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Fuzzy Multiobjective LP

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Monte Carlo Methods in Fuzzy Optimization

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 222))

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Introduction

This chapter continues Chapters 7 and 8. However now we have multiple objective functions we wish to maximize. We first discuss the general multiobjective fully fuzzified linear program in the next section. Then we study an example problem in Section 9.3. We have previously obtained an approximate fuzzy solution to this type of problem using an evolutionary algorithm [2]. In Section 9.4 we will apply our fuzzy Monte Carlo method to the problem to generate another approximate solution. Unfortunately, we will be unable to compare our Monte Carlo solution to our previous solution because we now are forced to use a different method of evaluating fuzzy inequalities.

Fuzzy multiobjective linear programming has also (along with fuzzy linear programming) become a large area of research. A few recent references to this topic are the papers ([1],[3],[6],[7],[9],[10],[16],[17]) and books (or articles in these books) ([4],[5],[8],[11]-[15]).

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References

  1. Ammar, E.E., Kassem, M.A.E.-H.: On Stability Analysis of Multicriteria LP Problems with Fuzzy Parameters. Fuzzy Sets and Systems 82, 331–334 (1996)

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  2. Buckley, J.J., Feuring, T., Hayashi, Y.: Multiobjective Fully Fuzzified Linear Programming. Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems 9, 605–622 (2001)

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  3. Cadenas, J.M., Verdegay, J.L.: Using Ranking Functions in Multiobjective Fuzzy Linear Programming. Fuzzy Sets and Systems 111, 47–53 (2000)

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  4. Carlsson, C., Fuller, R.: Fuzzy Reasoning in Decision Making and Optimization. Physica-Verlag, Heidelberg (2002)

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  5. Ehrgott, M., Gandibleux, X.: Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys. Kluwer Academic Press, Norwell, Mass. (2002)

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  6. Fuller, R., Carlsson, C.: Fuzzy Multiple Criteria Decision Making: Recent Developments. Fuzzy Sets and Systems 78, 139–153 (1996)

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  7. Gen, M., Ida, K., Kobuchi, R.: Neural Network Techniques for Fuzzy Multiobjective Linear Programming. Computers and Industrial Engineering 35, 543–546 (1998)

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  8. Gen, M., Cheng, R.: Genetic Algorithms and Engineering Optimization. Wiley Interscience, N.Y. (1999)

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  9. Phruksaphanrat, B., Ohsato, A.: Linear Coordination Method for Fuzzy Multi-Objective Linear Programming Problems with Convex Polyhedral Membership Functions. Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems 12, 269–285 (2004)

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  12. Sakawa, M.: Large Scale Interactive Fuzzy Multiobjective Programming. Springer, Heidelberg (2000)

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  13. Sakawa, M.: Genetic Algorithms and Fuzzy Multiobjective Optimization. Kluwer Academic Press, Norwell, Mass. (2001)

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  14. Tanino, T., Tanaka, T., Inuiguichi, M.: Multi-Objective Programming and Goal Programming: Theory and Applications. Springer, Heidelberg (2003)

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  15. Trzaskalik, T., Michnik, J. (eds.): Multiple Objective and Goal Programming. Physica-Verlag, Heidelberg (2002)

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  16. Wang, H.-F., Wang, M.-L.: A Fuzzy Multiobjective Linear Programming. Fuzzy Sets and Systems 86, 61–72 (1997)

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  17. Yu, C.S., Li, H.L.: Method for Solving Quasi-Concave and Non-Concave Fuzzy Multi-Objective Programming Problems. Fuzzy Sets and Systems 122, 205–227 (2001)

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  18. Zeleny, M.: Multiple Criteria Decision Making. McGraw Hill, N.Y. (1982)

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Authors and Affiliations

  1. Mathematics Department University of Alabama at Birmingham Birmingham, AL 35294, USA

    James J. Buckley

  2. Department of Computer and Information Sciences University of Alabama at Birmingham Birmingham, AL 35294, USA

    Leonard J. Jowers

Authors
  1. James J. Buckley
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  2. Leonard J. Jowers
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© 2007 Springer-Verlag Berlin Heidelberg

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Buckley, J.J., Jowers, L.J. (2007). Fuzzy Multiobjective LP. In: Monte Carlo Methods in Fuzzy Optimization. Studies in Fuzziness and Soft Computing, vol 222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76290-4_9

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  • DOI: https://doi.org/10.1007/978-3-540-76290-4_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76289-8

  • Online ISBN: 978-3-540-76290-4

  • eBook Packages: EngineeringEngineering (R0)

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