Analyses And Applications Of Hierarchical Structures In Granular Computing Theory

Granular Computing(GrC) was firstly proposed by Professor Zadeh, which can be considered as a structured way of thinking, structured problem solving and paradigm of information processing. Presently, granular computing has become a new method to simulate human thinking and complex problem solving in the field of computational intelligence. It is also an effective tool to huge amounts of data mining, fuzzy information processing, machine learning, etc. The granular structure in granular computing provides a structured description of a system or a problem, and there are multiple explanations and descriptions to the system or the problem at the same time. The formation of a granular structure is often modeled as a variety of hierarchies. Therefore, hierarchy plays an important role in the granular computing. In this paper, the hierarchies on granular computing are researched, there are several innovations as follows:(1) To research the hierarchy on covering, the concept of knowledge distance is proposed on covering. Moreover, two different algebra lattices are constructed through the new proposed knowledge distance lattices. Finally, the partial relations induced by such two algebraic lattices are used to characterize the hierarchy on covering.(2) To research the hierarchy on covering based multigranularion space, i.e., the information granule is formed by a family of coverings, two different kinds of knowledge distances are proposed on covering-based multigranultion space. Moreover, two different algebra lattices are constructed through the new proposed knowledge distance lattices. Finally, the partial relations induced by such two algebraic lattices are used to characterize the hierarchy on covering-based multigranulation space.(3) To research the hierarchy on fuzzy information granulation, not only the fuzzy information granulations derived from the fuzzy binary relations are presented in this paper, but also three orderings are explored for expressing the hierarchies on fuzzy information granulations. Furthermore, the concept of knowledge distance is introduced into fuzzy information granulations, which can be used to construct the knowledge distance lattices. Finally, the partial relations induced by such algebraic lattices are used to characterize the hierarchy on fuzzy information granulations.(4) To further extend the applications of fuzzy rough set, in the view of the most existing fuzzy rough set models are not adjustable, an adjustable fuzzy rough set is proposed by using a parameterized binary operator. Moreover, the approximate quality is regarded as a measurement and then the heuristic algorithm is used to calculate the reduct of the adjustable fuzzy rough set. Finally, the approximate quality and the reduct of adjustable fuzzy rough set are compared with those of the strong fuzzy rough set and the weak fuzzy rough set, respectively.