Abstract
Any dynamic decision model or procedure for acquisition of knowledge must deal with conditional events and should refer to (not necessarily structured) domains containing only the elements and the information of interest. We consider conditional possibility theory as numerical reference model to handle uncertainty and to study binary relations, defined on an arbitrary set of conditional events expressing the idea of “no more possible than”. We give the necessary conditions for the representability of a relation by a T-conditional possibility, for any triangular norm T, and we provide a complete characterization in terms of necessary and sufficient conditions for the representability by a conditional possibility (i.e. when T is the minimum).
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References
Ben Amor, N., Mellouli, K., Benferhat, S., Dubois, D., Prade, H.: A theoretical framework for possibilistic independence in a weakly ordered setting. Int. J. of Uncert., Fuzziness and Knowledge-Based Systems 10(2), 117–155 (2002)
Bouchon-Meunier, B., Coletti, G., Marsala, C.: Independence and Possibilistic Conditioning. Annals of Mathematics and Artificial Intelligence 35, 107–124 (2002)
Bouchon-Meunier, B., Coletti, G., Marsala, C.: Conditional possibility and necessity. Technologies for Constructing Intelligent Systems. In: Bouchon-Meunier, Gutierréz-Rions, Magdalena, Yager (eds.), pp. 59–71. Springer, Heidelberg (2000) (Selected papers from IPMU 2000)
Chateauneuf, A., Kast, R., Lapied, A.: Conditioning capacities and choquet integrals: the role of comonotony. Theory and Decision 51, 367–386 (2001)
Coletti, G., Scozzafava, R.: From conditional events to conditional measures: a new axiomatic approach. Annals of Mathematics and Artificial Intelligence 32, 373–392 (2001)
Coletti, G., Scozzafava, R.: Probabilistic logic in a coherent setting. Trends in logic. Kluwer, Dordrecht (2002)
Coletti, G., Scozzafava, R.: Toward a general theory of conditional beliefs. In: Proc. of the 6th Workshop on Uncertainty Processing, Hejnice, pp. 65–76 (2003)
Coletti, G., Vantaggi, B.: Independence in conditional possibility theory. In: Proc. IPMU 2004, Perugia, pp. 849–856 (2004)
Coletti, G., Vantaggi, B.: Representability of ordinal relations on a set of conditional events. Extended abstract of Conference FUR XI, Paris. An extended version has been submitted to Theory and Decision (2004)
de Cooman, G.: Possibility theory II: conditional possibility. Int. J. General Systems 25, 325–351 (1997)
de Finetti, B.: Sul significato soggettivo della probabilità. Fundamenta Matematicae 17, 293–329 (1931)
Dubois, D.: Belief structure, possibility theory and decomposable confidence measures on finite sets. Comput. Artificial Intelligence 5, 403–416 (1986)
Dubois, D., Prade, H.: Possibility Theory. Plenum Press, New York (1988)
Hisdal, E.: Conditional possibilities independence and noninteraction. Fuzzy Sets and Systems 1, 283–297 (1978)
Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht (2000)
Rumbos, B.: Representing subjective orderings of random variables: an extension. Journal of Mathematical Economics 36, 31–43 (2001)
Savage, L.J.: The Foundations of Statistics. Wiley, New York (1954)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)
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Coletti, G., Vantaggi, B. (2005). Comparative Conditional Possibilities. In: Godo, L. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2005. Lecture Notes in Computer Science(), vol 3571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11518655_73
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DOI: https://doi.org/10.1007/11518655_73
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