Relations of granular worlds

• Autorzy: Witold Pedrycz , George Vukovich
• Języki publikacji: EN

Abstrakty

EN

In this study, we are concerned with a two-objective development of information granules completed on a basis of numeric data. The first goal of this design concerns revealing and representing a structure in a data set. As such it is very much oriented towards coping with the underlying it relational aspects of the experimental data. The second goal deals with a formation of a mapping between information granules constructed in two spaces (thus it concentrates on the it directional aspect of information granulation). The quality of the mapping is directly affected by the information granules over which it operates, so in essence we are interested in the granules that not only reflect the data but also contribute to the performance of such a mapping. The optimization of information granules is realized through a collaboration occurring at the level of the data and the mapping between the data sets. The operational facet of the problem is cast in the realm of fuzzy clustering. As the standard techniques of fuzzy clustering (including a well-known approach of FCM) are aimed exclusively at the first objective identified above, we augment them in order to accomplish sound mapping properties between the granules. This leads to a generalized version of the FCM (and any other clustering technique for this matter). We propose a generalized version of the objective function that includes an additional collaboration component to make the formed information granules in rapport with the mapping requirements (that comes with a it directional component captured by the information granules). The additive form of the objective function with a modifiable component of collaborative activities makes it possible to express a suitable level of collaboration and to avoid a phenomenon of potential competition in the case of incompatible structures and the associated mapping. The logic-based type of the mapping (that invokes the use of fuzzy relational equations) comes as a consequence of the logic framework of information granules. A complete optimization method is provided and illustrated with several numeral studies.

Słowa kluczowe

EN

granular modeling; models of collaborative computing; collaboration and competition; clustering; fuzzy models; granular computing; FCM

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2002
• Tom: 12
• Numer: 3
• Strony: 347-357

Daty

wydano

2002

otrzymano

2002-03-01

poprawiono

2002-06-01

Twórcy

autor

Witold Pedrycz

• Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada

autor

George Vukovich

• Canadian Space Agency, Spacecraft Engineering, 6767 Route de l'Aeroport, Saint-Hubert, Quebec J3Y 8Y9, Canada

Bibliografia

• Anderberg M.R. (1973): Cluster Analysis for Applications. -New York: Academic Press.
• Bezdek J.C. (1981): Pattern Recognition with Fuzzy Objective Function Algorithms. - New York: Plenum Press.
• Di Nola A., Sessa S., Pedrycz W. and Sanchez E. (1989): Fuzzy Relational Equations and Their Applications in Knowledge Engineering. - Dordrecht: Kluwer.
• Delgado M., Gomez-Skarmeta F. and Martin F. (1997): A fuzzy clustering-based prototyping for fuzzy rule-based modeling. - IEEE Trans. Fuzzy Syst., Vol. 5, No. 2, pp. 223-233.
• Delgado M., Gomez-Skarmeta A.F. and Martin F. (1998): A methodology to model fuzzy systems using fuzzy clustering in a rapid-prototyping approach. - Fuzzy Sets Syst., Vol. 97, No. 3, pp. 287-302.
• Duda R.O., Hart P.E. and Stork D.G. (2001): Pattern Classification, 2-nd Ed. - New York: Wiley.
• Dunn J.C. (1973): A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. - J. Cybern., Vol. 3, No. 3, pp. 32-57.
• Hoppner F., Klawonn F., Kruse R. and Runkle T. (1999): Fuzzy Cluster Analysis. - Chichester: Wiley.
• Jang J.-S.R. (1993): ANFIS: Adaptive-network-based fuzzy inference system. - IEEE Trans. Syst. Man Cybern., Vol. 23, No. 3, pp. 665-685.
• Kandel A. (1986): Fuzzy Mathematical Techniques with Applications. - Reading: Addison-Wesley.
• Kowalczyk R. and Bui V. (2000): On constraint-based reasoning in e-negotiation agents, In: Agent Mediated Electronic Commerce (F. Didnum and U. Cortes, Eds.). - Berlin: Springer-Verlag, pp. 31-46.
• Ma M., Zhang Y.-Q., Langholz G. and Kandel A. (2000): On direct construction of fuzzy systems. - Fuzzy Sets Syst., Vol. 112, No. 1, pp. 165-171.
• Pedrycz W. (1991): Neurocomputations in relational systems. - IEEE Trans. Pattern Anal. Mach. Intell., Vol. 13, No. 3, pp. 289-296.
• Pedrycz W. and Rocha A. (1993): Knowledge-based neural networks. - IEEE Trans. Fuzzy Syst., Vol. 1, No. 4, pp. 254-266.
• Pedrycz W., Lam P. and Rocha A.F. (1995): Distributed fuzzy modelling. - IEEE Trans. Syst. Man Cybern., Vol. 1, No. 4, pp. 769-780.
• Pedrycz W. (1995): Fuzzy Sets Engineering. - Boca Raton, FL: CRC Press.
• Pedrycz W. (1998): Conditional fuzzy clustering in the design of radial basis function neural networks. - IEEE Trans.Neural Netw., Vol. 9, No. 4, pp. 601-612.
• Pedrycz W. and Vasilakos A.V. (1999): Linguistic models and linguistic modeling. - IEEE Trans. Syst. Man Cybern., Vol. 29, No. 6, pp. 745-757.
• Setnes M. (2000): Supervised fuzzy clustering for rule extraction. - IEEE Trans. Fuzzy Syst., Vol. 8, No. 4, pp. 416-424.
• Sugeno M. and Yasukawa T. (1993): A fuzzy-logic-based approach to qualitative modeling. - IEEE Trans. Fuzzy Syst., Vol. 1, No. 1, pp. 7-31.
• Zhang Y.-Q. and Kandel A. (1998): Compensatory Genetic Fuzzy Neural Networks and Their Applications. - Singapore: World Scientific.