Granular Computing: Granular Classifiers and Missing Values

  • Authors:
  • Lech Polkowski;Piotr Artiemjew

  • Affiliations:
  • Polish-Japanese Institute of Information Technology, Koszykowa str. 86, 02008 Warsaw, Poland/ Department of Mathematics and Computer Science, University of Warmia and Mazury, Zolni;Department of Mathematics and Computer Science, University of Warmia and Mazury, Zolnierska 14, 10560 Olsztyn, Poland, email:artem@matman.uwm.edu.pl

  • Venue:
  • COGINF '07 Proceedings of the 6th IEEE International Conference on Cognitive Informatics
  • Year:
  • 2007

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Abstract

Granular Computing is a paradigm destined to study how to compute with granules of knowledge that are collective objects formed from individual objects by means of a similarity measure. The idea of granulation was put forth by Lotfi Zadeh: granulation is inculcated in fuzzy set theory by the very definition of a fuzzy set and inverse values of fuzzy membership functions are elementary forms of granules. Similarly, rough sets admit granules defined naturally as classes of indiscernibility relations; the search for more flexible granules has led to granules based on blocks (Grzymala-Busse), templates (H.S.Nguyen), rough inclusions (Polkowski, Skowron), and tolerance or similarity relations, and more generally, binary relations (T.Y. Lin, Y. Y. Yao). Granulation is an essential ingredient of humane thinking and it is playing a vital role in cognitive processes which are studied in Cognitive Informatics as emulations by computing machines of real cognitive processes in humane thinking. Rough inclusions establish a form of similarity relations that are reflexive but not necessarily symmetric; in applications presented in this work, we restrict ourselves to symmetric rough inclusions based on the set DIS(u, v) = {a ε A: a(u) ≠ a(v)} of attributes discerning between given objects u, v without any additional parameters.