Some Asymptotic Properties of Fuzzy Set Systems
Abstract
In previous work, a number of close connections was established between fuzzy set theory and probability theory. This basically involved the (many-to-one) correspondences of random sets to fuzzy sets through the former's one-point coverage functions. Other parallels between the two disciplines were established where multivalued logic theory was used as a basis for generating entire classes of fuzzy set systems. In this paper, the genesis of a fuzzy set sampling technique is presented, paralleling to a certain extent the ordinary Bayesian approach to random sampling and parameter estimation. As a consequence, an analysis is carried out concerning the structure of posterior possibilities and related functions for both finite and infinite sample size cases for various fuzzy set systems. Although some fuzzy set systems are shown not to admit nontrivial asymptotic forms, others indeed admit well-defined computable results that also differ significantly from the finite sampling size case.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1982
- Accession Number
- ADA241216
Entities
People
- I. R. Goodman