In this chapter, we embark on a more specific granulation theory, stemming from the mereological theory of things. This mechanism provides us with tolerance and weak tolerance relations forming a graded similarity in the sense of Chap.1 and with resulting therefrom granules. To put the necessary notions in a proper order, we are going to discuss mereology, rough mereology and the mereological g...

We address in principle the notion of a boundary and we propose a version of mereology better adapted to rough set theory than the original version. We discuss the motivation and differences between the original and proposed now versions of rough mereology and we show that the Pawlak notion of a boundary in rough set theory is a particular case of the more general notion of a boundary in the ro...

We propose a uniied formal treatment of design, analysis, synthesis and control in distributed systems of intelligent agents. Our approach goes back to rough set the+ory and we propose rough mereology as a foundational basis for our approach. Rough mereology is a theory of the relation of being a part in a degree which can be regarded as a particular implementation of a general idea of fuzzy co...

We outline a rough–neuro computing model as a basis for granular computing. Our approach is based on rough sets, rough mereology and information granule calculus.

Mereotopology aims at a reconstruction of notions of set topology in mereological universa. Because of foundational differences between set theory and mereology, most notably, the absence of points in the latter, the rendering of notions of topology in mereology faces serious difficulties. On the other hand, some of those notions, e.g., the notion of a boundary, belong in the canon of the most ...

The first paper by Polkowski and Artiemjew, entitled “On Knowledge Granulation and Applications to Classifier Induction in the Framework of Rough Mereology” presents basic ideas of rough mereology and a description of basic similarity measures called rough inclusions along with the idea of granulated data sets. It then discusses how to construct classifiers from granular data and obtain results...

In this paper we propose a fuzzy rule generation approach based on granular computing using rough mereology (FRGAGCRM). The proposed system works in two phases. In the first phase, the pre-processing phase which use fuzzification methodology which map the numeric dataset into categorical dataset according to membership function described in this paper. In other hand, the second phase consists o...

We introduce a system of cooperating intelligent agents acting as an adaptive controller for synthesis of complex objects from elementary parts and transforming a semantic input (a constraint on the nal assembly) into the assembly with a decision attribute (quality) value. The input-output transition is eeected by logic of rough mereology , an extension of the Lesniewski mereology.

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We present a brief account of rough mereology-an approach to problems of approximate reasoning about complex objects and we outline possible applications of the presented formalism. 1 Approximate reasoning based on rough mereology We would like to give here a brief account of the rough mere-ological approach to approximate reasoning. We propose this formalization as a tool for solving multi-age...