Advertisement

Trabajos de Investigacion Operativa

, Volume 4, Issue 1, pp 21–38 | Cite as

Modelos auxiliares para problemas de programacion lineal con coeficientes imprecisos en las restricciones

  • Campos L. 
  • Verdegay J. L. 
Article

Resumen

En este artículo se considera un problema de Programación Lineal en el que los coeficientes del sistema de inecuaciones lineales, que definen el conjunto de restricciones, están dados de forma imprecisa o vaga. Se supone entonces que tales coeficientes pueden ser definidos mediante números difusos. Se propone un enfoque de resolución basado en las distintas versiones existentes para la comparación de números difusos. Finalmente, se obtienen diferentes modelos auxiliares de Programación Lineal, que corresponden a las distintas formas de comparación de números difusos y a partir de los cuales se queede dar una solución al problema inicialmente propuesto.

Palabras clave

Número Difuso Indices de Comparación Programación Lineal 

Clasificación AMS

90C50 90C99 

Abstract

In this paper it is considered a Linear Programming problem in which the coefficients in the system of linear inequalities defining the constraint set are given in an imprecise, or vague, way. It is supposed those coefficients may be defined by means of fuzzy numbers. An approach of solution based upon the several versions that exist to compare fuzzy numbers is proposed. Finally, corresponding to the different ways to compare fuzzy numbers, distinct auxiliary models of Linear Programming are obtained. From each of which, a solution to the former problem may be obtained.

Key words

Fuzzy Number Index of Comparison Linear Programming 

AMS Classification

90C50 90C99 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Referencias

  1. ADAMO, J. M. (1980): ≪Fuzzy Decision Trees≫,Fuzzy Sets and System, 4, 207–219.MATHCrossRefMathSciNetGoogle Scholar
  2. BORTOLAN, G., y DEGANI, R. (1985): ≪A Review of Some Methods for Ranking Fuzzy Subsets≫,Fuzzy Sets and System, 10, 57–63.MathSciNetGoogle Scholar
  3. CAMPOS, L. (1986):Modelos de la PL Difusa para la Resolución de Juegos Matriciales Imprecisos, Tesis Doctoral, Universidad de Granada.Google Scholar
  4. CHANG, W. (1981): ≪Ranking of Fuzzy Utilities with Triangular Membership Functions≫,Proc. Int. Conf. on Policy Analysis and Information Systems, 263–272.Google Scholar
  5. DELGADO, M.; VERDEGAY, J. L., y VILA, M. A. (1987): ≪A Procedure for Ranking Fuzzy Numbers≫, en prensa enFuzzy Sets and Systems.Google Scholar
  6. DELGADO, M.; VERDEGAY, J. L., y VILA, M. A. (1987): ≪Imprecise Costs in Mathematical Programming Problems≫, en prensa enControl and Cybernetics.Google Scholar
  7. DUBOIS, D., y PRADE, H. (1980): ≪Fuzzy Sets and Systems≫,Theory and Applications, Academic Press.Google Scholar
  8. DUBOIS, D., y PRADE, H. (1983): ≪Ranking Fuzzy Numbers in the Setting of Possibility Theory≫,Inf. Sci., 30, 183–224.MATHCrossRefMathSciNetGoogle Scholar
  9. KACPRZYK, J., y ORLOVSKI, S. A., eds. (1987):Optimization Models Using Fuzzy Sets and Possibility Theory, D. Reidel Publishing Co.Google Scholar
  10. RAMIK J., y RIMANEK, J. (1985): ≪Inequality Relations between Fuzzy Numbers and its use in Fuzzy Optimization≫,Fuzzy Sets and Systems, 16, 123–138.MATHCrossRefMathSciNetGoogle Scholar
  11. TANAKA, H.; ISHIHASHI, H., y ASAI, K. (1984): ≪A Formulation of Fuzzy Linear Programming Problems based on Comparison of Fuzzy Numbers”,Control and Cybernetics, 13, 185–194.MATHMathSciNetGoogle Scholar
  12. YAGER, R. R. (1981): ≪A Procedure for Ordering Fuzzy Subsets of the Unit Interval≫,Inf. Sci. 24, 143–161.MATHCrossRefMathSciNetGoogle Scholar
  13. ZADEH, L. A. (1975): ≪The Concept of a Linguistic Variable and its Application to Approximate Reasoning. Partes I, II y III≫,Inf. Sci., 8, 199–249, 8, 301–357 y 9, 43–80.CrossRefMathSciNetGoogle Scholar
  14. ZADEH, L. A. (1978): ≪Fuzzy Sets as a Basis for a Theory of Possibility”,Fuzzy Sets and Systems, 1, 3–28.MATHCrossRefMathSciNetGoogle Scholar
  15. ZIMMERMANN, H. J. (1975): ≪Description and Optimization of Fuzzy Systems≫,Int. Jour. og General Systems, 2, 209–215.CrossRefGoogle Scholar

Copyright information

© SEIO 1989

Authors and Affiliations

  • Campos L. 
    • 1
  • Verdegay J. L. 
    • 1
  1. 1.Departamento de Ciencias de la Computación e Inteligencia ArtificialFacultad de Ciencias Universidad de GranadaGranadaSpaña

Personalised recommendations