Abstract
In their book, Granular Computing: An Introduction, Bargiela and Pedrycz present a view that granular computing is an emerging conceptual and computing paradigm of information processing. A central notion is an information-processing pyramid with multiple levels. Different levels involve different types of processing. The lowest level concerns numeric processing, the intermediate level concerns larger information granules, and the highest level concerns symbol-based processing. This chapter examines the notion of integrative levels of granularity as a basis of granular computing. The notion of levels had been studied extensively in different branches of sciences and different fields of computer sciences. By extracting a set of common features and principles of integrative levels of granularity, the triarchic theory of granular computing is developed.
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References
Ahl, V., Allen, T.F.H.: Hierarchy Theory, a Vision, Vocabulary and Epistemology. Columbia University Press (1996)
Allen, T.F.: A Summary of the Principles of Hierarchy Theory (accessed March 11, 2005), http://www.isss.org/hierarchy.htm
Bargiela, A., Pedrycz, W.: Granular Computing: An Introduction. Kluwer Academic Publishers, Boston (2002)
Bargiela, A., Pedrycz, W.: The roots of granular computing. In: Proceedings of 2006 IEEE International Conference on Granular Computing, pp. 806–809 (2006)
Bargiela, A., Pedrycz, W.: Toward a theory of granular computing for human-centered information processing. IEEE Transactions on Fuzzy Systems (to appear, 2008)
Capra, F.: The Web of Life. Anchor Books, New York (1997)
Chen, Y.H., Yao, Y.Y.: A multiview approach for intelligent data analysis based on data operators. Information Sciences 178, 1–20 (2008)
Conger, G.P.: The doctrine of levels. The Journal of Philosophy 22, 309–321 (1925)
Craik, F.I.M.: Levels of processing: past, present ...and future? Memory 10, 305–318 (2002)
Craik, F.I.M., Lockhart, R.S.: Levels of processing: a framework for memory research. Journal of Verbal Learning and Verbal Behavior 11, 671–684 (1972)
Feibleman, J.K.: Theory of integrative levels. The British Journal for the Philosophy of Science 5, 59–66 (1954)
Flower, L.: Problem-Solving Strategies for Writing. Harcourt Brace Jovabovich, Inc., New York (1981)
Flower, L.S., Hayes, J.R.: Problem-solving strategies and the writing process. College English 39, 449–461 (1977)
Foster, C.L.: Algorithms, Abstraction and Implementation: Levels of Detail in Cognitive Science. Academic Press, London (1992)
Frank, S.D.: Remember Everything You Read. Times Books, New York (1990)
Friske, M.: Teaching proofs: a lesson from software engineering. American Mathematical Monthly 92, 142–144 (1995)
Gray, W., Rizzo, N.D. (eds.): Unity Through Diversity, I & II. Gordon and Breach Science Publishers, New York (1973)
Hawkins, J., Blakeslee, S.: On Intelligence. Henry Holt and Company, New York (2004)
Hobbs, J.R.: Granularity. In: Proceedings of the Ninth International Joint Conference on Artificial Intelligence, pp. 432–435 (1985)
Inuiguchi, M., Hirano, S., Tsumoto, S. (eds.): Rough Set Theory and Granular Computing. Springer, Berlin (2003)
Keet, C.M.: A taxonomy of types of granularity. In: Proceeding of 2006 IEEE International Conference on Granular Computing, pp. 106–111 (2006)
Keet, C.M.: A Formal Theory of Granularity, PhD Thesis, KRDB Research Centre, Faculty of Computer Science, Free University of Bozen-Bolzano, Italy (2008) (accessed June 8, 2008), http://www.meteck.org/files/AFormalTheoryOfGranularity_CMK08.pdf
Lamport, L.: How to write a proof. American Mathematical Monthly 102, 600–608 (1995)
Laszlo, E.: The Systems View of the World: the Natural Philosophy of the New Developments in the Science. George Brasiller, New York (1972)
Ledgard, H.F., Gueras, J.F., Nagin, P.A.: PASCAL with Style: Programming Proverbs. Hayden Book Company, Inc., New Jersey (1979)
Leron, U.: Structuring mathematical proofs. American Mathematical Monthly 90, 174–185 (1983)
Lin, T.Y., Yao, Y.Y., Zadeh, L.A. (eds.): Data Mining, Rough Sets and Granular Computing. Physica-Verlag, Heidelberg (2002)
Marr, D.: Vision, A Computational Investigation into Human Representation and Processing of Visual Information. W.H. Freeman and Company, San Francisco (1982)
Miller, G.A.: The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychological Review 63, 81–97 (1956)
Minsky, M.: The Emotion Machine: Commonsense Thinking, Artificial Intelligence, and the Future of the Human mind. Simon & Schuster Paperbacks, New York (2006)
Minto, B.: The Pyramid Principle: Logic in Writing and Thinking. Prentice Hall/Financial Times, London (2002)
