模糊逻辑、信息量与贝叶斯决策问题
Fuzzy Logic, Informativeness and Bayesian Decision-Making Problems
摘要：
本文发展了一种范畴论方法来处理不确定性、信息性和决策问题。它是基于适当的一阶模糊逻辑，其中不仅逻辑连接词，而且量词具有模糊解释。证明了联合分布、条件分布等概率统计的基本概念，在新的语境中有意义的类比。这种方法使得利用丰富的统计概念经验成为可能。与底层模糊逻辑的连接揭示了模糊决策的逻辑语义。决策问题的IT范畴的框架内，并推广贝叶斯方法的决策与先验信息。该方法引入了模糊贝叶斯决策方法，为构造最优策略提供了方法。
英文摘要：
This paper develops a category-theoretic approach to uncertainty, informativeness and decision-making problems. It is based on appropriate first order fuzzy logic in which not only logical connectives but also quantifiers 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. Connection with underlying fuzzy logic reveals the logical semantics for fuzzy decision making. Decision-making problems within the framework of IT-categories and generalizes Bayesian approach to decision-making with a prior information are considered. It leads to fuzzy Bayesian approach in decision making and provides methods for construction of optimal strategies.
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