Not All Fuzzy Set Operations Have Weak Homomorphic Random Set Counterparts.
Abstract
This paper is a further contribution to the problem of determining which fuzzy set operations are most appropriate for modeling a given situation. In review, a choice function, as defined by the author, is a mapping from the class of all fuzzy subsets of a given base space into the class of all random subsets of the same space such that any fuzzy set corresponds to some equivalent random set, where equivalence is with respect to membership function and one point coverage function, respectively. This, in turn, induces an equivalence class relation over the class of all random subsets of the given space. In previous work, a number of characterizations have been obtained for these fuzzy set and ordinary (and hence, random) set operations which have weak (i.e., up to the equivalence described above) homomorphic correspondence, relative to certain families of choice functions and joint distributions of random sets.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1991
- Accession Number
- ADA240878
Entities
People
- I. R. Goodman