Relations among efficient solutions in uncertain multiobjective programming

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...

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Published in:Fuzzy optimization and decision making Vol. 16; no. 3; pp. 329 - 357
Main Authors: Zheng, Mingfa, Yi, Yuan, Wang, Zutong, Liao, Tianjun
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2017
Springer Nature B.V
Subjects:
Artificial Intelligence
Calculus of Variations and Optimal Control; Optimization
Decision making
Decision theory
Deviation
Efficiency
Mathematical Logic and Foundations
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Multiple objective analysis
Operations Research/Decision Theory
Optimization
Pareto optimum
Probability Theory and Stochastic Processes
Expected-value standard-deviation efficiency
Efficiency with belief degree
Uncertain multiobjective programming
Uncertainty theory
ISSN:1568-4539, 1573-2908
Online Access:Get full text
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Summary: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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ISSN:1568-4539
1573-2908
DOI:10.1007/s10700-016-9252-x