Maximum entropy membership functions for discrete fuzzy variables

Information Sciences

Volumn 179, Issue 14, 2009, Pages 2353-2361

  Gao, Xin ^a   You, Cuilian ^b  

^a TSINGHUA UNIVERSITY   (China)

^b HEBEI UNIVERSITY   (China)

Author keywords

Entropy; Expected value; Fuzzy variable; Genetic algorithm; Moment

Indexed keywords

EXPECTED VALUE; FUZZY VARIABLE; MAXIMUM ENTROPIES; MAXIMUM ENTROPY MODELS; MAXIMUM ENTROPY PRINCIPLES; MOMENT; NUMERICAL EXPERIMENTS; PARTIAL INFORMATIONS;

ENTROPY; FUZZY SETS; GENETIC ALGORITHMS; MICROCONTROLLERS;

MEMBERSHIP FUNCTIONS;

EID: 67349269941     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2009.03.010     Document Type: Article

References (30)

1. Bhandari D., and Pal N.R. Some new information measures for fuzzy sets. Information Sciences 67 (1993) 209-228
2. De Cooman G. Possibility theory I-III. International Journal of General Systems 25 (1997) 291-371
3. De Luca A., and Termini S. A definition of nonprobabilistic entropy in the setting of fuzzy sets theory. Information and Control 20 (1972) 301-312
4. Dubois D., and Prade H. Possibility Theory: An Approach to Computerized Processing of Uncertainty (1998), Plenum, New York
5. Kaufmann A. Introduction to the Theory of Fuzzy Subsets (1975), Academic Press, New York
6. Knopfmacher J. On measures of fuzziness. Journal of Mathematical Analysis and Applications 49 (1975) 529-534
7. Li P., and Liu B. Entropy of credibility distributions for fuzzy variables. IEEE Transactions on Fuzzy Systems 16 1 (2008) 123-129
8. Li X., and Liu B. A sufficient and necessary condition for credibility measures. International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems 14 5 (2006) 527-535
9. Li X., and Liu B. Maximum entropy principle for fuzzy variables. International Journal of Uncertainty Fuzziness & Knowledge-Based Systems 15 Supplement 2 (2007) 43-52
10. Liu B., and Liu Y.K. Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems 10 4 (2002) 445-450
11. Liu B. Uncertainty Theory: An Introduction to its Axiomatic Foundations (2004), Springer-Verlag, Berlin
12. Liu B. A survey of credibility theory. Fuzzy Optimization and Decision Making 5 4 (2006) 387-408
13. Liu B. A survey of entropy of fuzzy variables. Journal of Uncertain Systems 1 1 (2007) 4-13
14. Liu B. Uncertainty Theory. second ed. (2007), Springer-Verlag, Berlin
15. Loo S.G. Measures of fuzziness. Cybernetica 20 (1977) 201-210
16. Nahmias S. Fuzzy variables. Fuzzy Sets and Systems 1 (1978) 97-110
17. Pal N.R., and Pal S.K. Object-background segmentation using new definitions of entropy. IEE Proceedings E 136 (1989) 284-295
18. Pal N.R., and Pal S.K. Higher order fuzzy entropy and hybrid entropy of a set. Information Sciences 61 (1992) 211-231
19. Parkash O., Sharma P.K., and Mahajan R. New measures of weighted fuzzy entropy and their applications for the study of maximum weighted fuzzy entropy principle. Information Sciences 178 (2008) 2389-2395
20. Yager R.R. On measures of fuzziness and negation, Part I: Membership in the unit interval. International Journal of General Systems 5 (1979) 221-229
21. Yager R.R. On measures of fuzziness and negation, Part II: Lattices. Information and Control 44 (1980) 236-260
22. Yager R.R. Entropy and specificity in a mathematical theory of evidence. International Journal of General Systems 9 (1983) 249-260
23. Yager R.R. Measures of entropy and fuzziness related to aggregation operators. Information Sciences 82 (1995) 147-166
24. Yager R.R. On the entropy of fuzzy measures. IEEE Transactions on Fuzzy Systems 8 (2000) 453-461
25. You C., and Wen M. The entropy of fuzzy vectors. Computers and Mathematics with Applications 56 (2008) 1626-1633
26. Zadeh L.A. Fuzzy sets. Information and Control 8 (1965) 338-353
27. Zadeh L.A. Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications 23 (1968) 421-427
28. Zadeh L.A. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1 (1978) 3-28
29. Zadeh L.A. Toward a generalized theory of uncertainty (GTU) - an outline. Information Sciences 172 (2005) 1-40
30. Zadeh L.A. Is there a need for fuzzy logic. Information Sciences 178 (2008) 2751-2779