Measuring uncertainty associated with convex sets of probability distributions: A new approach

Annual Conference of the North American Fuzzy Information Processing Society - NAFIPS

Volumn 2005, Issue , 2005, Pages 61-64

  Klir, George J ^a  

^a State University of New York at Binghamton   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DATA PROCESSING; INFORMATION ANALYSIS; INFORMATION THEORY; UNCERTAIN SYSTEMS;

GENERALIZED INFORMATION THEORY (GIT); INFORMATION-BASED UNCERTAINTY; UNCERTAINTY MEASUREMENT;

PROBABILITY DISTRIBUTIONS;

EID: 33744980674     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/NAFIPS.2005.1548508     Document Type: Conference Paper

References (27)

1. Abellan, J. and Moral, S. [2000], "A non-specificity measure for convex sets of probability distributions." Intern, J. of Uncertainty, Fuzziness and Knowledge-Based Systems, 8(3), pp. 357-367.
2. Abellan, J. and Moral.S. [2003], "Maximum of entropy for credal sets." Intern. J. of Uncertainty, Fuzziness, and Knowledge-Based Systems, 11(5), pp. 587-597.
3. Abellan, J. and Moral, S. [2004] "Range of entropy for credal sets." In: López-Diaz, M. et al. (eds.), Soft Methodology and Random Information Systems, Springer, Berlin and Heidelberg, pp.157-164.
4. Abellan, J. and Moral, S. [2005], "Difference of entropies as a non-specificity function on credal sets." Intern. J. of General Systems, 34(3).
5. Abellan, J. and Moral, S. [2005], "An algorithm that attains the maximum of entropy for order-2 capacities." Intern. J. of Uncertainty, Fuzziness, and Knowledge-Based Systems (in production).
6. Choquet, G. [1953-54], "Theory of capacities." Annales de L'Institut Fourier, 5, pp. 131-295.
7. Dubois, D. and Prade H. [1985], "A note on measures of specificity for fuzzy sets." Intern. J. of General Systems, 10(4), pp. 279-283.
8. Guiasu, S. [1977], Information Theory with Applications. McGraw-Hill, New York.
9. Halmos, P. R. [1950], Measure Theory. D.Van Nostrand, Princeton, NJ.
10. Harmanec D., Resconi, G., Klir, G. J. and Pan Y. [1996], "On the computation of uncertainty measure in Dempster-Shafer theory." Intern. J. of General Systems, 25(2), pp. 153-163.
11. Hartley, R. V. L [1928], "Transmission of information." The Bell System Technical J., 7(3),pp. 535-563.
12. Higashi, M. and Klir, G. J. [1983], "Measures of uncertainty and information based on possibility distributions," Intern. J. of General Systems, 9(1), pp. 43-58,
13. Kapur, J. N. [1994], Measures of Information and Their Applications. John Wiley, New York.
14. Kapur, J. N., Baciu, G. and Kesavan, H. K. [1995], "The MinMax information measure." Intern. J. of Systems Science, 26(1), pp. 1-12.
15. Klir, G. J. [1991], "Generalized information theory." Fuzzy Sets and Systems, 40(1), pp. 127-142.
16. Klir, G. J. [2001], "Foundations of fuzzy set theory and fuzzy logic: a historical overview." Intern. J. of General Systems, 30(2), pp.91-132.
17. Klir, G. J. [2004], "Generalized information theory: aims, results, and open problems." Reliability Engineering and System Safety, 85(1-3), pp. 21-38,
18. Klir, G. J. and Mariano, M. [1987], "On the uniqueness of possibilistic measure of uncertainty and information." Fuzzy Sets and Systems, 24(2), pp. 197-219.
19. Klir, G. J. and Smith, R. M. [2001], "On measuring uncertainty and uncertainty-based information: recent developments." Annals of Mathematics and Artificial Intelligent, 32(1), pp. 5-33.
20. Klir, G. J. and Wierman M.J. [1999], Uncertainty-Based Information: Elements of Generalized Information Theory (Second Edition). Physica-Verlag/Springer-Verlag, Heidelberg and New York.
21. Klir, G. J. and Yuan, B. [1995], Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, PTR, Upper Saddle River, NJ.
22. Ramer, A. [1987], "Uniqueness of information measure in the theory of evidence." Fuzzy Sets and Systems, 24(2), pp. 183-196.
23. Shafer G. [1976], A Mathematical Theory of Evidence. Princeton Univ. Press, Princeton, NJ.
24. Shannon, C. E. [1948], "The mathematical theory of communication." The Bell System Technical J.,21, pp. 379-423, 623-656.
25. Smith, R. M. [2000], Generalized Information Theory: Resolving Some Old Questions and Opening Some New Ones. PhD. Dissertation, Binghamton University - SUNY, Binghamton.
26. Wang, Z. and Klir, G. J. [1992], Fuzzy Measure Theory. Plenum Press, New York.
27. Weichselberger, K. and Pöhlmann, S. [1990], A Methodology for Uncertainty in Knowledge-Based Systems. Springer-Verlag, New York.