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

Voir la notice de l'article

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 
@article{AUPO_2011_50_2_a13,
     author = {Zimmermann, Karel},
     title = {A {Note} on {Application} of {Two-sided} {Systems} of $(\max , \min )${-Linear} {Equations} and {Inequalities} to {Some} {Fuzzy} {Set} {Problems}},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
     pages = {129--135},
     year = {2011},
     volume = {50},
     number = {2},
     mrnumber = {2920715},
     zbl = {1244.90259},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPO_2011_50_2_a13/}
}
TY  - JOUR
AU  - Zimmermann, Karel
TI  - A Note on Application of Two-sided Systems of $(\max , \min )$-Linear Equations and Inequalities to Some Fuzzy Set Problems
JO  - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY  - 2011
SP  - 129
EP  - 135
VL  - 50
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AUPO_2011_50_2_a13/
LA  - en
ID  - AUPO_2011_50_2_a13
ER  - 
%0 Journal Article
%A Zimmermann, Karel
%T A Note on Application of Two-sided Systems of $(\max , \min )$-Linear Equations and Inequalities to Some Fuzzy Set Problems
%J Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
%D 2011
%P 129-135
%V 50
%N 2
%U http://geodesic.mathdoc.fr/item/AUPO_2011_50_2_a13/
%G en
%F AUPO_2011_50_2_a13
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/