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Fuzzy Random Dependent-Chance Bilevel Programming with Applications

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Advances in Neural Networks – ISNN 2007 (ISNN 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4492))

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Abstract

In this paper, a two-level decentralized decision-making problem is formulated as fuzzy random dependent-chance bilevel programming. We define the fuzzy random Nash equilibrium in the lower level problem and the fuzzy random Stackelberg-Nash equilibrium of the overall problem. In order to find the equilibria, we propose a hybrid intelligent algorithm, in which neural network, as uncertain function approximator, plays a crucial role in saving computing time, and genetic algorithm is used for optimization. Finally, we apply the fuzzy random dependent-chance bilevel programming to hierarchical resource allocation problem for illustrating the modelling idea and the effectiveness of the hybrid intelligent algorithm.

This work was supported by National Natural Science Foundation of China (No.70601034) and Research Foundation of Renmin University of China.

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References

  1. Aiyoshi, E., Shimizu, K.: Hierarchical decentralized system and its new sollution by a barrier method. IEEE Transactions on System, Man, and Cybernetics 11, 444–449 (1981)

    Article  MathSciNet  Google Scholar 

  2. Bard, J.F., Plummer, J., Sourie, J.C.: A bilevel programming approach to determining tax credits for biofuel production. European Journal of Operational Research 120, 30–46 (2000)

    Article  MATH  Google Scholar 

  3. Ben-Ayed, O., Blair, C.E.: Computational difficulties of bilevel linear programming. Operations Research 38, 556–560 (1990)

    MATH  MathSciNet  Google Scholar 

  4. Bracken, J., McGill, J.M.: Mathematical programs with optimization problems in the constraints. Operations Research 21, 37–44 (1973)

    MATH  MathSciNet  Google Scholar 

  5. Bracken, J., McGill, J.M.: A method for solving Mathematical programs with nonlinear problems in the constraints. Operations Research 22, 1097–1101 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  6. Candler, W., Fortuny-Amat, W., McCarl, B.: The potential role of multi-level programming in agricultural economics. American Journal of Agricultural Economics 63, 521–531 (1981)

    Article  Google Scholar 

  7. Clark, P.A., Westerberg, A.: Bilevel programming for chemical process design—I. Fundamentals and algorithms. Computer and Chemical Engineering 14, 87–97 (1990)

    Article  Google Scholar 

  8. Cybenko, G.: Approximations by superpositions of a sigmoidal function. Mathematics of Control, Signals and Systems 2, 183–192 (1989)

    Article  MathSciNet  Google Scholar 

  9. Dempe, S.: Foundations of bilevel programming. Kluwer Academic Publishers, Dordrecht (2002)

    MATH  Google Scholar 

  10. Gao, J., Liu, B.: New primitive chance measures of fuzzy random event. International Journal of Fuzzy Systems 3, 527–531 (2001)

    MathSciNet  Google Scholar 

  11. Gao, J., Liu, B., Gen, M.: A hybrid intelligent algorithm for stochastic multilevel programming. IEEJ Transactions on Electronics, Information and Systems 124-C, 1991–1998 (2004)

    Article  Google Scholar 

  12. Gao, J., Liu, B.: On crisp equivalents of fuzzy chance-constrained multilevel programming. In: Proceedings of the 2004 IEEE International Conference on Fuzzy Systems, Budapest, Hungary, July 26-29, 2004, pp. 757–760 (2004)

    Google Scholar 

  13. Gao, J., Liu, B.: Fuzzy multilevel programming with a hybrid intelligent algorithm. Computer & Mathmatics with applications 49, 1539–1548 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  14. Gao, J., Liu, B.: Fuzzy dependent-chance multilevel programming with application to resource allocation problem. In: Proceedings of the 2005 IEEE International Conference on Fuzzy Systems, Reno, Nevada, May 22-25, 2005, pp. 541–545 (2005)

    Google Scholar 

  15. Gao, J., Liu, Y.: Stochastic Nash equilibrium with a numerical solution method. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3496, pp. 811–816. Springer, Heidelberg (2005)

    Google Scholar 

  16. Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2, 359–366 (1989)

    Article  Google Scholar 

  17. Kwakernaak, H.: Fuzzy random variables–I: Defnitions and theorems. Information Sciences 15, 1–29 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  18. Kwakernaak, H.: Fuzzy random variables–II: Algorithms and examples for the discrete case. Information Sciences 17, 253–278 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  19. Lee, E.S., Shih, H.S.: Fuzzy and Multi-level Decision Making. Springer, London (2001)

