpotent cases uniformly, and recovers the known results for Archimedean operators as a special case.

math.FA↗

arXiv2025

On the pointwise supremum of the set of copulas with a given curvilinear section

Making use of the total variation of particular functions, we give an explicit formula for the pointwise supremum of the set of all copulas with a given curvilinear section. When the pointwise supremum is a copula is characterized. We also characterize the coincidence of the pointwise supremum and the greatest quasi-copula with the same curvilinear section.

math.ST↗

arXiv2024

On an upper bound of the set of copulas with a given curvilinear section

The characterizations when two natural upper bounds of the set of copulas with a given diagonal section are copulas have been well studied in the literature. Given a curvilinear section, however, there is only a partial result concerning the characterization when a natural upper bound of the set of copulas is a copula. In this paper, we completely solve the characterization problem for this natural upper bound to be a copula in the curvilinear case.

math.ST↗

arXiv2023

A Radon-Nikodym theorem for monotone measures

A version of Radon-Nikodym theorem for the Choquet integral w.r.t. monotone measures is proved. Without any presumptive condition, we obtain a necessary and sufficient condition for the ordered pair $(μ, ν)$ of finite monotone measures to have the so-called Radon-Nikodym property related to a nonnegative measurable function $f$. If $ν$ is null-continuous and weakly null-additive, then $f$ is uniquely determined almost everywhere by $ν$ and thus is called the Radon-Nikodym derivative of $μ$ w.r.t. $ν$. For $σ$-finite monotone measures, a Radon-Nikodym type theorem is also obtained under the assumption that the monotone measures are lower continuous and null-additive.

math.FA↗

arXiv2020

Ordinal sums of triangular norms on a bounded lattice

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 interval states that a triangular norm is continuous if and only if it is uniquely representable as an ordinal sum of continuous Archimedean triangular norms. However, the ordinal sum of triangular norms on subintervals of a bounded lattice is not always a triangular norm (even if only one summand is involved), if one just extends the ordinal sum construction to a bounded lattice in a na\"ıve way. In the present paper, appropriately dealing with those elements that are incomparable with the endpoints of the given subintervals, we propose an alternative definition of ordinal sum of countably many (finite or countably infinite) triangular norms on subintervals of a complete lattice, where the endpoints of the subintervals constitute a chain. The completeness requirement for the lattice is not needed when considering finitely many triangular norms. The newly proposed ordinal sum is shown to be always a triangular norm. Several illustrative examples are given.

math.RA↗

arXiv2016

On linearity of pan-integral and pan-integrable functions space

$L\sp{p}$ space is a crucial aspect of classical measure theory. For nonadditive measure, it is known that $L\sp{p}$ space theory holds for the Choquet integral whenever the monotone measure $μ$ is submodular and continuous from below. The main purpose of this paper is to generalize $L\sp{p}$ space theory to $+,\cdot$-based pan-integral. Let $(X, {\cal A}, μ)$ be a monotone measure space. We prove that the $+,\cdot$-based pan-integral is additive with respect to integrands if $μ$ is subadditive. Then we introduce the pan-integral for real-valued functions(not necessarily nonnegative), and prove that this integral possesses linearity if $μ$ is subadditive. By using the linearity of pan-integral, we finally show that all of the pan-integrable functions form a Banach space. Since the $+,\cdot$-based pan-integral coincides with the concave integral for subadditive measure, the results obtained in this paper remain valid for the concave integral. Noticing that an outer measure is subadditive, we can define a Lebesgue-like integral(possesses linearity) from an outer measure, and the $L\sp{p}$ theory holds for this integral. {\it Keywords:} Monotone measure; Subadditivity; Pan-integral; Linearity; Pan-integrable space; Completeness

math.FA↗