Redefined fuzzy rough set models in fuzzy β-covering group approximation spaces

Abstract

The research purpose of this paper is to explore some new fuzzy rough set models in the fuzzy β-covering group approximation space (FβCGAS) and study the related properties, thereby provide new thinking directions for the theoretical development and application expansion of fuzzy rough set models. Firstly, in the fuzzy β-covering approximation space (FβCAS), in light of some existing fuzzy covering rough set (FCRS) models which do not satisfy the inclusion relations between the fuzzy upper and lower approximations, we define the concepts of parameterized fuzzy β-neighborhoods and parameterized fuzzy complementary β-neighborhoods to eliminate part of the noise data and establish four types of parameterized FCRS models that satisfy the inclusion relationship between the fuzzy lower and upper approximations. Meanwhile, the properties of the models are discussed. Further, in the FβCGAS, we define the concepts of the parameterized pessimistic (optimistic) fuzzy β-fitting neighborhoods and the parameterized pessimistic (optimistic) fuzzy complementary β-fitting neighborhoods and construct the parameterized pessimistic and optimistic FCRS models that satisfy the inclusion relationship between the fuzzy lower and upper approximations. At the same time, we likewise explore the properties of the models. Besides, we further use the newly proposed parameterized fuzzy neighborhoods to study the variable precision multi-granulation fuzzy decision-theoretic rough set models in the FβCGAS. Finally, for all the models mentioned above, we recommend them for solving the criteria weight determination problem, ranking problem, optimal selection problem and qualitative classification problem in multi-criteria decision-making. Meanwhile, we complete the relationships of all the new models mentioned in this paper and discuss them.