Identification of Fuzzy Sets with a Class of Canonically Induced Random Sets and Some Applications.

Abstract

Any random subset of a space X clearly determines the membership function of a fuzzy subset through its one point coverages. This paper shows, conversely, that any fuzzy subset A of X can always be identified with, in general, many random subsets S(A) of X with respect to one point coverages. In a related manner, it is shown that any fuzzy set can be uniformly closely approximated with respect to one point coverages by a random set having a finite number of outcomes. Applications of the results to fuzzy attribute reasoning in both military and general contexts are presented, emphasizing the close connection between fuzzy and random confidence sets. Extensions of the above results to non-canonical mappings and multiple point coverage functions are also treated.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Sep 15, 1980
Accession Number
ADA089852

Entities

People

  • Irwin R. Goodman

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • C4I
  • Ground and Sea Platforms
  • Sensors

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Fuzzy Logic
  • Fuzzy Sets
  • Identification
  • Intervals
  • Logic
  • Numbers
  • Probability
  • Random Variables
  • Real Numbers
  • Reasoning
  • Set Theory
  • Standards
  • Target Discrimination
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Mathematical Modeling and Probability Theory.
  • Neural Network Machine Learning.

Technology Areas

  • Space