A (NEW) MEASURE OF FUZZY UNCERTAINTY VIA INTERVAL ANALYSIS, WHICH IS FULLY CONSISTENT WITH SHANNON THEORY
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Abstract
Many authors have suggested different measures of the amount of uncertainty involved in fuzzy sets, but most of these concepts suffer from drawbacks: mainly, they are indexes of fuzziness rather than measures of uncertainty, and they are not fully consistent with Shannon theory. The question is herein once more considered by combining the information theory of deterministic functions, recently initiated by the author, with the viewpoint of interval analysis; and one so derive the new concept of "uncertainty of order c of fuzzy sets". It is shown that it satisfies the main properties which are desirable for a measure of uncertainty. Some topics are outlined, such as informational distance between fuzzy sets, and mutual infonnation between fuzzy sets for instance. One so has at hand a unified approach to Shannon information expressed in terms of probability, and to fuzzy information described by weighting coefficients commonly referred to as possibility distribution.
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