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

Karel Zimmermann

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2011)

  • Volume: 50, Issue: 2, page 129-135
  • ISSN: 0231-9721

Abstract

top
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.].

How to cite

top

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 50.2 (2011): 129-135. <http://eudml.org/doc/196840>.

@article{Zimmermann2011,
abstract = {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.].},
author = {Zimmermann, Karel},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {multiple fuzzy global optimization; $(\max , \min )$-linear equation and inequality systems; multiple fuzzy global optimization; -linear equation and inequality systems},
language = {eng},
number = {2},
pages = {129-135},
publisher = {Palacký University Olomouc},
title = {A Note on Application of Two-sided Systems of $(\max , \min )$-Linear Equations and Inequalities to Some Fuzzy Set Problems},
url = {http://eudml.org/doc/196840},
volume = {50},
year = {2011},
}

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
PB - Palacký University Olomouc
VL - 50
IS - 2
SP - 129
EP - 135
AB - 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.].
LA - eng
KW - multiple fuzzy global optimization; $(\max , \min )$-linear equation and inequality systems; multiple fuzzy global optimization; -linear equation and inequality systems
UR - http://eudml.org/doc/196840
ER -

References

top
  1. Bezem, M., Nieuwenhuis, R., Rodríguez-Carbonell, E., 10.1016/j.dam.2008.03.016, Discrete Applied Mathematics 156 (2008), 3506–3509. (2008) Zbl1178.68637MR2467321DOI10.1016/j.dam.2008.03.016
  2. Cuninghame-Green, R. A., Minimax Algebra, Lecture Notes in Economics and Mathematical Systems 166, Springer Verlag, Berlin, 1979. (1979) Zbl0399.90052MR0580321
  3. Gavalec, M., Zimmermann, K., Solving systems of two-sided (max,min)-linear equations, Kybernetika 46 (2010), 405–414. (2010) Zbl1195.65037MR2676078
  4. Litvinov, G. L., Maslov, V. P., Sergeev, S. N., Idempotent and Tropical Mathematics and Problems of Mathematical Physics, vol. I, Independent University Moscow, Moscow, 2007. (2007) 
  5. Maslov, V. P., Samborskij, S. N., Idempotent Analysis, Advances in Soviet Mathematics 13, AMS, Providence, 1992. (1992) Zbl0772.00015MR1203781
  6. Vorobjov, N. N., Extremal algebra of positive matrices, Datenverarbeitung und Kybernetik 3 (1967), 39–71, (in Russian). (1967) MR0216854

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.