A Simple View of the Dempster-Shafer Theory of Evidence and its Implication for the Rule of Combination [chapter]

Lotfi A, Zadeh
1996 Advances in Fuzzy Systems — Applications and Theory  
The emergence of expert systems as one of the major areas of activity within AI has resulted in a rapid growth of interest within the AI community in issues relating to the management of uncertainty and evidential reasoning. During the past two years, in particular, the Dempster-Shafer theory of evidence has att,ract,ed considerable attention as a promising method of dealing with some of the basic problems arising in combination of evidence and data fusion. To develop an adequate understanding
more » ... f this theory requires considerable effort and a good background in probability theory. There is, however, a simple way of approaching the Dempster-Shafer theory that only requires a minimal familiarity with relational models of data. For someone with a background in AI or database management, this approach has the advantage of relating in a natural way to the familiar framework of AI and databases. Furthermore, it clarifies some of the controversial issues in the Dempster-Shafer theory and points to ways in which it can be extended and made useful in AI-oriented app1ications.l The Basic Idea The basic idea underlying the approach in question is that in the context of relational databases the Dempster-Shafer theory can be viewed as an instance of inference from second-order relations, that is; relations in which the entries are first-order relations.' 'In the terminology of relational databases, a first-order relation is us first consider a standard example of retrieval from a first-order relation, such as the relation EMPLOYEE1 (or EMPl, for short) that is tabulated in the following: EMPI Name Age 23 28 21 27 30 As a point of departure, consider a simple example of a range query: What fraction of employees are between 20 and 25 years old, inclusively? In other words, During the past two years, the Dempster-Shafer theory of evi-Abstract dence has attracted considerable attention within the AI community as a promising method of dealing with uncertainty in expert systems. As presented in the literature, the theory is hard to master. In a simple approach that is outlined in this paper, the Dempster-Shafer theory is viewed in the context of relational databases as the application of familiar retrieval techniques to second-order relations, that is, relations in which the data entries are relations in first normal form. The relational viewpoint clarifies some of the controversial issues in the Dempster-Shafer theory and facilitates its use in AI-oriented applications a relation which is in first normal form, that is, a relation whose elements are atomic rather than set-valued.
doi:10.1142/9789814261302_0033 fatcat:bn7i3qe2wfaapovvgdnrkitgo4