Toward a Theory of Granular Computing for Human-Centered Information Processing

Human-centered information processing has been pioneered by Zadeh through his introduction of the concept of fuzzy sets in the mid 1960s. The insights that were afforded through this formalism have led to the development of the granular computing (GrC) paradigm in the late 1990s. Subsequent research has highlighted the fact that many founding principles of GrC have, in fact, been adopted in other information-processing paradigms and, indeed, in the context of various scientific methodologies. This study expands on our earlier research exploring the foundations of GrC and casting it as a structured combination of algorithmic and non- algorithmic information processing that mimics human, intelligent synthesis of knowledge from information.

[1]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[2]  E. Zermelo Untersuchungen über die Grundlagen der Mengenlehre. I , 1908 .

[3]  A. Fraenkel Untersuchungen über die Grundlagen der Mengenlehre , 1925 .

[4]  S. Leśniewski Grundzüge eines neuen Systems der Grundlagen der Mathematik , 1929 .

[5]  S. Leśniewski Über Funktionen, deren Felder Gruppen mit Rücksicht auf diese Funktionen sind , .

[6]  A. Turing On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[7]  Willard Van Orman Quine,et al.  New Foundations for Mathematical Logic , 1937 .

[8]  K. Gödel The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis. , 1938, Proceedings of the National Academy of Sciences of the United States of America.

[9]  P. Bernays Review: Kurt Godel, George W. Brown, The Consistency of the Axiom of Choice and of the Generalized Continuum- Hypothesis with the Axioms of Set Theory , 1941, Journal of Symbolic Logic.

[10]  Lotfi A. Zadeh,et al.  Fuzzy sets and information granularity , 1996 .

[11]  Vijay K. Rohatgi,et al.  Advances in Fuzzy Set Theory and Applications , 1980 .

[12]  Witold Pedrycz,et al.  Fuzzy control and fuzzy systems , 1989 .

[13]  Timothy Williamson,et al.  Parts. A Study in Ontology , 1990 .

[14]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[15]  Lotfi A. Zadeh,et al.  Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic , 1997, Fuzzy Sets Syst..

[16]  Witold Pedrycz,et al.  An Introduction to Fuzzy Sets , 1998 .

[17]  Z. Pawlak Granularity of knowledge, indiscernibility and rough sets , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[18]  Yiyu Yao Granular Computing using Neighborhood Systems , 1999 .

[19]  Hava T. Siegelmann,et al.  Neural networks and analog computation - beyond the Turing limit , 1999, Progress in theoretical computer science.

[20]  Lotfi A. Zadeh From Computing with Numbers to Computing with Words - From Manipulation of Measurements to Manipulation of Perceptions , 2000, Intelligent Systems and Soft Computing.

[21]  Granular computing: an introduction , 2001 .

[22]  Andrzej Skowron,et al.  Information granules: Towards foundations of granular computing , 2001, Int. J. Intell. Syst..

[23]  Andrzej Skowron,et al.  Toward Intelligent Systems: Calculi of Information Granules , 2001, JSAI Workshops.

[24]  Andrzej Bargiela,et al.  Granular clustering: a granular signature of data , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[25]  Tsau Young Lin,et al.  Granular Computing on Binary Relations , 2002, Rough Sets and Current Trends in Computing.

[26]  Andrzej Bargiela,et al.  From numbers to information granules: a study of unsupervised learning and feature analysis , 2002 .

[27]  J. Yao,et al.  Granular Computing as a Basis for Consistent Classification Problems , 2002 .

[28]  L. Zadeh,et al.  Data mining, rough sets and granular computing , 2002 .

[29]  S. Tsumoto,et al.  Rough Set Theory and Granular Computing , 2003 .

[30]  Sre Bains,et al.  Intelligence as Physical Computation , 2003 .

[31]  Andrzej Bargiela,et al.  Recursive information granulation: aggregation and interpretation issues , 2003, IEEE Trans. Syst. Man Cybern. Part B.

[32]  A. Bargiela Hypercomputational characteristics of granular computing , 2004 .

[33]  Yiyu Yao,et al.  A Partition Model of Granular Computing , 2004, Trans. Rough Sets.

[34]  Andrzej Bargiela,et al.  An inclusion/exclusion fuzzy hyperbox classifier , 2004, Int. J. Knowl. Based Intell. Eng. Syst..

[35]  Andrzej Bargiela,et al.  Granular prototyping in fuzzy clustering , 2004, IEEE Transactions on Fuzzy Systems.

[36]  A. Tsvelikh,et al.  Preprocessing of triangulated multiply connected surfaces for quadrilateral mesh generation , 2004 .

[37]  Andrzej Bargiela,et al.  Granular mappings , 2005, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[38]  Sunny Rukhsana Elynn Bains Physical computation and embodied artificial intelligence , 2005 .

[39]  Andrzej Bargiela,et al.  A model of granular data: a design problem with the Tchebyschev FCM , 2005, Soft Comput..

[40]  Lotfi A. Zadeh,et al.  From Computing with Numbers to Computing with Words - from Manipulation of Measurements to Manipulation of Perceptions , 2005, Logic, Thought and Action.

[41]  Yiyu Yao,et al.  Perspectives of granular computing , 2005, 2005 IEEE International Conference on Granular Computing.

[42]  Andrzej Bargiela,et al.  The roots of granular computing , 2006, 2006 IEEE International Conference on Granular Computing.

[43]  Lotfi A. Zadeh,et al.  Granular Computing - The Concept of Generalized Constraint-Based Computation , 2006, RSCTC.

[44]  Rainer Schubert,et al.  A mathematical analysis of theories of parthood , 2006, Data Knowl. Eng..

[45]  Evtim Peytchev,et al.  Granular Analysis of Traffic Data for Turning Movements Estimation , 2006, Int. J. Enterp. Inf. Syst..

[46]  Yiyu Yao,et al.  Granular Computing , 2008 .

[47]  Tsau Young Lin,et al.  Granular Computing , 2003, RSFDGrC.