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Uncertain Multiobjective Programming as a Game Against Nature

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Interactive Fuzzy Optimization

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 368))

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Abstract

We consider a multiobjective linear program whose parameters have uncertain values. We first present a method of modelling the uncertainty, based on t-norms and co-t-norms, which contains possibility theory and probability theory as special cases. We then present a procedure for modelling the decision problem, which is independent of the uncertainty model, based on a game against Nature.

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References

  • Bellman, R.E. and L.A. Zadeh (1970) Decision-making in a Fuzzy Environment. Management Science 17, 141–164.

    Article  Google Scholar 

  • Buckley, J.J. (1989) Modelling Uncertainty in Operations Research: the Discrete Case. In J.L. Verdegay and M. Delgado (Eds.): Interfaces Between Artificial Intelligence and Operations Research, Verlag TÃœV Rheinland, Köln, W. Germany, pp. 13–33.

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  • Buckley, J.J. (1990a) Stochastic Versus Possibilistic Programming. Fuzzy Sets and Systems 34, 173–177.

    Article  Google Scholar 

  • Buckley, J.J. (1990b) Stochastic Versus Possibilistic Multiobjective Programming. In R. Slowinski and J. Teghem (Eds.): Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming Under Uncertainty, Kluwer Academic Publishers, Dordrecht (to appear).

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  • Buckley, J.J. (1990c) A General Theory of Uncertainty Based on Co-t-Norms. Fuzzy Sets and Systems (under review).

    Google Scholar 

  • Geoffrion, A.M. (1968) Proper Efficiency and the Theory of Vector Maximization. J. Math. Anal. Appl. 22, 618–630.

    Article  Google Scholar 

  • R. D. Luce and H. Raiffa (1957) Games and Decisions. Wiley, New York.

    Google Scholar 

  • Sugeno, M. (1974) Theory of Fuzzy Integrals at its Applications. Ph.D. Thesis, Tokyo Institute of Technology, Tokyo.

    Google Scholar 

  • L.A. Zadeh (1975) The Concept of a Linguistic VAriable and its Application to Approximate Reasoning 1, Info. Sciences 8, 199–249.

    Article  Google Scholar 

  • L.A. Zadeh (1978) Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets and Systems 1, 3–28.

    Article  Google Scholar 

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© 1991 Springer-Verlag Berlin Heidelberg

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Buckley, J.J. (1991). Uncertain Multiobjective Programming as a Game Against Nature. In: Fedrizzi, M., Kacprzyk, J., Roubens, M. (eds) Interactive Fuzzy Optimization. Lecture Notes in Economics and Mathematical Systems, vol 368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45700-5_8

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  • DOI: https://doi.org/10.1007/978-3-642-45700-5_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54577-4

  • Online ISBN: 978-3-642-45700-5

  • eBook Packages: Springer Book Archive

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