命题逻辑公式模糊软集语义及其在决策分析中的应用

基于论域公式引入软命题逻辑公式概念,给出软命题逻辑公式的模糊软语义解释.将决策模糊信息系统转化为决策模糊软集,软决策规则表示为包含有蕴含联结词的软命题逻辑公式.引入软命题逻辑公式的基本真度、条件真度、绝对真度等指标,从充分性、必要性等方面评价软决策规则的有效性、合理性.提出基于决策软集的典型软决策规则提取算法和基于软决策分析的推荐算法,并通过实例和数值实验证明算法的有效性.

Fuzzy Soft Set Semantics of Propositional Logic Formulas and Its Application to Decision Analysis

Soft propositional logic formulas based on a fuzzy soft set S=(F,A) of domain U are introduced, and the fuzzy soft semantics interpretation of soft propositional logic formulas is provided. A decision fuzzy information system is transformed into a decision fuzzy soft set, and a soft decision rule is expressed as an implication logic formula composed of some atomic formulas. The concepts of basic truth degree, condition truth and absolute truth are introduced. The availability and the rationality of soft decision rule are evaluated from different aspects, such as sufficiency and necessity. An extraction algorithm of typical decision rules based on the decision soft set and a recommendation algorithm based on soft decision analysis are proposed, and the practical examples and numerical experiment verify the effectiveness of the proposed algorithms.