Decomposition of Possibilistic Belief Functions into Simple Support Functions
In Shafer evidence theory some belief functions, called separable belief functions, can be decomposed in terms of simple support functions. Moreover this decomposition is unique. Recently, a qualitative counterpart to Shafer evidence theory has been proposed. The mass functions in Shafer (addition-based) evidence theory are replaced by basic possibilistic assignments. The sum of weights is no longer 1, but their maximum is equal to 1. In such a context, a maxitive counterpart to belief functions, called possibilistic belief functions can be defined, replacing the addition by the maximum. The possibilistic evidence framework provides a general setting for describing imprecise possibility and necessity measures. This paper investigates a qualitative counterpart of the result about the decomposition of belief functions. Considering the qualitative Möbius transform, conditions for the existence of a decomposition of possibilistic belief functions into simple support functions are presented. Moreover the paper studies the unicity of such a decomposition.
KeywordsMass Function Combination Rule Belief Function Fuzzy Measure Evidence Theory
Unable to display preview. Download preview PDF.
- 1.Mihailović, B., Pap, E.: Decomposable signed fuzzy measures. In: Proc. of EUSFLAT 2007, Ostrava, Czech Rep, pp. 265–269 (2007)Google Scholar
- 2.Dubois, D.: Fuzzy measures on finite scales as families of possibility meas. In: Proc. European Society For Fuzzy Logic and Technology (EUSFLAT-LFA), Aix-Les-Bains, France (July 2011)Google Scholar
- 4.Dubois, D., Prade, H.: Upper and lower possibilities induced by a multivalued mapping. In: Sanchez, E. (ed.) Proc. IFAC Symp. on Fuzzy Information, Knowledge Representation and Decision Analysis, Fuzzy Information, Knowledge Representation and Decision Analysis, July 19-21, pp. 152–174. Pergamon Press, Sanchez (1984)Google Scholar
- 11.Marichal, J.-L.: Aggregation Operations for Multicriteria Decision Aid. Thesis, University of Liège, Belgium (1998)Google Scholar
- 12.Mesiar, R.: k-order Pan-discrete fuzzy measures. In: Proc. 7th Inter. Fuzzy Systems Assoc. World Congress (IFSA 1997), Prague, June 25-29, vol. 1, pp. 488–490 (1997)Google Scholar
- 14.Smets, P.: The canonical decomposition of a weighted belief. In: Proc. of the 14th Inter. Joint Conf. on Artificial Intelligence (IJCAI 1995), Montreal, August 20-25, pp. 1896–1901 (1995)Google Scholar