Some New Results Concerning Random Sets and Fuzzy Sets.

Abstract

This paper is a continuation of past work showing direct connections between fuzzy set theory and classical probability theory through the use of random sets. This includes characterizations of random intervals one-point- coverage-equivalent to fuzzy sets, determination of all nested random sets equivalent to fuzzy sets, the solution of the one- and multiple-point coverage problems for random sets in finite spaces, and the use of entropy for ordering random sets within the class of one-point-coverage-equivalent ones for any given fuzzy set. Finally, a connection between random variables, random sets, and fuzzy sets is pointed out. During the past few years a number of investigations has been carried out directly connecting fuzzy sets with random sets. In addition, there has been work in interpreting fuzzy sets through subjective probability.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1984
Accession Number
ADA240741

Entities

People

  • I. R. Goodman

Tags

Communities of Interest

  • Air Platforms
  • Ground and Sea Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Availability
  • Distribution Functions
  • Equations
  • Fuzzy Sets
  • Information Science
  • Intervals
  • New York
  • Probability
  • Probability Density Functions
  • Probability Distribution Functions
  • Probability Distributions
  • Random Variables
  • Set Theory
  • Standards
  • Stochastic Processes
  • Theorems

Readers

  • Approximation Theory.
  • Computer Engineering
  • Theoretical Analysis.

Technology Areas

  • Space