TY - JOUR
T1 - Computing generalized belief functions for continuous fuzzy sets
AU - Yen, John
N1 - Funding Information:
The research described in the paper was supported by Texas Engineering Excellence Fund at Texas A&M University and was supported by the Defense Advanced Research Projects Agency under Contract No. MDA903-86-C-0178 while the author was at USC/Information Sciences Institute. Views and conclusions contained in this paper are those of the author, and should not be interpreted as representing the official opinion or policy of the sponsoring agencies.
PY - 1992/1
Y1 - 1992/1
N2 - Intelligent 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.
AB - Intelligent 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.
UR - http://www.scopus.com/inward/record.url?scp=38249015332&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=38249015332&partnerID=8YFLogxK
U2 - 10.1016/0888-613X(92)90037-Z
DO - 10.1016/0888-613X(92)90037-Z
M3 - Article
AN - SCOPUS:38249015332
SN - 0888-613X
VL - 6
SP - 1
EP - 31
JO - International Journal of Approximate Reasoning
JF - International Journal of Approximate Reasoning
IS - 1
ER -