Set-theoretic Approaches to Granular Computing

• Autorzy: Yao Y. , Miao D. , Zhang N. , Xu F.
• Języki publikacji: EN

Abstrakty

EN

A framework is proposed for studying a particular class of set-theoretic approaches to granular computing. A granule is a subset of a universal set, a granular structure is a family of subsets of the universal set, and relationship between granules is given by the standard set-inclusion relation. By imposing different conditions on the family of subsets, we can define several types of granular structures. A number of studies, including rough set analysis, formal concept analysis and knowledge spaces, adopt specific models of granular structures. The proposed framework therefore provides a common ground for unifying these studies. The notion of approximations is examined based on granular structures.

Słowa kluczowe

EN

granular computing; granular structures; rough set analysis; formal concept analysis; knowledge spaces

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2012
• Tom: Vol. 115, nr 2/3
• Strony: 247--264
• Opis fizyczny: Bibliogr. 39 poz., tab., wykr.

Twórcy

autor

Yao Y.

autor

Miao D.

autor

Zhang N.

autor

Xu F.

• Room 501, School of Electronics and Information Engineering, Tongji University, Shanghai, China 201804,

Bibliografia

• [1] Bargiela, A., Pedrycz, W.: Granular Computing: An Introduction, Kluwer Academic Publishers, Boston, 2002.
• [2] Caspard, N., Monjardet, B.: Some lattices of closure systems on a finite set, Discrete Mathematics and Theoretical Computer Science, 6, 163-190, 2004.
• [3] Cattaneo, G.: Abstract approximation spaces for rough theories, in: Polkowski, L. and Skowron, A. (Eds.), Rough Sets in Knowledge Discovery 1: Methodology and Applications, Physica-Verlag, Heidelberg, 59-98, 1998.
• [4] Ciucci, D.: Approximation algebra and framework, Fundamenta Informaticae, 94, 147-161, 2009.
• [5] Ciucci, D.: Orthopairs: a simple and widely used way to model uncertainty, Fundamenta Informaticae, 108, 287-304, 2011.
• [6] Doignon, J.P., Falmagne, J.C.: Spaces for the assessment of knowledge, International Journal of Man-Machine Studies, 23, 175-196, 1985.
• [7] Doignon, J.P., Falmagne, J.C.: Knowledge Spaces, Springer-Verlag, Berlin, 1999.
• [8] Falmagne, J.C., Koppen, M., Villano, M., Doignon, J.P., Johanessen, L.: Introduction to knowledge spaces:how to test and search them, Psychological Review, 97, 201-224, 1990.
• [9] Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations, Springer-Verlag, Berlin, 1999.
• [10] Hobbs, J.R.: Granularity, Proceedings of the 9th International Joint Conference on Artificial Intelligence, 432-435, 1985.
• [11] Järvinen, J.: Lattice theory for rough sets, LNCS Transactions on Rough Sets, 6, LNCS 4374, 400-498, 2007.
• [12] Keet, C.M.: A taxonomy of types of granularity, Proceeding of the 2006 IEEE International Conference on Granular Computing, 106-111, 2006.
• [13] Keet, C.M.: A Formal Theory of Granularity, PhD Thesis, KRDB Research Centre, Faculty of Computer Science, Free University of Bozen-Bolzano, Italy (2008), http://www.meteck.org/files/AFormalTheoryOfGranularity CMK08.pdf (accessed June 8, 2008)
• [14] Li, T.J., Jing, Y.L.: Rough set approximations on granular structures and feature characterizations, in: Zhang, Y.C., Alfredo, C., Ma, J.H., Chung, K.I., Arslan, T. and Song, X.F. (Eds.). Database Theory and Application, Bio-Science and Bio-Technology, Springer, Berlin, 79-88, 2010.
• [15] Miao, D.Q., Fan, S.D.: The calculation of knowledge granulation and its application, System Engeering-Theory and Practice, 22, 48-56, 2002.
