Expert Systems and Fuzzy Systems: A New Approach via Possibility‐Probability Conversion

Abstract

In the framework of his theory of relative information, derives formulae to convert probability into possibility and conversely, and shows how they can be utilized to reconsider many questions related to fuzzy sets and approximate reasoning on a meaningful information theoretic standpoint. The key of this approach is that the membership of a fuzzy set is now thought of as equivalent to the pair (probability, fuzziness coefficient). Therefore a sound new concept of informational membership entropy, which is fully consistent with Shannon theory, is evolved. In this new paradigm, the fuzzy object is simultaneously defined by the set itself and its complement. Thus obtains a new modelling for the union and the intersection of fuzzy sets, and new approaches to quantitatively modelling “If A then B”.

Citation

Jumarie, G. (1993), "Expert Systems and Fuzzy Systems: A New Approach via Possibility‐Probability Conversion", Kybernetes, Vol. 22 No. 8, pp. 21-36. https://doi.org/10.1108/eb006003