Approximation Spaces Based on Relations of Similarity and Dissimilarity of Objects

• Autorzy: Gomolińska A.
• Języki publikacji: EN

Abstrakty

EN

In this article, we aim at extension of similarity-based approximation spaces to the case, where both similarity and dissimilarity of objects are taken into account. Apart from the well-known notions of lower rough approximation, upper rough approximation, and variable-precision positive regions of concepts, adapted to our case, the notions of exterior, possibly negative region, and ignorance region of concepts are introduced and investigated.

Słowa kluczowe

EN

approximation space; concept approximations; similarity relation; dissimilarity relation

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2007
• Tom: Vol. 79, nr 3-4
• Strony: 319--333
• Opis fizyczny: bibliogr. 36 poz., tab.

Twórcy

autor

Gomolińska A.

• Department of Mathematics University of Białystok, Akademicka 2, 15-267 Białystok, Poland,

Bibliografia

• [1] Albatineh, A. N., Niewiadomska-Bugaj, M., Mihalko, D.: On similarity indices and correction for chance agreement, J. of Classification, 23, 2006, 301-313.
• [2] Baulieu, F. B.: Two variant axiom systems for presence/absence based dissimilarity coefficients, J. of Classification, 14, 1997, 159-170.
• [3] Chepoi, V., Fichet, B.: Recognition of Robinsonian dissimilarities, J. of Classification, 14, 1997, 311-325.
• [4] Cox, T. F., Cox, M. A. A.: A general weigthed two-way dissimilarity coefficient, J. of Classification, 17, 2000, 101-121.
• [5] Deja, R.: Conflict analysis, in: Rough Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems (L. Polkowski, S. Tsumoto, T. Y. Lin, Eds.), Physica-Verlag, Heidelberg New York, 2001, 491-520.
• [6] Gomolińska, A.: A comparative study of some generalized rough approximations, Fundamenta Informaticae, 51(1-2), 2002, 103-119.
• [7] Gomolińska, A.: Approximation spaces based on similarity and dissimilarity, in: [13], 2006, 446-457.
• [8] Gower, J. C., Legendre, P.: Metric and Euclidean properties of dissimilarity coefficients, J. of Classification, 3, 1986, 5-48.
• [9] Greco, S., Matarazzo, B., Słowiński, R.: Handling missing values in rough set analysis of multi-attribute and multi-criteria decision problems, Lecture Notes in Artificial Intelligence, 1711, 1999, 146-157.
• [10] Greco, S., Matarazzo, B., Słowiński, R., Zanakis, S.: Rough set analysis of information tables with missing values, in: Proc. 5th Int. Conf. Decision Sciences Institute, Athens, Greece, 1999, July 4-7, 1999, 1359-1362.
• [11] Grzymała-Busse, J. W., Grzymała-Busse,W. J., Goodwin, L. K.: Coping with missing attribute values based on closest fit in preterm birth data: A rough set approach, Comput. Intelligence, 17(3), 2001, 425-434.
• [12] Kryszkiewicz, M.: Properties of incomplete information systems in the framework of rough sets, in: [26], vol. 1, 1998, 422-450.
• [13] Lindemann, G., Schlingloff, B.-H., Eds.: Proc. Workshop on Concurrency, Specification, and Programming (CS&P'2006), Wandlitz, Germany, 2006, September 27-29, vol. 206 of Informatik-Berichte, Humboldt-Universität zu Berlin, Berlin, 2006.
• [14] Łukasiewicz, J.: Die logischen Grundlagen derWahrscheinlichkeitsrechnung, in: Jan Łukasiewicz - Selected Works (L. Borkowski, Ed.), North Holland, Polish Scientific Publ., Amsterdam London,Warsaw, 1970, 16-63, first published in Kraków in 1913.
• [15] von Luxburg, U.: Statistical Learning with Similarity and Dissimilarity Functions, Ph. D. thesis, Technische Universität Berlin, Berlin, 2004.
• [16] MacKay, D. B., Lilly, B.: Percept variance, subadditivity and the metric classification of similarity, and dissimilarity data, J. of Classification, 21, 2004, 185-206.
• [17] Pawlak, Z.: Information systems - Theoretical foundations, Information Systems, 6(3), 1981, 205-218.
• [18] Pawlak, Z.: Rough sets, Computer and Information Sciences, 11, 1982, 341-356.
• [19] Pawlak, Z.: On conflicts, Int. J. of Man-Machine Studies, 21, 1984, 127-134.
• [20] Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning About Data, Kluwer, Dordrecht, 1991.
• [21] Pawlak, Z.: An inquiry into anatomy of conflicts, J. of Information Sciences, 109, 1998, 65-78.
• [22] Pawlak, Z., Skowron, A.: Rough membership functions, in: Advances in the Dempster-Shafer Theory of Evidence (R. R. Yager, M. Fedrizzi, J. Kacprzyk, Eds.), John Wiley & Sons, New York, 1994, 251-271.
• [23] Peters, J. F., Skowron, A., Stepaniuk, J.: Nearness in approximation spaces, in: [13], 2006, 434-445.
• [24] Piasta, Z., Lenarcik, A.: Learning rough classifiers from large databases with missing values, in: [26], vol. 1, 1998, 451-499.
• [25] Polkowski, L., Skowron, A.: Rough mereology: A new paradigm for approximate reasoning, Int. J. Approximated Reasoning, 15(4), 1996, 333-365.
• [26] Polkowski, L., Skowron, A., Eds.: Rough Sets in Knowledge Discovery, Physica-Verlag, Heidelberg, 1998.
• [27] Polkowski, L., Skowron, A.: Rough mereological calculi of granules: A rough set approach to computation, Comput. Intelligence, 17(3), 2001, 472-492.
• [28] Ramanna, S., Peters, J. F., Skowron, A.: Analysis of conflict dynamics by risk patterns, in: [13], 2006, 469-479.
• [29] Skowron, A., Stepaniuk, J.: Tolerance approximation spaces, Fundamenta Informaticae, 27, 1996, 245-253.
• [30] Słowiński, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations, in: Advances in Machine Intelligence and Soft Computing (P. P. Wang, Ed.), vol. 4, Duke University Press, 1997, 17-33.
• [31] Stefanowski, J., Tsouki`as, A.: Incomplete information tables and rough classification, Int. J. Comput. Intelligence, 17(3), 2001, 545-566.
• [32] Wolski, M.: Similarity as nearness: Information quanta, approximation spaces and nearness structures, in: [13], 2006, 424-433.
• [33] Yao, Y., Zhao, Y.: Conflict analysis based on discernibility and indiscernibility, in: Proc. 1st IEEE Symposium on Foundations of Computational Intelligence (FOCI'2007), Honolulu, Hawaii, 2007, April 1-5 (D. Fogel et al., Ed.), 2007, 302-307.
• [34] Zadeh, L. A.: Outline of a new approach to the analysis of complex system and decision processes, IEEE Trans. on Systems, Man, and Cybernetics, 3, 1973, 28-44.
• [35] Ziarko,W.: Variable precision rough set model, J. Computer and System Sciences, 46(1), 1993, 39-59.
• [36] Ziarko, W.: Probabilistic decision tables in the variable precision rough set model, J. Comput. Intelligence, 17(3), 2001, 593-603.