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Currently displaying 1 – 18 of 18

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Celebrating eighty years of Professor Nožička

Karel Zimmermann — 1999

Mathematica Bohemica

Combination of t-norms and their conorms

Karel Zimmermann — 2023

Kybernetika

Non-negative linear combinations of $t_{min}$ -norms and their conorms are used to formulate some decision making problems using systems of max-separable equations and inequalities and optimization problems under constraints described by such systems. The systems have the left hand sides equal to the maximum of increasing functions of one variable and on the right hand sides are constants. Properties of the systems are studied as well as optimization problems with constraints given by the systems and appropriate...

Solvability of (max,+) and (min,+)-equation systems

Karel Zimmermann — 2025

Kybernetika

Properties of (max,+)-linear and (min,+)-linear equation systems are used to study solvability of the systems. Solvability conditions of the systems are investigated. Both one-sided and two-sided systems are studied. Solvability of one class of (max,+)-nonlinear problems will be investigated. Small numerical examples illustrate the theoretical results.

An approach to the solution of a conflict situation with $n$ participants

Karel Zimmermann — 1976

Aplikace matematiky

Zprávy. Prof. dr. František Nožička, DrSc. sedmdesátiletý

Karel Zimmermann — 1988

Aplikace matematiky

Prof. RNDr. Josef Bílý, CSc., zemřel

Karel Zimmermann — 1971

Časopis pro pěstování matematiky

A Note on Application of Two-sided Systems of $(max, min)$ -Linear Equations and Inequalities to Some Fuzzy Set Problems

Karel Zimmermann — 2011

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The aim of this short contribution is to point out some applications of systems of so called two-sided $(max, min)$ -linear systems of equations and inequalities of [Gavalec, M., Zimmermann, K.: Solving systems of two-sided (max,min)-linear equations Kybernetika 46 (2010), 405–414.] to solving some fuzzy set multiple fuzzy goal problems. The paper describes one approach to formulating and solving multiple fuzzy goal problems. The fuzzy goals are given as fuzzy sets and we look for a fuzzy set, the fuzzy intersections...

Optimization problem under two-sided (max, +)/(min, +) inequality constraints

Karel Zimmermann — 2020

Applications of Mathematics

$(max, +)$ -linear functions are functions which can be expressed as the maximum of a finite number of linear functions of one variable having the form $f (x_{1}, \dots, x_{h}) = {max}_{j} (a_{j} + x_{j})$ , where $a_{j}$ , $j = 1, \dots, h$ , are real numbers. Similarly $(min, +)$ -linear functions are defined. We will consider optimization problems in which the set of feasible solutions is the solution set of a finite inequality system, where the inequalities have $(max, +)$ -linear functions of variables $x$ on one side and $(min, +)$ -linear functions of variables $y$ on the other side. Such systems...

Eigenschaften offener und affiner Mengen in Verbandsstrukturen

Gerhard Heidekrüger; Karel Zimmermann — 1985

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Optimal starting times for a class of single machine scheduling problems with earliness and tardiness penalties

Milan Vlach; Karel Zimmermann — 1997

Kybernetika

Solving systems of two–sided (max, min)–linear equations

Martin Gavalec; Karel Zimmermann — 2010

Kybernetika

A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.

One generalization of the dynamic programming problem

Milan Vlach; Karel Zimmermann — 1970

Aplikace matematiky

The main purpose of this article is to provide an exact theory of the dynamic programming on a sufficiently general basis. Let $M$ be a compact topological Hausdorff’s space, let ${\tilde{T}}^{M}$ be the set of all continuous transformations of the space $M$ into itself. Suppose such a topology is introduced on ${\tilde{T}}^{M}$ that ${\tilde{T}}^{M}$ is Haousdorff’s space and that the transformation $φ (x, y) = y (x)$ of the product $M \otimes {\tilde{T}}^{M}$ into $M$ is continuous with respect to Tichonoff’s topology on $M \otimes {\tilde{T}}^{M}$ . Suppose ${\tilde{T}}^{M}$ is a compact subspace of ${\tilde{T}}^{M}$ and $ℳ = M \otimes T^{M} \otimes ... \otimes T^{M} \otimes ...$ . We define the transformations...

A note on some separable location problems - a multicriterial approach

Assem Tharwat; Karel Zimmermann — 2004

Acta Universitatis Carolinae. Mathematica et Physica

A service points location problem with Min-Max distance optimality criterion

Oto Hudec; Karel Zimmermann — 1993

Acta Universitatis Carolinae. Mathematica et Physica

Some optimization problems on solubility sets of separable Max-Min equations and inequalities

Assem Tharwat; Karel Zimmermann — 1997

Acta Universitatis Carolinae. Mathematica et Physica

Equation with residuated functions

Ray A. Cuninghame-Green; Karel Zimmermann — 2001

Commentationes Mathematicae Universitatis Carolinae

The structure of solution-sets for the equation $F (x) = G (y)$ is discussed, where $F, G$ are given residuated functions mapping between partially-ordered sets. An algorithm is proposed which produces a solution in the event of finite termination: this solution is maximal relative to initial trial values of $x, y$ . Properties are defined which are sufficient for finite termination. The particular case of max-based linear algebra is discussed, with application to the synchronisation problem for discrete-event systems;...