A probabilistic interpretation of the degree of fuzziness
Kenji Handa, Prasansa Kalukottege, Yukio Ogura · Journal of Applied Probability · 1994
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 .