Geodesic
A Note on Application of Two-sided Systems of $(\max , \min )$-Linear Equations and Inequalities to Some Fuzzy Set Problems
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 2, pp. 129-135 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 of which with the fuzzy goals satisfy certain requirements concerning the heights of the intersections. Both fuzzy goals and the set to be found are supposed to have a finite support. The formulated problems can be solved by the polynomial algorithm published in [Gavalec, M., Zimmermann, K.: Solving systems of two-sided (max,min)-linear equations Kybernetika 46 (2010), 405–414.].
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 of which with the fuzzy goals satisfy certain requirements concerning the heights of the intersections. Both fuzzy goals and the set to be found are supposed to have a finite support. The formulated problems can be solved by the polynomial algorithm published in [Gavalec, M., Zimmermann, K.: Solving systems of two-sided (max,min)-linear equations Kybernetika 46 (2010), 405–414.].
Classification : 90C26, 90C70
Keywords: multiple fuzzy global optimization; $(\max, \min )$-linear equation and inequality systems 
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     title = {A {Note} on {Application} of {Two-sided} {Systems} of $(\max , \min )${-Linear} {Equations} and {Inequalities} to {Some} {Fuzzy} {Set} {Problems}},
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Zimmermann, Karel. A Note on Application of Two-sided Systems of $(\max , \min )$-Linear Equations and Inequalities to Some Fuzzy Set Problems. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 2, pp. 129-135. http://geodesic.mathdoc.fr/item/AUPO_2011_50_2_a13/

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