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A probabilistic interpretation of the degree of fuzziness

Published online by Cambridge University Press:  14 July 2016

Kenji Handa*
Affiliation:
Saga University
Prasansa Kalukottege*
Affiliation:
Saga University
Yukio Ogura*
Affiliation:
Saga University
*
Postal address: Department of Mathematics, Saga University, Saga 840, Japan.
Postal address: Department of Mathematics, Saga University, Saga 840, Japan.
Postal address: Department of Mathematics, Saga University, Saga 840, Japan.

Abstract

In this paper we give a probabilistic interpretation for the function d(f), which has been proposed as a measure of fuzziness of a fuzzy set f. For this we construct random patterns which approximate the fuzzy set f and show that, for large n, the number of possible outcomes of the nth random pattern is approximately 2nd(f). We also give the best possible constant K in a more accurate approximation .

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1994 

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