Abstract: The concept of soft propositional logic formula based on a soft set is introduced, and the semantic interpretation of soft propositional logic formula is given. A parameter in the soft set is an atomic formula, and the function value of parameter is the valued set of atomic formula. A decision information system is transformed into a decision soft set, and a decision rule is expressed as an implication logic formula composed of some atomic formulas. Some concepts, such as basic soft truth degree, condition soft truth degree and absolute soft truth degree, etc, are introduced. These concepts evaluate the decision rule from adequacy, necessity and rationality, etc. An extraction algorithm of typical decision rules based on the decision soft set is proposed. The analysis of decision rule based on decision soft set is applied to intelligent recommendation, and a recommendation algorithm based on the soft decision analysis is proposed. The practical examples and numerical experiments show that the algorithms are effective.

Key words: decision information system, decision soft set, soft logic formula, soft decision rule, soft truth degree, recommendation algorithm

摘要： 引入基于软集的软命题逻辑公式，给出软命题逻辑公式的语义解释，软集中的参数是原子公式，参数的函数值是原子公式的赋值集。将决策信息系统转化为决策软集，而软决策规则表示为由原子公式组成的蕴含逻辑公式。引进基本软真度、条件软真度、绝对软真度等概念，从充分性、必要性、合理性等不同方面来评价软决策规则，提出基于决策软集的典型软决策规则提取算法。将基于软集的软决策规则分析方法应用于智能推荐，给出基于软决策规则分析的推荐算法，实际例子和数值实验表明提出的算法是有效的。

关键词: 决策信息系统, 决策软集, 软逻辑公式, 软决策规则, 软真度, 推荐算法