Relations among efficient solutions in uncertain multiobjective programming

Mingfa Zheng (), Yuan Yi (), Zutong Wang () and Tianjun Liao ()
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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

Fuzzy Optimization and Decision Making, 2017, vol. 16, issue 3, No 4, 329-357

Abstract: 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.

Keywords: Uncertainty theory; Uncertain multiobjective programming; Expected-value standard-deviation efficiency; Efficiency with belief degree (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10700-016-9252-x

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