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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 , ⋯ , x h ) = max j ( a j + x j ) , where a j , j = 1 , ⋯ , 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...

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 T ˜ M be the set of all continuous transformations of the space M into itself. Suppose such a topology is introduced on T ˜ M that T ˜ M is Haousdorff’s space and that the transformation φ ( x , y ) = y ( x ) of the product M ⊗ T ˜ M into M is continuous with respect to Tichonoff’s topology on M ⊗ T ˜ M . Suppose T ˜ M is a compact subspace of T ˜ M and ℳ = M ⊗ T M ⊗ ... ⊗ T M ⊗ ... . We define the transformations...

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;...

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