Difference of entropies as a non-specificity function on credal sets

International Journal of General Systems

Volumn 34, Issue 3, 2005, Pages 201-214

  Abellán, Joaquín ^a   Moral, Serafín ^a,b  

^a UNIVERSITY OF GRANADA   (Spain)

^b Computer Science and Artificial Intelligence ^*  (Spain)

Author keywords

Credal sets; Entropy; Imprecise probabilities; Order 2 capacities; Theory of evidence; Uncertainty

Indexed keywords

CREDAL SETS; IMPRECISE PROBABILITIES; ORDER-2 CAPACITIES; THEORY OF EVIDENCE; UNCERTAINTY;

ENTROPY; FUNCTIONS; PROBABILITY; SEARCH ENGINES; SET THEORY; UNCERTAIN SYSTEMS;

ALGORITHMS;

EID: 27344435303     PISSN: 03081079     EISSN: 15635104     Source Type: Journal    
DOI: 10.1080/03081070500108609     Document Type: Review

References (20)

1. J. Abellán and S. Moral, "A non-specificity measure for convex sets of probability distributions", Int. J. Uncertain. Fuzz. Knowledge-Based Syst., 8, pp. 357-367, 2000.
2. J. Abellán and S. Moral, "Maximum of entropy for credal sets", Int. J. Uncertain. Fuzz. Knowledge-Based Syst., 11(5), pp. 1215-1225, 2003.
3. L.M. de Campos and M.J. Bolaños, "Characterization of fuzzy measures trough probabilities", Fuzzy Sets Syst., 31, pp. 23-36, 1989.
4. L.M. de Campos, J.F. Huete and S. Moral, "Probability intervals: a tool for uncertainty reasoning", Int. J. Uncertain. Fuzz. Knowledge-Based Syst., 2, pp. 167-196, 1994.
5. G. Choquet, "Théorie des capacités", Ann. Inst. Fourier, 5, pp. 131-292, 1953/54.
6. A.P. Dempster, "Upper and lower probabilities induced by a multivaluated mapping", Ann. Math. Statistic, 38, pp. 325-339, 1967.
7. D. Dubois and H. Prade, "A note on measures of specificity for fuzzy sets", Int. J. Gen. Syst., 10, pp. 279-283, 1985.
8. D. Harmanec and G.J. Klir, "Measuring total uncertainty in Dempster-Shafer theory: a novel approach", Int. J. Gen. Syst., 22, pp. 405-419, 1994.
9. J.N. Kapur, Measures of Information and Their Applications, Chapter 23. New York: John Wiley, 1994.
10. J.N. Kapur, G. Baciu and H.K. Kesavan, "The MinMax information measure", Int. J. Syst. Sci., 26(1), pp. 1-12, 1995.
11. G.J. Klir and R.M. Smith, "On measuring uncertainty and uncertainty-based information: recent developments", Ann. Math. Artif. Intell., 32, pp. 5-33, 2001.
12. G.J. Klir and M.J. Wierman, Uncertainty-Based Information, Physica-Verlag, 1998.
13. Y. Maeda and H. Ichihashi, "A uncertainty measure with monotonicity under the random set inclusion", Int. J. Gen. Syst., 21, pp. 379-392, 1993.
14. A. Meyerowitz, F. Richman and E.A. Walker, "Calculating maximum-entropy probabilities densities for belief functions", Int. J. Uncertain. Fuzz. Knowledge-Based Syst., 2, pp. 377-389, 1994.
15. G. Shafer, A Mathematical Theory of Evidence, Princeton: Princeton University Press, 1976.
16. C.E. Shannon, "A mathematical theory of communication", Bell Syst. Technical J., 27, pp. 379-423
17. see also Bell Syst. Technical J., 623-656, 1948.
18. R.M. Smith, "Generalize information theory: resolving some old questions and opening some new ones". Ph.D. dissertation, Binghamton: Binghamton University- SUNY, 2000.
19. P. Walley, Statistical Reasoning with Imprecise Probabilities, New York: Chapman and Hall, 1991.
20. R.R. Yager, "Entropy and specificity in a mathematical theory of evidence", Int. J. Gen. Syst., 9, pp. 249-260, 1983.