A model of granular computing with applications. granules from rough inclusions in information systems
Lech Polkowski · 2006
The topic of granular computing, introduced by Zadeh and Lin, is steadily gaining interest due to its theoretical content as well as to possible applications. A framework that offers a natural context for discussing granulation mechanisms is rough set theory along with its formalization of knowledge by means of information systems in the sense of Pawlak, and this framework is adopted in our paper. Granulation by means of rough set theory has been studied, among others, by Lin, Yao, Skowron, Tsumoto, and the author. Granules of knowledge are induced naturally from the indiscernibility relations in information systems as equiv- alence classes of those relations; the induced structures are Boolean algebras of granules. A generalization has been proposed relaxing indiscernibility to similarity and discussing granules as similarity classes. A way of realization of this program has been proposed as the paradigm of rough mereology; although abstract, stemming from alternative set theory, yet it offers a calculus based on kind of weak metrics that allows for discussing granules from the point of view of their closeness. Rough mereology is based on rough inclusions, i.e., partial inclusions. Rough inclusions are predicates of the form an object x is a part of object y to degree at least r, in symbolic form: µ(x, y, r). The partial containment,