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A probabilistic interpretation of the degree of fuzziness

Part of: Fuzzy sets and logic

Published online by Cambridge University Press:  14 July 2016

Kenji Handa ,
Prasansa Kalukottege  and
Yukio Ogura
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.
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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 .

Keywords

FUZZY SETINFORMATIONSHANNON–MCMILLAN THEOREMLAW OF LARGE NUMBERSCENTRAL LIMIT THEOREM

MSC classification

Primary: 94D05: Fuzzy sets and logic (in connection with questions of Section 94)
Type
Research Article
Information
Journal of Applied Probability , Volume 31 , Issue 4 , December 1994 , pp. 1034 - 1048
Copyright
Copyright © Applied Probability Trust 1994 

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References

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