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Fuzzy information and combinatorial inequalities. (English) Zbl 0863.94041
Summary: Properties of information measures both in fuzzy theory and in the theory of evidence are closely related to combinatorial identities and inequalities. It is demonstrated how the study of information functions leads to new combinatorial results. Three cases are presented; 1) metric property of fuzzy information distance, 2) approximations of continuous fuzzy information, 3) maximum for a combined Dempster-Shafer evidence measure.

MSC:
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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References:
[1] D. Dubois, H. Prade: Possibility Theory. Plenum Press, New York 1988. · Zbl 0703.68004
[2] D. Dubois, H. Prade: Properties of measures of information in evidence and possibility theories. Fuzzy Sets Systems 21, (1987), 161 - 182. · Zbl 0633.94009 · doi:10.1016/0165-0114(87)90088-1
[3] M. Higashi, G. Klir: On the notion of distance representing information closeness. Internat. J. General Systems 9 (1983), 103 - 115. · Zbl 0498.94006 · doi:10.1080/03081078308960805
[4] M. Higashi, G.Klir: Measures of uncertainty and information based on possibility distributions. Internat. J. General Systems 8 (1982), 43 - 58. · Zbl 0497.94008 · doi:10.1080/03081078208960799
[5] G. Hardy J. Littlewood, G. Polya: Inequalities. Cambridge University Press, Cambridge 1934. · Zbl 0010.10703
[6] G. Klir: A principle of uncertainty and information invariance. Internat. J. General Systems 11 (1990), 249 - 276 . · Zbl 0703.94026 · doi:10.1080/03081079008935110
[7] G. Klir, M. Mariano: On the uniqueness of possibilistic measure of uncertainty and information. Fuzzy Sets Systems 2 (1987), 197 - 220. · Zbl 0632.94039 · doi:10.1016/0165-0114(87)90090-X
[8] A. Ramer: Structure of possibilistic information metrics and distances. Internat. J. General Systems 17(1990), 21 - 32, and 18 (1990), 1 - 10. · Zbl 0703.94002 · doi:10.1080/03081079008935093
[9] A. Ramer: Certain Inequalities Related to Rearrangements. Technical Report OU-PPI-TR-89-01, University of Oklahoma, Norman, OK 1989
[10] A. Ramer, L. Lander: Classification of possibilistic uncertainty and information functions. Fuzzy Sets Systems 24 (1987), 221 - 230. · Zbl 0637.94027 · doi:10.1016/0165-0114(87)90091-1
[11] G. Shafer: A Mathematical Theory of Evidence. Princeton University Press, Princeton 1976. · Zbl 0359.62002
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