A. Vesel (Czech Republic)
information, knowledge, fuzzy formula, information divergence
Information content of theoretical knowledge stated in predicate calculus formulas is considered. To behave efficiently in the surrounding world means to have a good approximation of the true probability distribution of its states p. Therefore the valid formula or theory enabling to estimate p is "informative", and it is the more informative the more accurate the estimate is. Getting a message that a formula is valid or valid with some probability leads to a refinement of the current estimate q by a natural rule into a new estimate q´. The difference of information-theoretic divergences D (pq) - D (pq´ ) is a natural measure of the amount of information contained in the formula. In this paper we proved that a theory or a fuzzy theory that is more informative according to the introduced information measure enables more precise approximation of the underlying true distribution p. We also proved that the introduced information measure can be evaluated even if the distribution p is not known. Generating knowledge by data mining methods usually leads to many IF-THEN rules. So far no quantitative measure of their “informative strength” or “importance” has been proposed. The new information measure can be used for this purpose.
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