Newell, A.: The knowledge level. Artificial Intelligence 18, 87–127 (1982)
Newell, A.: Reflections on the knowledge level. Artificial Intelligence 59, 31–38 (1993)
Nguyen, S.H., Skowron, A., Stepaniuk, J.: Granular computing: a rough set approach. Computational Intelligence 17, 514–544 (2001)
Novikoff, A.B.: The concept of integrative levels and biology. Science 101, 209–215 (1945)
Patrides, C.A.: Hierarchy and order. In: Dictionary of the History of Ideas, pp. 434–449. Scribners, New York (1973)
Pattee, H.H.: Unsolved problems and potential applications of hierarchy theory. In: Pattee, H.H. (ed.) Hierarchy Theory, The Challenge of Complex Systems, pp. 129–156. George Braziller, New York (1973)
Pawlak, Z.: Granularity of knowledge, indiscernibility and rough sets. In: Proceedings of 1998 IEEE International Conference on Fuzzy Systems, pp. 106–110 (1998)
Pedrycz, W., Skowron, A., Kreinovich, V. (eds.): Handbook of Granular Computing. Wiley, New York (2008)
Peikoff, L.: Objectivism: the Philosophy of Ayn Rand. Dutton, New York (1991)
Poli, R.: Levels. Axiomathes 9, 197–211 (1998)
Poli, R.: The basic problem of the theory of level of reality. Axiomathes 12, 261–283 (2002)
Posner, M.I. (ed.): Foundations of Cognitive Science. The MIT Press, Cambridge (1989)
Ramberg, B., Gjesdal, K.: Hermeneutics. The Stanford Encyclopedia of Philosophy (accessed June 14, 2005)
Reif, F., Heller, J.: Knowledge structure and problem solving in physics. Educational Psychologist 17, 102–127 (1982)
Salthe, S.N.: Evolving Hierarchical Systems, Their Structure and Representation. Columbia University Press (1985)
Simon, H.A.: The organization of complex systems. In: Pattee, H.H. (ed.) Hierarchy Theory, The Challenge of Complex Systems, pp. 1–27. George Braziller, New York (1973)
Simpson, S.G.: What is foundations of mathematics? (accessed November 21, 1996), http://www.math.psu.edu/simpson/hierarchy.html
Skyttner, L.: General Systems Theory, Ideas & Applications. World Scientific, Singapore (2001)
Verdier, B.: Hierarchy: a short history of a word in western thought. In: Pumain, D. (ed.) Hierarchy in Natural and Social Sciences, pp. 13–37. Springer, The Netherlands (2006)
von Bertalanffy, L.: An outline of general system theory. The British Journal for the Philosophy of Science 1, 134–165 (1950)
Wilson, T.D.: Philosophical foundations and research relevance: issues for information research. Journal of Information Science 29, 445–452 (2003)
Yao, J.T.: A ten-year review of granular computing. In: Proceedings of 2007 IEEE International Conference on Granular Computing, pp. 734–739 (2007)
Yao, Y.Y.: Granular computing: basic issues and possible solution. In: Proceedings of the 5th Joint Conference on Information Sciences, pp. 186–189 (2000)
Yao, Y.Y.: A partition model of granular computing. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 232–253. Springer, Heidelberg (2004)
Yao, Y.Y.: Granular computing. Computer Science (Ji Suan Ji Ke Xue) 31, 1–5 (2004b)
Yao, Y.Y.: Perspectives of granular computing. In: Proceedings of 2005 IEEE International Conference on Granular Computing, pp. 85–90 (2005)
Yao, Y.Y.: Three perspectives of granular computing. Journal of Nanchang Institute of Technology 25, 16–21 (2006)
Yao, Y.Y.: The art of granular computing. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds.) RSEISP 2007. LNCS, vol. 4585, pp. 101–112. Springer, Heidelberg (2007)
Yao, Y.Y.: Structured writing with granular computing strategies. In: Proceedings of 2007 IEEE International Conference on Granular Computing, pp. 72–77 (2007b)
Yao, Y.Y.: The rise of granular computing. Journal of Chongqing University of Posts and Telecommunications (Natural Science Edition) 20, 299–308 (2008)
Young, G.L.: Hierarchy and central place: some questions of more general theory. Geografiska Annaler, Series B, Human Geography 60, 71–78 (1978)
Zadeh, L.A.: Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets and Systems 90, 111–127 (1997)
Zhang, L., Zhang, B.: Theory and Application of Problem Solving – Theory and Application of Granular Computing in Quotient Spaces, 2nd edn. Tsinghua University Press, Beijing (2007)
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Yao, Y. (2009). Integrative Levels of Granularity. In: Bargiela, A., Pedrycz, W. (eds) Human-Centric Information Processing Through Granular Modelling. Studies in Computational Intelligence, vol 182. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92916-1_2
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DOI: https://doi.org/10.1007/978-3-540-92916-1_2
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