Affiliations: Department of Electrical & Computer Engineering, University of Alberta, Edmonton, Canada. [email protected]
Note: [] Address for correspondence: Department of Electrical & Computer Engineering, University of Alberta, Edmonton AB T6R 2V4 Canada Also works: Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia and Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland
Abstract: Fuzzy sets (membership functions) are numeric constructs. In spite of the underlying semantics of fuzzy sets (which is inherently linked with the higher level of abstraction), the membership grades and processing of fuzzy sets themselves emphasize the numeric facets of all pursuits stressing the numeric nature of membership grades and in this way reducing the interpretability and transparency of results. In this study, we advocate an idea of a granular description of membership functions where instead of numeric membership grades, introduced are more interpretable granular descriptors (say, low, high membership, etc.). Granular descriptors are formalized with the aid of various formal schemes available in Granular Computing, especially sets (intervals), fuzzy sets, and shadowed sets. We formulate a problem of a design of granular descriptors as a certain optimization task, elaborate on the solutions and highlight some areas of applications.
