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Definicja subiektywnej możliwości
Języki publikacji
Abstrakty
The problem of finding a suitable belief function consistent with a given possibility distribution is considered. It is proved that this function is unique and consonant thus representable by means of a possibility distribution. The possibility distribution is subjective and unique. The results obtained in the paper allow us to define subjective possibility degrees, hence the membership function of fuzzy number.
W pracy proponuje się subiektywne spojrzenie na teorię możliwości, polegające na założeniu, że kiedy konstruuje się pewien rozkład prawdopodobieństwa jest on faktycznie indukowany przez pewną funkcję ufności (belief function) reprezentującą rzeczywisty stan wiedzy. Zakłada się również, że przejście pewnej funkcji ufności do rozkładu prawdopodobieństwa jest realizowane za pomocą transformacji ( pignistic transformation), znanej jako wartość Shapleya. Rozważa się problem znalezienia odpowiedniej funkcji ufności zgodnej z danym rozkładem prawdopodobieństwa. Dowodzi się, ze funkcja ta jest jednoznacznie określona i zgodna. Można ją zatem reprezentować za pomocą rozkładu możliwości. Rozkład ten jest subiektywny i jednoznaczny. Otrzymane w pracy wyniki pozwalają na definiowanie subiektywnych stopni możliwości, a co za tym idzie - funkcji przynależności liczby mnogiej.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
7--22
Opis fizyczny
Bibliogr. 35 poz.
Twórcy
autor
- IRIT, Universite Paul Sabatier, 118 route de Narbonne, 31062, Toulouse, cedex 4, France
autor
- IRIT, Universite Paul Sabatier, 118 route de Narbonne, 31062, Toulouse, cedex 4, France
autor
- IRIDIA, Universite Libre ode Bruxelles, 50 av. Roosvelt, CP 194-6, 1050 Bruxelles, Belgium
Bibliografia
- [1] BORGELT C., KRUSE R„ Learning graphical possibilistic models from data, IEEE trans. On Fuzzy Systems. 2003, II, 159-171.
- [2] CHANAS S., NOWAKOWSKI M., Single value simulation of fuzzy variable. Fuzzy Sets and Systems, 1988, 25, 43-57.
- [3] CHANAS S., KUCHTA D., Discrete fuzzy optimization, [in:l Fuzzy Sets in Decision Analysis, Operations Research and Statistics, R. Slowinski (Ed.), p. 249-277, The Handbooks of Fuzzy Sets Series, Kluwer Acad. Publ., Boston 1998.
- [4] CHANAS S., ZIELINSKI P.. Critical path analysis in the network with fuzzy activity times. Fuzzy Sets and Systems. 2001, 122 (2). 195-204.
- [5] DE COOMAN G., AEYELS D., Supremum-preserving upper probabilities. Inform. Sciences, 1999, 118, 173-212.
- [6] DELGADO M., MORAL S., On the concept of possibility-probability consistency. Fuzzy Sets and Systems, 1987,21,311-318.
- [7] DENNEBERG D., GRABISCH M., Interaction transform of set-functions over a finite set. Information Sciences, 1999, 121(1-2). 149-170.
- [8] DUBOIS D., JAULENT M.C.. A general approach to parameter evaluation in fuzzy digital pictures. Pattern Recognition Letters, 1987, 6. 251-259.
- [9] DUBOIS D., PRADE H., On several representations of an uncertain body of evidence, [in:] Fuzzy Information and Decision Processes (M.M. Gupta, E. Sanchez, eds.), North-Holland, 1982, 167-181.
- [10] DUBOIS D., PRADE H., Unfair coins and necessity measures: towards a possibilistic interpretation of histograms. Fuzzy Sets and Systems, 1983, 10, 15-20.
- [11] DUBOIS D., PRADE H„ A set-theoretic view of belief functions. Int. J. of General Systems, 1986, 12(3), 193-226.
- [12] DUBOIS D., PRADE H., Possibility Theory, Plenum Press, New York 1988.
- [13] DUBOIS D., PRADE H., Coping with uncertain knowledge - In defense of possibility and evidence theories. Computers and Artificial Intelligence (Bratislava), 1990,9(2), 115-144.
