Distributivity of strong implications over conjunctive and disjunctive uninorms

Daniel Ruiz-Aguilera; Joan Torrens

Displaying similar documents to “Distributivity of strong implications over conjunctive and disjunctive uninorms”

On the structure of continuous uninorms

Paweł Drygaś (2007)

Kybernetika

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Uninorms were introduced by Yager and Rybalov [13] as a generalization of triangular norms and conorms. We ask about properties of increasing, associative, continuous binary operation $U$ in the unit interval with the neutral element $e \in [0, 1]$ . If operation $U$ is continuous, then $e = 0$ or $e = 1$ . So, we consider operations which are continuous in the open unit square. As a result every associative, increasing binary operation with the neutral element $e \in (0, 1)$ , which is continuous in the open unit square may be...

Optimality conditions for maximizers of the information divergence from an exponential family

František Matúš (2007)

Kybernetika

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The information divergence of a probability measure $P$ from an exponential family $ℰ$ over a finite set is defined as infimum of the divergences of $P$ from $Q$ subject to $Q \in ℰ$ . All directional derivatives of the divergence from $ℰ$ are explicitly found. To this end, behaviour of the conjugate of a log-Laplace transform on the boundary of its domain is analysed. The first order conditions for $P$ to be a maximizer of the divergence from $ℰ$ are presented, including new ones when $P$ is not projectable...

On Ozeki’s inequality for power sums

Horst Alzer (2000)

Czechoslovak Mathematical Journal

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Let $p \in (0, 1)$ be a real number and let $n \geq 2$ be an even integer. We determine the largest value $c_{n} (p)$ such that the inequality $\sum_{i = 1}^{n} {| a_{i} |}^{p} \geq c_{n} (p)$ holds for all real numbers $a_{1}, ..., a_{n}$ which are pairwise distinct and satisfy ${min}_{i \neq j} | a_{i} - a_{j} | = 1$ . Our theorem completes results of Ozeki, Mitrinović-Kalajdžić, and Russell, who found the optimal value $c_{n} (p)$ in the case $p > 0$ and $n$ odd, and in the case $p \geq 1$ and $n$ even.

Comparison of two methods for approximation of probability distributions with prescribed marginals

Albert Pérez, Milan Studený (2007)

Kybernetika

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Let $P$ be a discrete multidimensional probability distribution over a finite set of variables $N$ which is only partially specified by the requirement that it has prescribed given marginals ${P_{A}; A \in 𝒮}$ , where $𝒮$ is a class of subsets of $N$ with $⋃ 𝒮 = N$ . The paper deals with the problem of approximating $P$ on the basis of those given marginals. The divergence of an approximation $\hat{P}$ from $P$ is measured by the relative entropy $H (P | \hat{P})$ . Two methods for approximating $P$ are compared. One of them uses formerly introduced...

Stochastic control optimal in the Kullback sense

Jan Šindelář, Igor Vajda, Miroslav Kárný (2008)

Kybernetika

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The paper solves the problem of minimization of the Kullback divergence between a partially known and a completely known probability distribution. It considers two probability distributions of a random vector $(u_{1}, x_{1}, ..., u_{T}, x_{T})$ on a sample space of $2 T$ dimensions. One of the distributions is known, the other is known only partially. Namely, only the conditional probability distributions of $x_{τ}$ given $u_{1}, x_{1}, ..., u_{τ - 1}, x_{τ - 1}, u_{τ}$ are known for $τ = 1, ..., T$ . Our objective is to determine the remaining conditional probability distributions of $u_{τ}$ ...