Computing generalized belief functions for continuous fuzzy sets

AbstractIntelligent systems often need to deal with various kinds of uncertain information. It is thus essential to develop evidential reasoning models that (1) can cope with different kinds of uncertain information in a theoretically sound manner and (2) can be implemented efficiently in a computer system. Generalizing the Dempster-Shafer theory to fuzzy sets has been suggested as a promising approach for dealing with probabilistic data, vague concepts, and incomplete information in a uniform framework. However, previous efforts in this area do not preserve an important principle of D-S theory—that belief and plausibility measures are the lower and upper bounds on belief measures. Recently, Yen proposed an alternative approach in which the degree of belief and the degree of plausibility of a fuzzy set are interpreted as its lower and upper belief measure, respectively. This paper briefly describes his generalized D-S reasoning model and discusses the computational aspects of the model. In particular, efficient algorithms are presented for computing the generalized belief function and plausibility functions for strong convex fuzzy sets, which are a wide class of fuzzy sets used most frequently in existing fuzzy intelligent systems. The algorithm not only facilitates the application of the generalized D-S model but also provides the basis for developing efficient algorithms for more general cases