Granular Computing: At the Frontiers of Knowledge-Based Representation and Knowledge Processing

Witold Pedrycz1

1Department of Electrical & Computer Engineering, University of Alberta, Edmonton AB, T6R 2V4, Canada and Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland
wpedrycz@ualberta.ca

 

In the plethora of rapidly progressing and advanced areas of information technology, it is anticipated that the resulting artefacts involved in system analysis and synthesis take into consideration available data and domain knowledge. They lead to the development of tangible and experimentally legitimized descriptors (concepts), and associations. Concepts constitute a concise manifestation of data and serve as a backbone of efficient user-centric processing. As being built at the higher level of abstraction than the data themselves, they capture the essence of data and usually emerge in the form of information granules. Processing information granules is carried out in the framework of Granular Computing (including a spectrum of formal frameworks of interval calculus, fuzzy sets, probabilities, and rough sets among others). We identify three main ways in which concepts are encountered and characterized: (i) numeric, (ii) symbolic, and (iii) granular. Each of these views comes with advantages and limitations. The views complement each other. The numeric concepts are built by engaging various clustering techniques. The quality of numeric concepts evaluated at the numeric level is described by a reconstruction criterion. The symbolic description of concepts, which is predominant in the realm of Artificial Intelligence (AI) and symbolic computing, can be represented by sequences of labels (integers). In such a way qualitative aspects of data are captured. This facilitates further qualitative analysis of concepts and constructs involving them by reflecting the bird’s-eye view at data and relationships. The granular concepts augment numeric concepts by bringing information granularity into the picture and invoking the principle of justifiable granularity in their development.

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