The notion of covering based multigranulation fuzzy rough set (CMGFRS) models is a generalization of both granular computing and covering based fuzzy rough sets. Therefore it has become a powerful tool for coping with vague and multigranular information in cognition. In this paper we introduce three kinds of CMGFRS models by means of fuzzy β -neighborhoods and fuzzy complementary β -neighborhoods, and we investigate their axiomatic properties. We investigate three respective types of coverings based CMGFRS models, namely, optimistic, pessimistic and variable precision setups. In particular, by using multigranulation fuzzy measure degrees and multigranulation fuzzy complementary measure degrees, we derive three types of coverings based γ -optimistic ( γ -pessimistic) CMGFRSs and E ( F , G )-optimistic and E ( F , G )-pessimistic CMGFRSs, respectively. We discuss the interrelationships among these three types of CMGFRS models and covering based Zhan-CMGFRS models. In view of the theoretical analysis for these three types of CMGFRS models, we put forward a novel methodology to multiple attribute group decision-making problem with evaluation of fuzzy information. An effective example is fully developed, hence concluding the applicability of the proposed methodology.

中文翻译：

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基于多粒度模糊粗糙集的新型覆盖类及其在多属性群决策中的应用

基于覆盖的多粒度模糊粗糙集 (CMGFRS) 模型的概念是粒计算和基于覆盖的模糊粗糙集的推广。因此，它已成为应对认知中模糊和多粒度信息的有力工具。在本文中，我们通过模糊β-邻域和模糊互补β-邻域介绍了三种CMGFRS模型，并研究了它们的公理性质。我们研究了基于 CMGFRS 模型的三种不同类型的覆盖，即乐观、悲观和可变精度设置。特别地，通过使用多粒度模糊测度度和多粒度模糊互补测度度，我们推导出三种基于覆盖的γ-乐观（γ-悲观）CMGFRS和E（F，G）-乐观和E（F，G）-悲观CMGFRS，分别。我们讨论了这三类 CMGFRS 模型和基于覆盖的 Zhan-CMGFRS 模型之间的相互关系。针对这三类 CMGFRS 模型的理论分析，我们提出了一种新的方法来解决具有模糊信息评价的多属性群决策问题。一个有效的例子得到了充分开发，从而得出了所提出方法的适用性。