Granular computing: Models and applications

Granular computing (GrC) is a general computing paradigm that effectively deals with elements and granules, vaguely generalized subsets. The objective of granular computing research is to build an efficient computational model for handling huge amounts of data, information, and knowledge. The terminology of granular computing was first proposed by Professor T. Y. Lin in 19961 as a label of family of theories, methodologies, and techniques that make use of granules, although its basic ideas and principles have been studied in various application domains for a long time. Especially in the form of partitions, the theory has been accumulated for thousands of years in mathematics. So the focus of GrC is on the nonpartition models. Let us first recall some results and thoughts in the pre-GrC era, namely before the terms was invented. The explicit study of granular computing can be dated back to the late 1970s. In 1979, Zadeh2 introduced the notion of information granulation and suggested that fuzzy set theory might find potential applications in this respect. Although we address the nonpartition theories, nevertheless, the partition case was the main source of inspiration. In 1982, Pawlak3 proposed rough set theory to deal with inexact information. It is an uncertainty theory using a special form of granules, called equivalence classes. It is primarily the rough set theory (partition theory) that causes researchers to realize the importance of the systematic study of the generalized notion, GrC. In 1985, Hobbes4 presented a theory of granularity as the base of knowledge representation, abstraction, heuristic search, and reasoning. In his theory the problem world is represented as various grains and only interesting ones are abstracted to learn concepts. The conceptualization of the world can be performed at different granularities and switched between them. Even though his discussion mainly focused on the partition cases, his model is more general than rough sets. It includes reflexive and symmetric binary relations.

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