Granular Computing and Rough Set Theory

  • Authors:
  • Lotfi A. Zadeh

  • Affiliations:
  • Department of EECS, University of California, Berkeley, CA 94720-1776,

  • Venue:
  • RSEISP '07 Proceedings of the international conference on Rough Sets and Intelligent Systems Paradigms
  • Year:
  • 2007

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Abstract

Granulation plays an essential role in human cognition and has a position of centrality in both granular computing and rough set theory. Informally, granulation involves partitioning of an object into granules, with a granule being a clump of elements drawn together by indistinguishability, equivalence, similarity, proximity or functionality. For example, an interval is a granule; so is a fuzzy interval; so is a gaussian distribution; so is a cluster of points; and so is an equivalence class in rough set theory. A granular variable is a variable which takes granules as values. If Gis value of X, then Gis referred to as a granular value of X. If Gis a singleton, then Gis a singular value of X. A linguistic variable is a granular variable whose values are labeled with words drawn from a natural language. For example, if Xis temperature, then 101.3 is a singular value of temperature, while "high" is a granular (linguistic) value of temperature.