A Unified Approach to Modeling and Combining of Evidence through Random Set Theory,
Abstract
It has been shown in previous work that generalized fuzzy set theory and infinite-valued logic provide a systematic approach to the modeling and use of both natural language and numerical/statistical information which occurs in the tracking-data association and related problems. This paper continues efforts in establishing connections between these disciplines and classical probability theory. It has been shown that over discrete spaces, probabilistic concepts are all special cases of generalized fuzzy set ones. Conversely, many fuzzy set systems can be shown to be natural extensions of ordinary set operators through isomorphic-like relations with corresponding random set representations via one point coverage functions. Among the new results presented here, it is shown that any fuzzy set membership function has naturally compatible random set and random variable representations. In the latter case, the membership function is the same as the evaluation function of the (non-unique) corresponding random variable over a suitably chosen collection of compound- and, in general, overlapping- sets or events. An application to the classification problem is presented. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1983
- Accession Number
- ADP002880
Entities
People
- I. R. Goodman