Large Scale Interactive Fuzzy Multiobjective Programming Decomposition Approaches

Simultaneous considerations of multiobjectiveness, fuzziness and block angular structures involved in the real-world decision making problems lead us to the new field of interactive multiobjective optimization for large scale programming problems under fuzziness. The aim of this book is to introduce the latest advances in the new field of interactive multiobjective optimization for large scale programming problems under fuzziness on the basis of the author's continuing research. Special stress is placed on interactive decision making aspects of fuzzy multiobjective optimization for human-centered systems in most realistic situations when dealing with fuzziness. The book is intended for graduate students, researchers and practitioners in the fields of operations research, industrial engineering, management science and computer science.

1. Introduction.- 1.1 Introduction and historical remarks.- 1.2 Organization of the book.- 2. Mathematical Preliminaries.- 2.1 Fuzzy sets.- 2.2 Fuzzy numbers.- 2.3 Fuzzy decision.- 2.4 Multiobjective linear programming.- 2.5 Interactive multiobjective linear programming.- 2.6 Interactive fuzzy multiobjective linear programming.- 2.7 Genetic algorithms.- 3. The Dantzig-Wolfe Decomposition Method.- 3.1 Linear programming problems with block angular structures.- 3.2 Development of the decomposition algorithm.- 3.3 Initial feasible basic solution.- 3.4 Unbounded subproblem.- 3.5 Restricted master problem.- 4. Large Scale Fuzzy Linear Programming.- 4.1 Linear programming problems with block angular structures.- 4.2 Fuzzy goal and fuzzy constraints.- 4.3 Fuzzy linear programming.- 4.4 Numerical example.- 5. Large Scale Fuzzy Multiobjective Linear Programming.- 5.1 Multiobjective linear programming problems with block angular structures.- 5.2 Fuzzy goals.- 5.3 Fuzzy multiobjective linear programming.- 5.4 Interactive fuzzy multiobjective linear programming.- 6. Large Scale Multiobjective Linear Programming with Fuzzy Numbers.- 6.1 Introduction.- 6.2 Interactive multiobjective linear programming with fuzzy numbers.- 6.3 Interactive fuzzy multiobjective linear programming with fuzzy numbers.- 6.4 Conclusion.- 7. Genetic Algorithms with Decomposition Procedures.- 7.1 Introduction.- 7.2 Multidimensional 0–1 knapsack problems with block angular structures.- 7.3 Genetic algorithms with decomposition procedures.- 7.4 Numerical experiments.- 8. Large Scale Fuzzy Multiobjective 0–1 Programming.- 8.1 Multiobjective multidimensional 0–1 knapsack problems with block angular structures.- 8.2 Fuzzy goals.- 8.3 Fuzzy multiobjective 0–1 programming.- 8.4 Interactive fuzzymultiobjective 0–1 programming.- 9. Large Scale Interactive Multiobjective 0–1 Programming with Fuzzy Numbers.- 9.1 Introduction.- 9.2 Interactive multiobjective 0–1 programming with fuzzy numbers.- 9.3 Interactive fuzzy multiobjective 0–1 programming with fuzzy numbers.- 9.4 Conclusion.- 10. Further Research Directions.- 10.1 Large scale fuzzy multiobjective linear fractional programming.- 10.2 Large scale fuzzy multiobjective nonlinear programming.- References.