Two-objective method for crisp and fuzzy interval comparison in optimization

Computers and Operations Research

Volumn 33, Issue 1, 2006, Pages 115-131

  Sevastjanov, Pavel ^a   Róg, Pawel ^a  

^a CZESTOCHOWA UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Crisp interval; Fuzzy interval; Interval comparison; Optimization; Probabilistic approach

Indexed keywords

FUNCTIONS; NUMBER THEORY; OPTIMIZATION; PROBABILITY; PROBLEM SOLVING; RISK MANAGEMENT;

CRISP INTERVAL; FUZZY INTERVAL; INTERVAL COMPARISONS; PROBABILISTICS APPROACH;

FUZZY CONTROL;

EID: 21544477274     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cor.2004.07.002     Document Type: Article

References (30)

1. E.R. Hansen Global optimization using interval analyses 1992 Marcel Dekker New York
2. L. Jaulin, M. Kieffin, O. Didrit, and E. Walter Applied interval analysis 2001 Springer London
3. S.M. Baas, and H. Kwakernaak Rating and ranking multiple-aspect alternatives using fuzzy sets Automatica 13 1977 47 58
4. H. Ishihashi, and M. Tanaka Multiobjective programming in optimization of the interval objective function European Journal of Operational Research 48 1990 219 225
5. S. Chanas, and D. Kuchta Multiobjective programming in optimization of the interval objective functions - a generalized approach European Journal of Operational Research 94 1996 594 598
6. Moore RE. Interval analysis. Englewood Cliffs, NJ: Prentice-Hall; 1966.
7. Z. Kulpa. Diagrammatic representation for a space of intervals. Machine Graphics and Vision 1997;6(1):5-24.
8. S. Hielpern Representation and application of fuzzy numbers Fuzzy Sets and Systems 91 1997 259 268
9. D. Dubois, and H. Prade Ranking of fuzzy numbers in the setting of possibility theory. Information Sciences 30 1983 183 224
10. R.R. Yager A procedure for ordering fuzzy subsets of the unit interval Information Sciences 24 1981 143 161
11. R.R. Yager On ranking fuzzy numbers using valuations International Journal of Intelligent Systems 14 1999 1249 1268
12. H. Rommelfanger Fuzzy decision support-system 1994 Springer Berlin
13. R.R. Yager, and M. Detyniecki Ranking fuzzy numbers using α -weighted valuations International Journal of Uncertainty, Fuzziness and Knowledge Based Systems 8 2000 573 591
14. G. Bartolan, and R. Degani A review of some methods for ranking fuzzy subsets Fuzzy Sets and Systems 15 1985 1 19
15. G. Facchinetti, R.G. Ricci, and S. Muzzioli Note on ranking fuzzy triangular numbers International Journal of Intelligent Systems 13 1998 613 622
16. D. Dubois, and H. Prade Fuzzy numbers an overview J.C Bezdek Analysis of fuzzy information vol. 2 1988 CRC-Press Boca Raton 3 39
17. W. Hauke Using Yager's t -norms for aggregation of fuzzy intervals Fuzzy Sets and Systems 101 1999 59 65
18. D.Y. Choi, and K.W. Oh Asa and its application to multi-criteria decision making Fuzzy Sets and Systems 114 2000 89 102
19. H.S. Shih, and E.S. Lee Compensatory fuzzy multiple level decision making Fuzzy Sets and Systems 114 2000 71 87
20. R. Yager Multiple objective decision-making using fuzzy sets International Journal of Man-Machine Studies 9-14 1979 375 382
21. D. Dubois, and J.L. Koenig Social choice axioms for fuzzy set aggregation Fuzzy Sets and Systems 43 1991 257 274
22. R. Luus, and T. Jaakola Optimization by direct search and systematic reduction of size of search region AIChE Journal 19 1973 760 766
23. D. Wadman, M. Schneider, and E. Schnaider On the use of interval mathematics in fuzzy expert system International Journal of Intelligent Systems 9 1994 241 259
24. R.R. Yager, M. Detyniecki, and B. Bouchon-Meunier A context-dependent method for ordering fuzzy numbers using probabilities Information Sciences 138 2001 237 255
25. P. Sevastjanov, and A. Venberg Modelling and simulation of power units work under interval uncertainty Energy 3 1998 66 70 [in Russian]
26. P.V. Sevastjanov, and P. Róg A probabilistic approach to fuzzy and interval ordering Task Quarterly. Special Issue Artificial and Computational Intelligence 7 1 2003 147 156
27. P. Sevastianov, P. Róg, and K. Karczewski A probabilistic method for ordering group of intervals Computer Science 2 2 2002 45 53
28. P. Sevastianov, P. Róg, and A. Venberg The constructive numerical method of interval comparison Proceedings of the International Conference on PPAM'01, Naleczow 2001 756 761
29. Wang X, Kerre EE. Reasonable properties for the ordering of fuzzy quantities (I), (II). Fuzzy Sets and Systems 2001; 112:375-85, 387-405.
30. T. Bayes An assay toward solving a problem in the doctrine of chances Philosophical Transactions of the Royal Society (London) 53 1763 370 418