基于直觉模糊相似关系的三支决策模型

Three-Way Decision Model Based on Intuitionistic Fuzzy Similarity

针对一些直觉模糊相似关系使直觉模糊集中对象间的相似度过于集中或者相异度过高,导致不合理的分类结果的问题,以及在构造直觉模糊相似关系时,对象间的相似度和相异度容易受到不重要属性条件信息影响的问题,本文在直觉模糊集和可能性理论基础上,提出一种基于直觉模糊相似关系的三支决策模型。首先,给出可能性测度和必要性测度的定义,结合Hausdorff度量,构造一种距离公式,并证明其性质,定义了直觉模糊集中对象间的相似度和相异度,构造了新的直觉模糊相似关系;然后定义了直觉模糊相似关系下的(λ_(1),λ_(2))-截集及其直觉模糊(λ_(1),λ_(2))-截集下的相似类,并进一步求出目标集的正域、负域和边界域;最后通过UCI数据集和实例验证了该模型的合理性和有效性。

Intuitionistic fuzzy similarity relations cause the similarity degree between objects in the intuitionistic fuzzy set too concentrated or the dissimilarity degree too high,leading to nreasonable classification results,and when constructing intuitionistic fuzzy similarity relation,the similarity degree and dissimilarity degree between objects are vulnerable to unimportant attributes.Therefore,a three-way decision model based on intuitionistic fuzzy similarity relation is proposed according to the intuitionistic fuzzy sets and the possibility theory.Firstly,the definitions of possibility measure and necessity measure are given.Combining with the Hausdorff measure,a distance formula is constructed and its properties are proved.The similarity degree and dissimilarity degree between objects in intuitionistic fuzzy sets are defined,and a new intuitionistic fuzzy similarity relationship is constructed.Then,the(λ_(1),λ_(2))-cut set under intuitionistic fuzzy similarity relation and the similar class under intuitionistic fuzzy(λ_(1),λ_(2))-cut set are defined,and the positive,negative and boundary fields of target set are further obtained.Finally,the rationality and effectiveness of the proposed model are verified through UCI data sets and examples.