×

Two characterizations of a minimum-information principle for possibilistic reasoning. (English) Zbl 0814.68121

Summary: We show that the principle of maximum \(U\)-uncertainty for ampliative possibilistic reasoning can be characterized as uniquely satisfying a small set of normative axioms. Two proofs are given – one each for Hisdal’s and Dempster’s definitions of conditional possibility. These results complement a similar characterization of maximum entropy for ampliative probabilistic inference, given by Paris and Vencovska.

MSC:

68T30 Knowledge representation
68T27 Logic in artificial intelligence
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Dubois, D.; Prade, H., An introduction to possibilistic and fuzzy logic, (Smets, P.; Mamdami, E. H.; Dubois, D.; Prade, H., Non-standard Logics for Automated Reasoning (1988), Academic: Academic New York), 287-315
[2] Nilsson, N. J., Probabilistic logic, Artif. Intell, 28, 71-88 (1986) · Zbl 0589.03007
[3] Shafer, G. A., A Mathematical Theory of Evidence (1976), Princeton U.P: Princeton U.P Princeton, N.J · Zbl 0359.62002
[4] Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1, 3-28 (1978) · Zbl 0377.04002
[5] Dubois, D.; Prade, H., A set-theoretic view of belief functions, Internat. J. Gen. Systems, 12, 193-226 (1986)
[6] Dubois, D.; Prade, H., Théorie des Possibilités: Applications lá la Representation des Connaissances en Informatique (1985), Masson, Paris · Zbl 0674.68059
[7] Sugeno, M., Fuzzy measures and fuzzy integrals: A survey, (Gupta, M. M.; Saridis, G. N.; Gaines, B. R., Fuzzy Automata and Decision Processes (1977), North-Holland: North-Holland New York), 89-102
[8] Klir, G. J.; Folger, T. A., Fuzzy Sets, Uncertainty and Information (1989), Academic: Academic New York
[9] Dubois, D.; Prade, H., Properties of measures of information in evidence and possibility theories, Fuzzy Sets and Systems, 24, 2, 161-182 (1987) · Zbl 0633.94009
[10] (Klir, G. J., Special issue on measures of uncertainty. Special issue on measures of uncertainty, Fuzzy Sets and Systems, 24 (1987)), (2)
[11] Yager, R. R., Measuring tranquility and anxiety in decision-making: An application of fuzzy sets, Internat. J. Gen. Systems, 8, 139-146 (1982) · Zbl 0487.90007
[12] Yager, R. R., Entropy and specificity in a mathematical theory of evidence, Internat. J. Gen. Systems, 9, 249-260 (1983) · Zbl 0521.94008
[13] Dubois, D.; Prade, H., A note on measures of specificity for fuzzy sets, Internat. J. Gen. Systems, 10, 279-283 (1985) · Zbl 0569.94032
[14] Paris, J. B.; Vencovska, A., A budget of principles 1, (Internal Report (1991), Dept. of Mathematics, Univ. of Manchester, Manchester: Dept. of Mathematics, Univ. of Manchester, Manchester England) · Zbl 0787.68097
[15] Paris, J. B.; Vencovska, A., A note on the inevitability of maximum entropy, Internat. J. Approx. Reason., 14, 183-223 (1990) · Zbl 0697.68089
[16] Paris, J. B.; Vencovska, A., On the applicability of maximum entropy to inexact reasoning, Internat. J. Approx. Reason., 3, 1-34 (1989) · Zbl 0665.68079
[17] Maung, I., Possibilistic inference processes, (presented at Logic and Computer Science Section, Ninth International Congress on Logic, Methodology and Philosophy of Science. presented at Logic and Computer Science Section, Ninth International Congress on Logic, Methodology and Philosophy of Science, Uppsala, Sweden (1989)) · Zbl 0717.68045
[18] Dubois, D.; Prade, H., The logical view of conditioning and its application to possibility and evidence theories, Internat. J. Approx. Reason., 4, 23-46 (1990) · Zbl 0696.03006
[19] Higashi, M.; Klir, G. J., Measures of uncertainty and information based on possibility distributions, Internat. J. Gen. Systems, 9, 43-58 (1983) · Zbl 0497.94008
[20] Klir, G. J.; Mariano, M., On the uniqueness of possibilistic measure of uncertainty and information, Fuzzy Sets and Systems, 24, 197-219 (1987) · Zbl 0632.94039
[21] Ramer, A.; Lander, L., Classification of possibilistic uncertainty and information functions, Fuzzy Sets and Systems, 24, 221-230 (1987) · Zbl 0637.94027
[22] Ramer, A., Uniqueness of an information measure in the theory of evidence, Fuzzy Sets and Systems, 24, 183-196 (1987) · Zbl 0638.94027
[23] Hisdal, E., Conditional possibilities: Independence and non-interaction, Fuzzy Sets and Systems, 1, 283-297 (1978) · Zbl 0393.94050
[24] deCampos, L. M.; Lamata, M. T.; Moral, S., The concept of conditional fuzzy measure, Internat. J. Intell. Systems, 5, 237-246 (1990) · Zbl 0694.68058
[25] Nguyen, H. T., On conditional possibility distributions, Fuzzy Sets and Systems, 1, 299-309 (1978) · Zbl 0423.94052
[26] Maung, I.; Paris, J. B., A note on the infeasibility of some inference processes, Internat. J. Intell. Systems, 5, 595-603 (1990) · Zbl 0717.68045
[27] Maung, I., Measures of information and inference processes, (PhD Thesis (1992), Dept. of Mathematics, Univ. of Manchester: Dept. of Mathematics, Univ. of Manchester Manchester, England) · Zbl 1023.68520
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.