- [14] DUBOIS D., PRADE H., Quantitative possibility theory and its probabilistic connections, [in:] Soft Methods in Probability, Statistics and Data Analysis (Grzegorzewski P. et al„ eds.), Physica Verlag, Heidelberg - Germany, 2002, 3-26.
- [15] DUBOIS D., NGUYEN H.T., PRADE H„ Possibility theory, probability and fuzzy sets: misunderstandings. bridges and gaps, [in:] Fundamentals of Fuzzy Sets (Dubois D., Prade H., eds.), Kluwer, Boston, Mass., The Handbooks of Fuzzy Sets Series, 2000, 343-438.
- [16] DUBOIS D., PRADE H., SANDRI S.A., On possibility/probability transformations, [in:] Fuzzy Logic: State of the Art. (R. Lowen, M. Lowen, eds.), Kluwer Academic Publ., 1993, 103-112.
- [17] DUBOIS D., PRADE H., SMETS P., Representing partial ignorance, IEEE Trans. on Systems, Man and Cybernetics, 26(3), 1996, 361-377.
- [18] DUBOIS D., PRADE H., SMETS P., New semantics for quantitative possibility theory, Proc. of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU 2001, Toulouse, France), Springer-Verlag, 2001, p. 410-421.
- [19] GILES R., Foundations for a theory of possibility. Fuzzy Information and Decision Processes (Gupta M.M. and Sanchez E., eds.), North-Holland, 1982, 183-195.
- [20] KAUFMANN A., La simulation des ensembles flous, CNRS Round Table on Fuzzy Sets, Lyon, France (unpublished proceedings), 1980.
- [21] KLIR G.. SMITH R.M., On measuring uncertainty and uncertainty-based information: recent developments, Annals Math, and AI., 2001, 32, 5-34.
- [22] SHAPLEY L.S., A value for n-person games, [in:] Kuhn and Tucker eds., Contributions to the Theory of Games, II, Princeton University Press, 1953, 307-317.
- [23] SHAFER G., A Mathematical Theory of Evidence, Princeton University Press, Princeton 1976.
- [24] SMETS P., Constructing the pignistic probability function in a context of uncertainty, Uncertainty in Artificial Intelligence 5 (Henrion M. et al., eds.), North-Holland, Amsterdam, 1990, 29-39.
- [25] SMETS P., KENNES R., The transferable belief model. Artificial Intelligence, 1994, 66, 191-234.
- [26] SMETS P., The normative representation of quantified beliefs by belief functions, Artificial Intelligence. 1997, 92. 229-242.
- [27] SMETS P., The transferable belief model for quantified belief representation. Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. 1. (D.M. Gabbay, P. Smets, eds.) Kluwer, Doordrecht, The Netherlands, 1998, 267-301.
- [28] SMETS P., Quantified possibility theory seen as an hypercautious transferable belief model, Rencontres Francophones sur les Logiques Floues et ses Applications (LFA 2000, La Rochelle, France), Cepadues-Editions, Toulouse, France, 2000, pp. 343-353.
- [29] SMETS P., Decision making in a context where uncertainty is represented by belief functions, [in:] Belief Functions in Business Decisions (R.P. Srivastava, T.J. Mock, Eds.). Physica-Verlag. Heidelberg, 2002, 17-61.
- [30] WALLEY P., Statistical Reasoning with Imprecise Probabilities, Chapman and Hall, 1991.
- [31] WILSON N., Decision-Making with Belief Functions and Pignistic Probabilities, [in:] Symbolic and Quantitative Approaches to Reasoning and Uncertainty (Proc. of the Europ. Conf. ECSQARU'93, Granada, Spain) (M. Clarke, R. Kruse. S. Moral, eds.). Lecture Notes in Computer Science, Vol. 747, 364-371. Springer Verlag, Berlin 1993.
- [32] YAGER R.R., Level sets for membership evaluation of fuzzy subsets, [in:] Fuzzy Sets and Possibility Theory: Recent Developments (R.R. Yager ed.), Pergamon Press, Oxford 1982, 90-97.
- [33] YAGER R.R., An introduction to applications of possibility theory, Human Systems Management, 1983, 3. 246-269.
- [34] YAGER R.R., The entailment principle for Dempster-Shafer granules. Tech. Report MI-512, 1985, Iona College, New Rochelle, N.Y.
- [35] ZADEH L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1978, 1, 3-28.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BUJ1-0025-0054