In the dissertation the solution approaches for different fuzzy optimization problems are presented. The single-level optimization problem with fuzzy objective is solved by its reformulation into a biobjective optimization problem. A special attention is given to the computation of the membership function of the fuzzy solution of the fuzzy optimization problem in the linear case. Necessary and sufficient optimality conditions of the the convex nonlinear fuzzy optimization problem are derived in differentiable and nondifferentiable cases. A fuzzy optimization problem with both fuzzy objectives and constraints is also investigated in the thesis in the linear case. These solution approaches are applied to fuzzy bilevel optimization problems.
In the case of bilevel optimization problem with fuzzy objective functions, two algorithms are presented and compared using an illustrative example. For the case of fuzzy linear bilevel optimization problem with both fuzzy objectives and constraints k-th best algorithm is adopted.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:105-qucosa-106378 |
| Date | 26 February 2013 |
| Creators | Ruziyeva, Alina |
| Contributors | TU Bergakademie Freiberg, Mathematik und Informatik, Prof. Dr. Stephan Dempe, Prof. Dr. Stephan Dempe, Prof. Dr. Andreas Fischer |
| Publisher | Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola" |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf |
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