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Relations among efficient solutions in uncertain multiobjective programming

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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.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (Nos. 71501184 and 61503405).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, P. R. China

    Mingfa Zheng & Yuan Yi

  2. College of Materiel Management and Safety Engineering, Air Force Engineering University, Xi’an, 710051, China

    Zutong Wang

  3. State Key Laboratory of Complex System Simulation, Beijing Institute of System Engineering, Beijing, China

    Tianjun Liao

Authors
  1. Mingfa Zheng
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  2. Yuan Yi
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  3. Zutong Wang
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  4. Tianjun Liao
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Correspondence to Yuan Yi.

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Zheng, M., Yi, Y., Wang, Z. et al. Relations among efficient solutions in uncertain multiobjective programming. Fuzzy Optim Decis Making 16, 329–357 (2017). https://doi.org/10.1007/s10700-016-9252-x

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