• [16] Miao, D Q.,Wang, G.Y., Liu, Q., Lin, T.Y., Yao, Y.Y. (Eds.): Granular Computing: Past, Present and Future, Science Press, Beijing, 2007.
• [17] Nguyen, H.S., Skowron, A., Stepaniuk, J.: Granular computing: a rough set approach, Computational Intelligence, 17, 514-544, 2001.
• [18] Pawlak, Z.: Rough sets, International Journal of Computer and Information Sciences, 11, 341-356, 1982.
• [19] Pawlak, Z.: Rough Sets-Theoretical Aspects of Reasoning About Data, Kluwer Academic Publishers, Boston, 1991.
• [20] Pawlak, Z., Skowron, A.: Rough sets: some extensions, Information Sciences, 177, 28-40, 2007.
• [21] Pedrycz, W., Skowron, A., Kreinovich, V. (Eds.): Handbook of Granular Computing, Wiley-Interscience, New York, 2008.
• [22] Shiu, L.P., Sin, C.Y.: Top-down, middle-out, and bottom-up processes: a cognitive perspective of teaching and learning economics, International Review of Economics Education, 5, 60-72, 2006.
• [23] Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts, in: Rival I. (Ed.), Ordered sets, Reidel, Boston, 445-470, 1982.
• [24] Wille, R.: Concept lattices and conceptual knowledge systems, Computers Mathematics with Applications, 23, 493-515, 1992.
• [25] Xu, F.F., Yao, Y.Y., Miao, D.Q.: Rough set approximations in formal concept analysis and knowledge spaces, Proceedings of 17th International Symposium of Foundations of Intelligent Systems, LNCS(LNAI) 4994, 319-328, 2008.
• [26] Yao, J.T.: A ten-year review of granular computing, Proceedings of 2007 IEEE Internationational Conference on Granular Computing, 734-739, 2007.
• [27] Yao, J.T. Recent developments in granular computing: a bibliometrics study, Proceedings of 2008 IEEE International Conference on Granular Computing, 74-79, 2008.
• [28] Yao, Y.Y.: On generalizing Pawlak approximation operators, Proceedings of the 1st International Conference on Rough Sets and Current Trends in Computing, LNCS(LNAI) 1424, 298-307, 1998.
• [29] Yao, Y.Y.: On generalizing rough set theory, Proceedings of the 9th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, LNCS(LNAI) 2639, 44-51, 2003.
• [30] Yao, Y.Y.: A comparative study of formal concept analysis and rough set theory in data analysis, Proceedings of 4th International Conference of Rough Sets and Current Trends in Computing, LNCS(LNAI) 3066, 59-68, 2004.
• [31] Yao, Y.Y.: Perspectives of granular computing, Proceedings of 2005 IEEE International Conference on Granular Computing, 85-90, 2005.
• [32] Yao, Y.Y.: Three perspectives of granular computing, Journal of Nanchang Institute of Technology, 25, 16-21, 2006.
• [33] Yao, Y.Y.: Granular computing: past, present and future, Proceedings of 2008 IEEE International Conference on Granular Computing, 80-85, 2008.
• [34] Yao, Y.Y.: Interpreting concept learning in cognitive informatics and granular computing, IEEE Transactions on Systems, Man, and Cybernetics (Part B), 39, 855-866, 2009.
• [35] Yao, Y.Y., Chen, Y.H.: Rough set approximations in formal concept analysis, LNCS Transactions on Rough Sets, V, LNCS 4100, 285-305, 2006.
• [36] Yao, Y.Y., Miao, D.Q., Xu, F.F.: Granular structures and approximations in rough sets and knowledge spaces, in: Abraham, A., Falc´on, R. and Bello, R. (Eds.), Rough Set Theory: A True Landmark in Data Analysis, Springer, Berlin, 71-84, 2009.
• [37] Yao, Y.Y., Miao, D.Q., Zhang, N., Xu, F.F.: Set-theoretic models of granular structures, Proceedings of the 5th International Conference on Rough Set and Knowledge Technology, LNCS(LNAI) 6401, 94-101, 2010.
• [38] Yao, Y.Y., Zhou, B.: A logic language of granular computing, Proceedings 6th IEEE International Conference on Cognitive Informatics, 178-185, 2006.
• [39] 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.