On the structure of continuous uninorms

Paweł Drygaś

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Displaying similar documents to “On the structure of continuous uninorms”

Distributivity of strong implications over conjunctive and disjunctive uninorms

Daniel Ruiz-Aguilera, Joan Torrens (2006)

Kybernetika

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This paper deals with implications defined from disjunctive uninorms $U$ by the expression $I (x, y) = U (N (x), y)$ where $N$ is a strong negation. The main goal is to solve the functional equation derived from the distributivity condition of these implications over conjunctive and disjunctive uninorms. Special cases are considered when the conjunctive and disjunctive uninorm are a $t$ -norm or a $t$ -conorm respectively. The obtained results show a lot of new solutions generalyzing those obtained in previous works...

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.

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...

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...