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On the unicity of Dempster rule of combination. (English) Zbl 0641.68159
Dempster has proposed a rule for the combination of uncertain items of information issued from several sources. This note proves the unicity of this rule under an independence assumption. The existence of alternative rules is stressed, some corresponding to different assumptions, other pertaining to different types of combination.

MSC:
68T99 Artificial intelligence
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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[1] Dempster, Ann. Math. Statist. 38 pp 325– (1967)
[2] and , ”A Statistical Approach to the Analysis and the Synthesis of Fuzzy Regions,” submitted to the Int. Conf. on Pattern Recognition, Paris, 1986.
[3] and , ”On Several Representations of an Uncertain Body of Evidence,” in Fuzzy information & Decision Processes, and , Eds., North-Holland, Amsterdam, 1982, pp. 167–181.
[4] and , Théorie des Possibilités, Applications à la Representation des Connaissances en Informatique, Masson, Paris, 1985.
[5] Dubois, Int. J. General Syst. 10 pp 279– (1985)
[6] Dubois, Inform. Sci. 36 pp 85– (1985)
[7] and , ”Combination and Propagation of Uncertainty with Belief Functions,” Proc. 9th Int. Conf. on Artificial Intelligence, Los Angeles, CA, 1985, 111–113.
[8] Dubois, Int. J. General Syst. (1986)
[9] Gordon, Artificial Intelligence 26 pp 323– (1985)
[10] , and , Foundations of Measurement, Academic, New York, 1971.
[11] Higashi, Int. J. General Syst. 9 pp 43– (1983)
[12] ”A Hybrid Uncertainty Theory.” Proc. 5th Int. Workshop Expert Systems and Their Applications, Avignon, France, 1985, pp. 1193–1201.
[13] A Mathematical Theory of Evidence, Princeton University Press, Princeton, NJ, 1976.
[14] ”Dempster Rule of Conditioning,” Unpublished manuscript, available at a Stanford University Seminar, January 22, 1979.
[15] ”Belief Functions and Possibility Measures,” in the Analysis of Fuzzy information, Ed., Boca Raton, FL, CRC Press, 1985.
[16] Yager, Int J. General Syst. 9 pp 249– (1983)
[17] ”Reasoning with Uncertainty for Expert Systems,” Proc. 9th Int. Conf. on Artificial Intelligence, Los Angeles, CA, 1985, pp. 1295–1297.
[18] Zadeh, Information & Cont. 8 pp 338– (1965)
[19] Zadeh, J. Math. Anal. & Appl. 23 pp 421– (1968)
[20] ”On the Validity of Dempster Rule of Combination,” Memo. UCB/ERL M 79/24, University of California, Berkeley, 1979.
[21] Zadeh, Al Magazine 5 pp 81– (1984)
[22] ”A Simple View of the Dempster-Shafer Theory of Evidence,” Berkeley Cognitive Science Rep. No. 27, University of California, 1984.
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