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Relations among efficient solutions in uncertain multiobjective programming

Author

Listed:
  • Mingfa Zheng

    (Xi’an Jiaotong University)

  • Yuan Yi

    (Xi’an Jiaotong University)

  • Zutong Wang

    (Air Force Engineering University)

  • Tianjun Liao

    (Beijing Institute of System Engineering)

Abstract

Based on uncertainty theory, this work deals with the relations among concepts of efficient solutions for uncertain multiobjective programming (UMOP) problems. Firstly, the UMOP model with uncertain vectors in objective functions is presented. Secondly, seven types of concepts of efficient solutions for the UMOP model, such as expected-value standard-deviation efficiency, expected-value properly efficiency, efficiency with belief degrees etc., are defined. Finally, the relations of these different efficiency concepts, especially the expected-value standard-deviation efficiency and efficiency with belief degrees, are established under certain conditions, and two numerical examples are given to illustrate these theoretical results. Our work helps to determine what types of efficient solutions are obtained by each of these concepts and also provides theoretical foundation for multiple attribute decision-making in uncertain systems.

Suggested Citation

  • Mingfa Zheng & Yuan Yi & Zutong Wang & Tianjun Liao, 2017. "Relations among efficient solutions in uncertain multiobjective programming," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 329-357, September.
    • Handle: RePEc:spr:fuzodm:v:16:y:2017:i:3:d:10.1007_s10700-016-9252-x
    DOI: 10.1007/s10700-016-9252-x
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    References listed on IDEAS

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    1. Ben Abdelaziz, Fouad & Masri, Hatem, 2010. "A compromise solution for the multiobjective stochastic linear programming under partial uncertainty," European Journal of Operational Research, Elsevier, vol. 202(1), pages 55-59, April.
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    6. Caballero, Rafael & Cerda, Emilio & del Mar Munoz, Maria & Rey, Lourdes, 2004. "Stochastic approach versus multiobjective approach for obtaining efficient solutions in stochastic multiobjective programming problems," European Journal of Operational Research, Elsevier, vol. 158(3), pages 633-648, November.
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    Cited by:

    1. Jin Peng & Bo Zhang & Lin Chen & Hui Li, 2024. "A survey on uncertain graph and uncertain network optimization," Fuzzy Optimization and Decision Making, Springer, vol. 23(1), pages 129-153, March.

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