Representing Heuristic Knowledge in D-S Theory

The Dempster-Shafer theory of evidence has been used intensively to deal with uncertainty in knowledge-based systems. However the representation of uncertain relationships between evidence and hypothesis groups (heuristic knowledge) is still a major research problem. This paper presents an approach to representing such heuristic knowledge by evidential mappings which are defined on the basis of mass functions. The relationships between evidential mappings and multivalued mappings, as well as between evidential mappings and Bayesian multi- valued causal link models in Bayesian theory are discussed. Following this the detailed procedures for constructing evidential mappings for any set of heuristic rules are introduced. Several situations of belief propagation are discussed.

[1]  Piero P. Bonissone,et al.  Editorial: Reasoning with Uncertainty in Expert Systems , 1985, Int. J. Man Mach. Stud..

[2]  John D. Lowrance,et al.  A Framework for Evidential-Reasoning Systems , 1990, AAAI.

[3]  Gerald Liu,et al.  Causal and Plausible Reasoning in Expert Systems , 1986, AAAI.

[4]  G. Shafer.  Jeffrey's Rule of Conditioning , 1981, Philosophy of Science.

[5]  Petr Hájek,et al.  On Belief Functions , 1992, Advanced Topics in Artificial Intelligence.

[6]  Edward H. Shortliffe,et al.  A model of inexact reasoning in medicine , 1990 .

[7]  A. Hasman,et al.  Probabilistic reasoning in intelligent systems: Networks of plausible inference , 1991 .

[8]  Judea Pearl,et al.  Bayesian and belief-functions formalisms for evidential reasoning: a conceptual analysis , 1990 .

[9]  Glenn Shafer,et al.  Perspectives on the theory and practice of belief functions , 1990, Int. J. Approx. Reason..

[10]  Rangasami L. Kashyap,et al.  Belief combination and propagation in a lattice-structured interference network , 1990, IEEE Trans. Syst. Man Cybern..

[11]  A. A. J. Marley,et al.  The Logic of Decisions. , 1972 .

[12]  Kathryn B. Laskey,et al.  Assumptions, Beliefs and Probabilities , 1989, Artif. Intell..

[13]  Jeffrey A. Barnett,et al.  Computational Methods for a Mathematical Theory of Evidence , 1981, IJCAI.

[14]  Glenn Shafer,et al.  Evidential Reasoning Using DELEF , 1988, AAAI.

[15]  Glenn Shafer,et al.  Implementing Dempster's Rule for Hierarchical Evidence , 1987, Artif. Intell..

[16]  Michael F. McTear,et al.  Representing heuristic knowledge and propagating beliefs in the Dempster-Shafer theory of evidence , 1994 .

[17]  John Yen,et al.  GERTIS: a Dempster-Shafer approach to diagnosing hierarchical hypotheses , 1989, CACM.

[18]  Matthew L. Ginsberg,et al.  Non-Monotonic Reasoning Using Dempster's Rule , 1984, AAAI.

[19]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[20]  Leonard P. Wesley.  Evidential-based control in knowledge-based systems , 1988 .

[21]  Khaled Mellouli,et al.  Propagating belief functions in qualitative Markov trees , 1987, Int. J. Approx. Reason..

[22]  Kathryn B. Laskey,et al.  Representing and eliciting knowledge about uncertain evidence and its implications , 1989, IEEE Trans. Syst. Man Cybern..

[23]  Frans Voorbraak,et al.  On the Justification of Dempster's Rule of Combination , 1988, Artif. Intell..