Journal
INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS
Volume 5, Issue 2, Pages 211-224Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s13042-012-0126-4
Keywords
Bilevel linear programming; Random fuzzy variable; Stackelberg solutions; Possibility; Value at risk
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Funding
- Grants-in-Aid for Scientific Research [24510190, 22240030, 21330048] Funding Source: KAKEN
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This article considers bilevel linear programming problems where random fuzzy variables are contained in objective functions and constraints. In order to construct a new optimization criterion under fuzziness and randomness, the concept of value at risk and possibility theory are incorporated. The purpose of the proposed decision making model is to optimize possibility-based values at risk. It is shown that the original bilevel programming problems involving random fuzzy variables are transformed into deterministic problems. The characteristic of the proposed model is that the corresponding Stackelberg problem is exactly solved by using nonlinear bilevel programming techniques under some convexity properties. A simple numerical example is provided to show the applicability of the proposed methodology to real-world hierarchical problems.
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