On Foundations and Applications of the Paradigm of Granular Rough Computing

On Foundations and Applications of the Paradigm of Granular Rough Computing

Lech Polkowski (Polish-Japanese Institute of Information Technology, Poland) and Maria Semeniuk-Polkowska (Warsaw University, Poland)
DOI: 10.4018/978-1-60566-902-1.ch018
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Abstract

Granular computing, initiated by Lotfi A. Zadeh, has acquired wide popularity as a tool for approximate reasoning, fusion of knowledge, cognitive computing. The need for formal methods of granulation, and means for computing with granules, has been addressed in this work by applying methods of rough mereology. Rough mereology is an extension of mereology taking as the primitive notion the notion of a part to a degree. Granules are formed as classes of objects which are a part to a given degree of a given object. In addition to an exposition of this mechanism of granulation, we point also to some applications like granular logics for approximate reasoning and classifiers built from granulated data sets.
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Notions Central To Granulation Of Knowledge

Granulation of knowledge is one of important aspects of the way in which the human brain works (see, e.g., Pal, 2004). A vast literature on emulating such aspects of the brain workings as granulation, fusion of knowledge, classification by means of neural networks, fuzzy logics, and so on, does witness the role the computer science society attaches to them. These aspects are studied with at least a twofold purpose. First, to get an insight into the processes of perception, concept formation, and reasoning in the brain; second, to transfer this knowledge into the realm of applications.

The emergence of ample paradigms like cognitive informatics and natural intelligence (see, e.g., Chan, Kisner, Wang. & Miller, 2004; Kinsner, Zang, Wang, & Tsai, 2005; Patel, Patel, & Wang, 2003; Wang, 2007, Wang, Johnston, & Smith, 2002; Yao, Shi, Wang, & Kinsner, 2006) is due in large part to these studies and emulations of vital aspects of the brain mechanism. This emergence is welcomed as it provides a forum for an intradisciplinary study of mechanisms of perception, cognition, and reasoning.

Our work is devoted to the aspect of granulation of knowledge with applications to synthesis (fusion) of knowledge from various sources, reasoning in uncertain situations by means of approximate logics and data classification: all these aspects vital for human intelligence.

In this section, we describe basic tools applied in our analysis of granulation. First, we discuss basic principles of rough set theory (Pawlak, 1982, 1991) in particular, the notion of an information system. Next, we give space to an introduction to mereology (Leśniewski, 1916) whose techniques are important in our development of granular computing. Then, similarity is discussed briefly as a bridge to the final part of this section devoted to rough mereology (Polkowski, 2005, 2006; Polkowski & Skowron, 1997).

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