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Towards a new strategy for solving fuzzy optimization problems

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Abstract

Fuzzy Optimization models and methods has been one of the most and well studied topics inside the broad area of Soft Computing. Particularly relevant is the field of fuzzy linear programming (FLP). Its applications as well as practical realizations can be found in all the real world areas. As FLP problems constitute the basis for solving fuzzy optimization problems, in this paper a basic introduction to the main models and methods in FLP is presented and, as a whole, Linear Programming problems with fuzzy costs, fuzzy constraints and fuzzy coefficients in the technological matrix are analyzed. But fuzzy sets and systems based optimization methods do not end with FLP, and hence in order to solve more complex optimization problems, fuzzy sets based Meta-heuristics are considered, and two main operative approaches described. Provided that these techniques obtain efficient and/or effective solutions, we present a fuzzy rule based methodology for coordinating Meta-heuristics and in addition, to provide intelligence, we propose a process of extraction of the knowledge to conduct the coordination of the system.

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References

  • Bellman R.E., Zadeh L.A. (1970) Decision making in a fuzzy environment. Management Science, 17(B(4): 141–164

    MathSciNet  Google Scholar 

  • Berthold M., Hand D.J. (2003) Intelligent data analysis: an introduction. Springer, New York

    Book  Google Scholar 

  • Blanco A., Pelta D., Verdegay J.L. (2002) A fuzzy valuation-based local search framework for combinatorial problems. Fuzzy Optimization and Decision Making 1: 177–193

    Article  MATH  MathSciNet  Google Scholar 

  • Bonissone, P. P., Cadenas, J. M., Garrido, M. C., & H ernandez, J. J. (2007). Minería de datos en el modelado de un sistema metaheurístico cooperativo: Una comparativa. V Congreso Español sobre Metaheursticas, Algoritmos Evolutivos y Bioinspirados, MAEB’2007, pp. 1–8.

  • Cadenas J.M., Verdegay J.L. (1997) Using fuzzy numbers in linear programming. IEEE Transactions on Systems, Man, and Cybernetic 27(B)(6): 1017–1022

    Google Scholar 

  • Cadenas, J. M., Garrido, M. C., Hernandez, L. D., & Muñoz, E. (2006). Towards the definition of a data mining process based in fuzzy sets for cooperative metaheuristic systems. 11th International Conference on Information Processing and Management of Uncertainty in Knowledgebased Systems, IPMU’2006, pp. 2828–2834.

  • Cadenas, J. M., Garrido, M. C., & Muñoz, E. (2007). A cooperative systems of metaheuristics. 7th International Conference on Hybrid Intelligent Systems, HIS 2007, pp. 120–125.

  • Campos L., Verdegay J.L. (1989) Linear programming problems and ranking of fyzzy numbers. Fuzzy Sets and Systems 32: 1–11

    Article  MATH  MathSciNet  Google Scholar 

  • Delgado M., Verdegay J.L., Vila M.A. (1987) Imprecise costs in mathematical programming problems. Control and Cybernet 16(2): 113–121

    MATH  MathSciNet  Google Scholar 

  • Delgado M., Verdegay J.L., Vila M.A. (1989) A general model for fuzzy linear programming. Fuzzy Sets and Systems 29: 21–29

    Article  MATH  MathSciNet  Google Scholar 

  • Dubois D., Prade H. (1983) Ranking of fuzzy numbers in the setting of possibility theory. Information Science 30: 183–244

    Article  MATH  MathSciNet  Google Scholar 

  • Fedrizzi M., Kacprzyk J., Verdegay J.L. (1991) A survey of fuzzy optimization and fuzzy mathematical programming. In: Fedrizzi M., Kacprzyk J., Roubens M. (eds) Interactive fuzzy optimization. Springer Verlag, Berlin, pp 15–28

    Google Scholar 

  • Ishibuchi H., Tanaka H. (1990) Multiobjective programming in optimization of the interval objective function. European Journal of Operational Research 48: 219–225

    Article  MATH  Google Scholar 

  • Pisinger D. (2005) Where are the hard knapsack problems?. Computer and Operations Research 32(9): 2271–2284

    Article  MATH  MathSciNet  Google Scholar 

  • Rommelfanger H., Hanuscheck R., Wolf J. (1990) Linear programming with fuzzy objectives. Fuzzy Sets and Systems 29: 31–48

    Article  MathSciNet  Google Scholar 

  • Sancho-Royo A., Verdegay J.L., Vergara E. (1999) Some practical problems in fuzzy sets-based DSS. MathWare and Soft Computing 2−3: 173–187

    Google Scholar 

  • Tanaka H., Okuda T., Asai K. (1974) On fuzzy mathematical programming. Journal of Cybernetics 3(4): 37–46

    Article  MathSciNet  Google Scholar 

  • Tanaka H., Ichihashi H., Asai F. (1984) A formulation of fuzzy linear programming problems based a comparison of fuzzy numbers. Control and Cybernet 13: 185–194

    MATH  MathSciNet  Google Scholar 

  • Verdegay, J. L. (1982). Fuzzy mathematical programming. In M. M. Gupta & E. Sanchez (Eds.), Fuzzy information and decision processes (pp. 231–237). North Holland: Elsevier Science.

  • Verdegay J.L., Vergara E. (2000) Fuzzy termination criteria in knapsack problem algorithms. Mathware and Soft Computing 2-3: 89–97

    Google Scholar 

  • Verdegay J.L., Vergara E. (2002) Fuzzy sets-based control rules for terminating algorithms. Computer Science Journal 10(1): 9–27

    MATH  Google Scholar 

  • Verdegay J.L., Yager R.R., Bonissone P.P. (2008) On heuristics as a fundamental constituent of soft computing. Fuzy Sets and Systems 159: 846–855

    Article  MathSciNet  Google Scholar 

  • Zadeh, L. A. (1975). The concept of a linguistic variable and its applications to approximate reasoning. Part I, Information sciences, 8, 199–249, Part II, Information sciences, 8, 301–357, Part III, Information sciences, 9, 43–80.

  • Zimmermann H.J. (1976) Description and optimization of fuzzy systems. International Journal of General Systems 2: 209–215

    Article  Google Scholar 

  • Zimmermann H.J. (1987) Fuzzy sets, decision making, and expert systems. Kluwer Academic Publishers, Boston

    Google Scholar 

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Authors and Affiliations

  1. Dept. Ingeniería de la Información y las Comunicaciones, Universidad de Murcia, Murcia, Spain

    J. M. Cadenas

  2. Dept. Ciencias de la Computación e Inteligencia Artificial, Universidad de Granada, Granada, Spain

    J. L. Verdegay

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  1. J. M. Cadenas
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  2. J. L. Verdegay
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Correspondence to J. M. Cadenas.

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Cadenas, J.M., Verdegay, J.L. Towards a new strategy for solving fuzzy optimization problems. Fuzzy Optim Decis Making 8, 231–244 (2009). https://doi.org/10.1007/s10700-009-9062-5

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