Discrete optimization algorithms and problems of decision making in a fuzzy environment

Nonlinear Analysis: Hybrid Systems

Volumn 1, Issue 4, 2007, Pages 593-602

  Araujo, Whester J ^a   Berredo, Roberto C ^b   Ekel, Petr Ya ^a   Palhares, Reinaldo M ^c  

^a PONTIFICAL CATHOLIC UNIVERSITY OF MINAS GERAIS   (Brazil)

^b CEMIG Distribution SA   (Brazil)

^c FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

Author keywords

Discrete optimization; Fuzzy coefficients; Fuzzy preference relations; Interrelated models; Multiobjective decision making

Indexed keywords

EID: 36549039560     PISSN: 1751570X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nahs.2006.03.005     Document Type: Article

References (33)

1. Ausiello G., Crescenzi P., Gambosi G., Kan V., Marchetti-Spaccamela A., and Protasi M. Complexity and Approximation (1999), Springer, Berlin
2. Band-Jensen J., Gutin G., and Yeo A. When the greedy algorithm fails. Discrete Optimization 1 (2004) 121-127
3. Berredo R.C., Ekel P.Ya., and Palhares R.M. Fuzzy preference relations in models of decision making. Nonlinear Analysis TMA 63 (2005) 735-741
4. Berzin E.A. Optimal Resource Allocation and Elements of System Synthesis (1974), Sovetskoe Radio, Moscow (in Russian)
5. Chen S.J., and Hwang C.L. Multiple Attribute Decision Making: Methods and Applications (1992), Springer, New York
6. Cheng C.H. A new approach for ranking fuzzy numbers by distance methods. Fuzzy Sets and Systems 95 (1998) 307-313
7. Cormen T.H., Leiserson C.E., and Rivest R.L. Introduction to Algorithms (1990), MIT Press, Cambridge, Massachusetts
8. Dobson G. Worst-case analysis of greedy heuristics for integer programming with nonnegative data. Mathematics of Operations Research 7 (1982) 515-531
9. Dubois D., and Prade H. Fuzzy real algebra: Some results. Fuzzy Sets and Systems 2 (1979) 327-348
10. Dubois D., and Prade H. Inverse operations for fuzzy numbers. In: Sanches E., and Gupta M.M. (Eds). Proceedings of the IFAC Symposium on Fuzzy Information, Knowledge Representation and Design Analysis (1984), Pergamon, Oxford 18-38
11. Ekel P.Ya. Models and Methods of Discrete Optimization of Power Supply Systems (1990), KPI, Kiev (in Russian)
12. Ekel P.Ya. Methods of decision making in fuzzy environment and their applications. Nonlinear Analysis TMA 47 (2001) 979-990
13. Ekel P.Ya. Fuzzy sets and models of decision making. International Journal of Computers and Mathematics with Applications 44 (2002) 863-875
14. Ekel P., Pedrycz W., and Schinzinger R. A general approach to solving a wide class of fuzzy optimization problems. Fuzzy Sets and Systems 97 (1998) 49-66
15. Ekel P.Ya., and Popov V.A. Consideration of the uncertainty factor in problems of modelling and optimizing electrical networks. Power Engineering 23 (1985) 45-52
16. Ekel P.Ya., Silva M.R., Schuffner Neto F.H., and Palhares R.M. Fuzzy preference modeling and its application to multiobjective decision making. International Journal of Computers and Mathematics with Applications 52 (2006) 179-196
17. Fodor J., and Roubens M. Fuzzy Preference Modelling and Multicriteria Decision Support (1994), Kluwer, Boston
18. Galperin E.A., and Ekel P.Ya. Synthetic realization approach to fuzzy global optimization via gamma algorithm. Mathematical and Computer Modelling 41 (2005) 1457-1468
19. Herrera F., and Verdegay J.L. Three models of fuzzy integer linear programming. European Journal of Operations Research 83 (1995) 581-593
20. Herrera F., and Verdegay J.L. Fuzzy Boolean programming problems with fuzzy costs: A general study. Fuzzy Sets and Systems 81 (1996) 57-76
21. Horiuchi K., and Tamura N. VSOP fuzzy numbers and their fuzzy ordering. Fuzzy Sets and Systems 93 (1998) 197-210
22. Hu T.C. Integer Programming and Network Flows (1969), Addison-Wesley, New York
23. Ibaraki T. Integer programming formulation of combinatorial optimization. Discrete Mathematics 16 (1976) 39-42
24. Korbut A.A., and Finkelshtein Yu.Yu. Aproximate methods of discrete programming. Soviet Journal of Computer and System Sciences 22 (1984) 155-167 Printed in the USA
25. Lee-Kwang H. A method for ranking fuzzy numbers and its application to decision-making. IEEE Transactions on Fuzzy Systems 7 (1999) 677-685
26. Orlovsky S.A. Decision making with a fuzzy preference relation. Fuzzy Sets and Systems 3 (1978) 155-167
27. Orlovsky S.A. Problems of Decision Making with Fuzzy Information (1981), Nauka, Moscow (in Russian)
28. Papadimitrou C.H., and Steiglitz K. Combinatorial Optimization: Algorithms and Complexity (1982), Prentice-Hall, Englewood Cliffs
29. Pedrycz W., and Gomide F. An Introduction to Fuzzy Sets: Analysis and Design (1998), MIT Press, Cambridge, Massachusetts
30. Saaty T.L. Optimization in Integers and Related Extremal Problems (1970), McGraw-Hill, New York
31. Taha H.A. Operations Research: An Introduction (1982), Macmillan, New York
32. Wang X., and Kerre E.E. Reasonable properties for the ordering of fuzzy quantities (I), (II). Fuzzy Sets and Systems 118 (2001) 375-405
33. Zorin V.V., and Ekel P.Ya. Discrete-optimization methods for electrical supply systems. Power Engineering 18 (1980) 19-30