基于$\sigma$优势关系下的直觉模糊三支决策

Intuitionistic Fuzzy Three-Way Decision Making Based on $\sigma$ Dominant Relationship

摘要: 针对多属性决策中经常含有模糊信息的难题，而传统的决策方法难以有效提取决策规则和实现方案排序。 为了解决此类问题，本文通过借助$\sigma$ 优势关系，提出$\sigma$ 优势信息熵，从而不仅避免了优势关系条件过于严格，容易导致信息损失的问题，而且同时实现了属性权重的客观评价。并以此为基础，在直觉模糊信息系统中构建了一种新的条件概率表示方法，重新制定了决策规则和排序策略。最后，通过实例分析验证了本文方法的合理性及有效性。

Abstract: In view of the problem that fuzzy information is often contained in multi-attribute decision making, traditional decision making methods are difficult to effectively extract decision rules and implement scheme ranking. In order to solve such problems, this paper proposes the entropy of $\sigma$ dominant information by virtue of the $\sigma$ dominant relation, which not only avoids the problem that the conditions of dominant relation are too strict, which is easy to lead to information loss, but also realizes the objective evaluation of attribute weights. Based on this, a new conditional probability representation method is constructed in intuitionistic fuzzy information system, and the decision rules and ranking strategy are reformulated. Finally, the rationality and effectiveness of the proposed method are verified by case analysis.