MBGrCA and its application in RST and fuzzy modelling

Abstract

Granular computing (GrC) has received great attention since its birth. Rough set theory (RST), as a concrete model of GrC, has been applied successfully to various fields. Many of its applications focus on the knowledge reductions that are partition-based, equivalence classes-based theory. By its extension, a matrix-based bit granular computing algorithm (MBGrCA) is proposed. Bit granular matrix (BGrM) and rough relation matrix (RRM) are defined and used to compute the fundamental concepts in RST and to analyse the interrelationships between equivalence classes. The MBGrCA can be adjusted to an appropriate granular levels by the parameter α. All the basic notions in RST and knowledge reduction can be easily realised by simple logic computations based on MBGrCA. An example is given to describe the new algorithm in detail. Furthermore, combined with fuzzy set theory, MBGrCA is applied to build optimal fuzzy forecast model for the traditional gas furnace problem. Examples and simulation results have shown that MBGrCA is simple, intuitive and easy to implement. It is a successful application of GrC to RST and fuzzy control.