On practical problems with the explanation of the difference between possibility and probability

• Autorzy: Piegat A.
• Języki publikacji: EN

Abstrakty

EN

In his famous paper "Fuzzy Sets as a Basis for a Theory of Possibility" (Zadeh, 1978) Professor Lofti Zadeh introduced the notion of possibility distribution [pi]x and tlie concept of possibility measure. He denned in the paper the possibility distribution function to be numerically equal to the membership function ([pi]x = [my]F). In this paper Professor Zadeh draws the special attention of the reader to the fact that: "... there is a fundamental difference between probability and possibility". To explain this difference he had given a special example illustrating the difference, which then was cited by many authors of books on Fuzzy Set Theory and gained great importance for understanding the notion of possibility. In the paper the author presents his doubts as to this important example, explains why it is incorrect and gives a correct version of the example based on the notion of possibility distribution of Dubois and Prade.

Słowa kluczowe

EN

fuzzy systems; fuzzy arithmetic; possibility; probability

PL

system rozmyty; arytmetyka rozmyta; możliwość; prawdopodobieństwo

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2005
• Tom: Vol. 34, no 2
• Strony: 505--524
• Opis fizyczny: Bibliogr. 16 poz., rys., wykr.

Twórcy

autor

Piegat A.

• Faculty of Computer Science and Information Systems, Technical University of Szczecin, Żołnierska 49, 71-210 Szczecin, Poland,

Bibliografia

• Borgelt, C. and Kruse, R. (2003) Learning possibilistic graphical models from data. IEEE Transactions on Fuzzy Systems 11 (2).
• Driankov, D., Hellendoorn, H. and Reinfrank, M. (1993) An Introduction to Fuzzy Control. Springer-Verlag Berlin, Heidelberg.
• Dubois, D. and Prade, H. (1988) Possibility Theory. An Approach to Computerized Processing of Uncertainty. Plenum Press, New York and London.
• Dubois, D. and Prade, H. (1993) Fuzzy sets and probability: misunder-standings, bridges and gaps. Proceedings of the Second IEEE Conference on Fuzzy Systems, 1059-1068.
• Dubois, D. and Prade, H. (1994) Possibility Theory, Belief Revision and Nonmonotonic Logic. Lecture Notes in Computer Science 847, 51-74.
• Dubois, D. and Prade, H. (2002) Quantitative possibility theory and its probabilistic connections. In: P. Grzegorzewski, O. Hryniewicz, M.A. Gil, eds., Soft Methods in Probability, Statistics and Data Analysis. Physica Verlag, Heidelberg-Germany, Advances in Soft Computing, 3-26.
• Dubois, D., Foulloy, L., Mauris, G. and Prade, H. (2004) Probability-possibility transformations, triangular fuzzy sets, and probabilistic inequalities. Reliable Computing 10 (4), 273-297.
• Kacprzyk, J. (1986) Zbiory rozmyte w analizie systemowej (Fuzzy sets in system analysis). Państwowe Wydawnictwo Naukowe, Warszawa.
• Klir, G.J. and Folger, T.A. (1988) Fuzzy Sets, Uncertainty and Information. Prentice-Hall International Inc., Englewood Cliffs, New Jersey.
• Klir, G.J. (1997) Fuzzy arithmetic with requisite constraints. Fuzzy Sets and Systems 91, 165-175.
• Piegat, A. (2003) Informative value of the possibilistic extension principle. Proceedings of 10th International Multi-Conference on Advanced Computer Systems ACS 2003, Międzyzdroje, Poland, October 22-24, CD (also to be published by Kluwer).
• Ruspini, E.H. (1990) Similarity based models for possibilistic logics. Proceedings of the 3rd International Conference on Information Processing and Management Uncertainty Knowledge Based Systems, Granada, Spain, 56-58.
• Spohn, W. (1990) A general nonprobabilistic theory of inductive reasoning. In: Schachter R.D., Levitt T.S., Kanal N. and Lemmer J.F., eds., Uncertainty in Artificial Intelligence 4, Amsterdam, Netherlands, 149-159.
• Spott, M. (1997) A theory of possibility distributions. Fuzzy Sets and Systems 102, 135-155.
• Zadeh, L.A. (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3-28.
• Zimmermann, H.-J. (1996) Fuzzy Set Theory and its Applications. Kluwer Academic Publishers, Boston/Dordrecht/London.