Granular computing and attribute reduction based on a new discernibility function

This paper first discusses the method of attribute reduction to determine the discernibility matrix and the discernibility function, which lead to some questions being asked. To find the answers, a new discernibility function is introduced based on information systems and a logical formula defined in the information system. Because each formula produces a granule, the new discernibility function also corresponds to a granule viewed as the semantics. Formulas and granules make it possible to connect the discernibility function with granular computing, which is a current topic of data processing in information science. It sets the stage for research on the new discernibility function using a granular computing method. Accordingly, a conclusion is reached which shows the granule produced by the new discernibility function is equal to the union of all discernibility relations generated by the attributes. Some theorems are proved based on the conclusion, which are answers to the questions. © 2016, UK Simulation Society. All rights reserved.