Further Results on the Application of Entropies of Deterministic Functions to Information of Fuzzy Sets and Related Topics

Abstract

The problem of expanding a meaningful entropic theory for fuzzy information cannot be thought of as being a mere (more or less formal) extension of Shannon theory. By using the information theory of deterministic functions, the present author had already obtained some results in this way, and he herein continues this approach. After a short background on the different entropies of deterministic functions and on membership entropy of fuzzy sets, successively mixed entropy of fuzzy sets, joint membership functions of independent fuzzy sets, and conditional entropy of fuzzy sets with respect to other fuzzy sets are considered; the problem of defining transinformation between fuzzy sets, as a generalisation of the well known Shannon concept, is then examined. One of the conclusions of the article is that it is possible to build up a meaningful information theory of fuzzy sets by using the entropy of deterministic functions.

Citation

Jumarie, G. (1991), "Further Results on the Application of Entropies of Deterministic Functions to Information of Fuzzy Sets and Related Topics", Kybernetes, Vol. 20 No. 4, pp. 12-27. https://doi.org/10.1108/eb005891