Solving large-scale fuzzy and possibilistic optimization problems

Fuzzy Optimization and Decision Making

Volumn 4, Issue 4, 2005, Pages 257-278

  Lodwick, Weldon A ^a   Bachman, Katherine A ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

Fuzzy optimization; Possibilistic optimization; Surprise functions

Indexed keywords

NONLINEAR PROGRAMMING; OPTIMIZATION; PROBLEM SOLVING; RADIOTHERAPY;

LARGE-SCALE PROBLEMS; OPTIMIZATION PROBLEM;

FUZZY SETS;

EID: 26844450209     PISSN: 15684539     EISSN: 15732908     Source Type: Journal    
DOI: 10.1007/s10700-005-3663-4     Document Type: Article

References (20)

1. Bellman, R. E. and L. A. Zadeh, (1970). "Decision-Making in a Fuzzy Environment," Management Science, Serial B, 17, 141-164.
2. Censor, Y., M. Altschuler, and W. Powlis (1988). "A Computational Solution of the Inverse Problem in Radiation Therapy Treatment Planning," Applied Mathematics and Computation 25, 57-87.
3. Cormack, A. M. (1995). "Some Early Radiotherapy Optimization Work," International Journal of Imaging Systems and Technology 6, 2-5.
4. Cormack, A. M. and E. T. Quinto (1990). "The Mathematics and Physics of Radiation dose Planning Using X-rays," Contemporary Mathematics 113, 41-55.
5. Dubois, D. and H. Prade (1997). "The Three Semantics of Fuzzy Sets," Fuzzy Sets and Systems 90, 141-150.
6. Jamison, K. D. and W. A. Lodwick(1999). "Minimizing Unconstrained Fuzzy Functions," Fuzzy Sets and Systems 103, 457-464.
7. Jamison, K. D. and W. A. Lodwick (2001). "Fuzzy Linear Programming Using Penalty Method," Fuzzy Sets and Systems 119, 97-110.
8. Jamison, K. D. and W. A. Lodwick (2002). "The Construction of Consistent Possibility and Necessity Measures," Fuzzy Sets and Systems 132(1), 1-10.
9. Kaymak, U. and J. M. Sousa (2003) "Weighting of Constraints in Fuzzy Optimization," Constraints 8, 61-78.
10. Klir, G. J. and B. Yuan (1995). Fuzzy Sets and Fuzzy Logic. Upper Saddle River, NJ: Prentice Hall.
11. Lodwick, W. A. and K. D. Jamison (1997). "A computational method for fuzzy optimization." In Ayyub, Bilal and Gupta, Madan (eds.), Uncertainty Analysis in Engineering and Sciences; Fuzzy Logic, Statistics, and Neural Network Approach. Boston: Kluwer Academic Publishers.
12. Lodwick, W. A. and K. D. Jamison (1997). "Interval Methods and Fuzzy Optimization," International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 5(3), 239-249.
13. Lodwick, W. A. and K. D. Jamison (2004). "Theory and Semantics of Fuzzy and Possibilistic Optimization," UCD/CCM Report No. 215.
14. Lodwick, W. A., S. McCourt, F. Newman, and S. Humphries (1998). "Optimization Methods for Radiation Therapy Plans." In C. Borgers and F. Natterer (eds.), IMA Volumes in Mathematics and its Applications, Computational Radiology and Imaging: Therapy and Diagnosis. New York: Springer-Verlag.
15. Lodwick, W. A., A. Neumaier, and F. Newman (2001). "Optimization Under Uncertainty: Methods and Applications in Radiation Therapy," Proceedings 10th IEEE International Conference on Fuzzy Systems 2001 3, 1219-1222.
16. Neumaier, A. (2003). "Fuzzy Modeling in Terms of Surprise," Fuzzy Sets and Systems 135(1), 21-38.
17. Tanaka, H., T. Okuda, and K. Asai (1974). "On Fuzzy Mathematical Programming," Journal of Cybernetics 3, 37-46.
18. Tanaka, H. and K. Asai (1984). "Fuzzy linear programming problems with fuzzy numbers," Fuzzy Sets and Systems 13, 1-10.
19. Zadeh, L. A. (1978). "Fuzzy Sets as a Basis for a Theory of Possibility," Fuzzy Sets and Systems 1, 3-28.
20. Zimmermann, H. (1976). "Description and Optimization of Fuzzy Systems," International J. of General Systems 2, 209-215.