Institute for Mathematical Physics Bayesian Decisions and Fuzzy Logic Bayesian Decisions and Fuzzy Logic
نویسندگان
چکیده
This paper develops a category-theoretic approach to uncertainty and decision-making problems. It is based on appropriate rst order fuzzy logic in which not only logical connectives but also quantiiers have fuzzy interpretation. It is shown that all fundamental concepts of probability and statistics such as joint distribution, conditional distribution, etc., have meaningful analogs in new context. This approach makes it possible to utilize rich conceptual experience of statistics. In particular it leads to fuzzy Bayesian approach in decision making and provides methods for construction of optimal strategies. Connection with underlying fuzzy logic reveals the logical semantics for fuzzy decision making.
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