    Google Scholar 

  20. Liu, B.: Stackelberg-Nash equilibrium for multi-level programming with multiple followers using genetic algorithm. Comput. Math. Appl. 36, 79–89 (1998)

    Article  MATH  Google Scholar 

  21. Liu, B.: Dependent-chance programming in fuzzy environments. Fuzzy Sets and Systems 109, 95–104 (2000)

    Article  Google Scholar 

  22. Liu, B.: Fuzzy random chance-constrained programming. IEEE Transactions on Fuzzy Systems 9, 713–720 (2001)

    Article  Google Scholar 

  23. Liu, B.: Fuzzy random dependent-chance programming. IEEE Transactions on Fuzzy Systems 9, 721–726 (2001)

    Article  Google Scholar 

  24. Liu, B., Liu, Y.: Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems 10, 445–450 (2002)

    Article  Google Scholar 

  25. Liu, B.: A Survey of Entropy of Fuzzy Variables. Journal of Uncertain Systems 1, 1–10 (2007)

    Google Scholar 

  26. Liu, B.: Uncertainty Theory, 2nd edn. Springer, Berlin (2007)

    MATH  Google Scholar 

  27. Liu, Y., Gao, J.: Convergence criteria and convergence relations for sequences of fuzzy random variables. In: Wang, L., Jin, Y. (eds.) FSKD 2005. LNCS (LNAI), vol. 3613, pp. 321–331. Springer, Heidelberg (2005)

    Google Scholar 

  28. Liu, Y.: Convergent results about the use of fuzzy simulation in fuzzy optimization problems. IEEE Transactions on Fuzzy Systems 14(2), 295–304 (2006)

    Article  Google Scholar 

  29. Liu, Y., Gao, J.: The dependence of fuzzy variables with applications to fuzzy random optimization. International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, to be published

    Google Scholar 

  30. Patriksson, M., Wynter, L.: Stochastic mathematicl programs with equilibrium constraints. Operations research letters 25, 159–167 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  31. Sahin, K.H., Ciric, A.R.: A dual temperature simulated annealing approach for solving bilevel programming problems. Computers and Chemical Engineering 23, 11–25 (1998)

    Article  Google Scholar 

  32. Shimizu, K., Aiyoshi, E.: A new computational method for Stackelberg and min-max problems by use a penalty method. IEEE Transactions on Automatic Control 26, 460–466 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  33. Suh, S., Kim, T.: Solving nonlinear bilevel programming models of the equilibrium network desing problem: A comparative review. Annals Operations Research 34, 203–218 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  34. Vicente, L., Calamai, P.H.: Bilevel programming and multi-level programming: A bibliography review. Journal of Global Optimization 5 (1994)

    Google Scholar 

  35. Wen, U.P.: Linear bilevel programming problems—A review. Journal of the Operational Research Society 42, 125–133 (1991)

    Article  MATH  Google Scholar 

  36. Yang, H., Bell, M.G.H.: Transport bilevel programming problems: recent methodological advances. Transportation Research: Part B 35, 1–4 (2001)

    Article  Google Scholar 

  37. Zhao, R., Liu, B.: Renewal Process with Fuzzy Interarrival Times and Rewards. International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems 11, 573–586 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  38. Zhao, R., Tang, W.: Some Properties of Fuzzy Random Processes. IEEE Transactions on Fuzzy Systems 14(2), 173–179 (2006)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Economy,Industry and Business Management College, Chongqing University, Chongqing 400044, China

    Rui Liang

  2. School of Information, Renmin University of China, Beijing 100872, China

    Jinwu Gao

  3. Department of Mathematics, Josai University, Sakado, Saitama 350-0248, Japan

    Kakuzo Iwamura

Authors
  1. Rui Liang
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  2. Jinwu Gao
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  3. Kakuzo Iwamura
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Editor information

Derong Liu Shumin Fei Zengguang Hou Huaguang Zhang Changyin Sun

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Liang, R., Gao, J., Iwamura, K. (2007). Fuzzy Random Dependent-Chance Bilevel Programming with Applications . In: Liu, D., Fei, S., Hou, Z., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72393-6_32

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  • DOI: https://doi.org/10.1007/978-3-540-72393-6_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72392-9

  • Online ISBN: 978-3-540-72393-6

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