Supported by the National Natural Science Foundation of China under Grant Nos.60573068, 60773113 (国家自然科学基金); theScience & Technology Research Program of Chongqing Education Committee of China under Grant Nos.KJ060517, KJ090512 (重庆市教委科学技术研究项目); the Natural Science Foundation of Chongqing of China under Grant No.2008BA2017 (重庆市自然科学基金重点项目); the Science Fund for Distinguished Young Scholars of Chongqing of China under Grant No.2008BA2041 (重庆市杰出青年科学基金)
粗糙集扩展模型的研究是粗糙集理论研究的一个重要问题.其中,基于覆盖的粗糙集模型扩展是粗糙集 扩展模型中的重要一类.覆盖近似空间中的概念近似是从覆盖近似空间中获取知识的关键.目前,研究者对覆盖近似空间中经典集合的近似进行了较多的研究.针对覆盖近似空间中模糊集合的近似,虽然不同的覆盖粗糙模糊集模型 被提了出来,但它们都存在不合理性.从规则的置信度出发,提出了一种新的覆盖粗糙模糊集模型.该模型修正了已 有模型中存在对象在下近似中不确定可分和上近似中不近似可分的问题.分析了具有偏序关系的两个覆盖近似空 间中上、下近似之间的关系,发现两个不同覆盖生成相同覆盖粗糙模糊集的充要条件是这两个覆盖的约简恒等.分 析了新模型与Wei 模型、Xu 模型之间的关系,发现这两种模型是新模型的两种极端情况,且其应用前提是覆盖为一 元覆盖.这些结论将为覆盖粗糙模糊集模型应用于决策为模糊的情形提供理论基础.
The extension of rough set is an important issue in rough set theory among which the covering based generalized rough set is vital. Concept approximation in covering approximation space (CAS) is a key issue for acquiring knowledge from it. Some researchers have done much on approximation of classical sets in covering approximation space. Some covering based generalized rough fuzzy set models have already been developed for approximation of fuzzy sets in covering approximation space. Unfortunately, there are limitations in these models. In this paper, a new covering based generalized rough fuzzy set model is proposed. It solves the problems of former models. Moreover, the lower and upper approximations in two different covering approximation spaces with partial order relation are studied, and the sufficient and necessary condition for generating the same covering based generalized rough fuzzy sets from two different covering approximation spaces is that these two coverings have the same reductions. In the end, the relationship of this new model with the models proposed by Wei and Xu is analyzed. Wei’s model and Xu’s model are proved to be two extremes of the new one, and they can be used in some special cases of unary covering. These results provide foundation for the application of covering based generalized rough fuzzy set models to fuzzy decisions.