覆盖多粒度Pythagorean模糊粗糙集及多属性决策研究

Covering based rough sets and granular computing are two important research topics in rough sets, which their fusion research is one of the hotspots in the field of artificial intelligence. In the view of granular computing, most of the rough set models can be reduced to the category of single granularity. However, in real life, it is difficult for us to use single granularity rough set model to deal with the problem of high dimensional data analysis for many complex systems we have encountered, such as, knowledge of multisource information systems and distributed information systems. Therefore, it is necessary and meaningful to study the multigranulation rough set models. This project put forwards covering based Pythagorean fuzzy rough set models by combining three uncertain models, such as, multigranulation rough sets, covering based rough sets and Pythagorean fuzzy sets, characterizes the structures of uncertain models and studies Pythagorean fuzzy information entropy and Pythagorean fuzzy aggregation operators. Finally, five kinds of multi-attribute decision-making methods are proposed, the algorithms are given and the detection analysis and comparison are carried out by some examples. This project will lay a theoretical framework for artificial intelligence and information processing for granular computing and knowledge discovery, and provide some new research ideas.

覆盖粗糙集和粒计算是粗糙集中两个重要的研究课题，其融合研究是人工智能领域的研究热点之一。在粒计算的观点下，粗糙集模型大多都可归结为单粒度粗糙集范畴。但在实际生活中，我们所遇到诸多复杂系统的高维数据分析问题，如多源信息系统和分布式信息系统等，都难以用单粒度粗糙集模型来处理。因此，研究多粒度粗糙集模型是十分必要和有意义的。本项目融合多粒度粗糙集、覆盖粗糙集和Pythagorean模糊集这三种不确定性分析模型，提出覆盖多粒度Pythagorean模糊粗糙集模型，刻画其不确定模型的结构特征，并研究Pythagorean模糊信息熵和模糊聚类算子。最后，基于上述理论，提出五类多属性决策方法，进而给出算法，通过实例进行检测分析和对比。本项目将为粒计算和知识发现等人工智能和信息处理领域提出新的理论框架，并提供新的研究思路。

覆盖粗糙集和粒计算是粗糙集中两个重要的研究课题，其融合研究是人工智能领域的研究热点之一。在粒计算的观点下，粗糙集模型大多都可归结为单粒度粗糙集范畴。但在实际生活中，我们所遇到诸多复杂系统的高维数据分析问题，如多源信息系统和分布式信息系统等，都难以用单粒度粗糙集模型来处理。因此，研究多粒度粗糙集模型是十分必要和有意义的。本项目融合多粒度粗糙集、覆盖粗糙集和Pythagorean模糊集这三种不确定性分析模型，提出覆盖多粒度Pythagorean模糊粗糙集模型，刻画其不确定模型的结构特征，并研究Pythagorean模糊信息熵和模糊聚类算子。最后，基于上述理论，提出五类多属性决策方法，进而给出算法，通过实例进行检测分析和对比。本项目将为粒计算和知识发现等人工智能和信息处理领域提出新的理论框架，并提供新的研究思路。