Abstract
The work presents an investigation of multiple-source approximation systems, which are collections of Pawlak approximation spaces over the same domain. We particularly look at notions of definability of sets in such a collection μ. Some possibilities for membership functions in μ are explored. Finally, a relation that reflects the degree to which objects are (in)discernible in μ is also presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Banerjee, M., Khan, M.A.: Propositional Logics from Rough Set Theory. Transactions on Rough Sets VI, 1–25 (2007)
Intan, R., Mukaidono, M.: Generalization of Rough Membership Function Based on α−Coverings of the Universe. In: Pal, N.R., Sugeno, M. (eds.) AFSS 2002. LNCS (LNAI), vol. 2275, pp. 129–135. Springer, Heidelberg (2002)
Liau, C.J.: An Overview of Rough Set Semantics for Modal and Quantifier Logics. Int. J. Uncertainty, Fuzziness and Knowledge Based Systems 8(1), 93–118 (2000)
Pagliani, P.: Pretopologies and Dynamic Paces. Fundamenta Informaticae 59(2-3), 221–239 (2004)
Pawlak, Z.: Rough Sets. Int. J. Comp. Inf. Sci. 11(5), 341–356 (1982)
Pawlak, Z., Wong, S.K.M., Ziarko, W.: Rough sets: Probabilistic Versus Deterministic Approach. Int. J. Man-Machine Studies 29, 81–95 (1988)
Pawlak, Z., Skowron, A.: Rough Membership Functions. In: Yager, R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster-Shafer Theory of Evidence, pp. 251–271. Wiley, New York (1994)
Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Rasiowa, R.: Mechanical Proof Systems for Logic of Reaching Consensus by Groups of Intelligent Agents. Int. J. Approximate Reasoning. 5(4), 415–432 (1991)
Rauszer, C.: Knowledge Representation Systems for Groups of Agents. In: Woleński, J. (ed.) Philosophical Logic in Poland, pp. 217–238. Kluwer, Dordrecht (1994)
Skowron, A., Stepaniuk, J.: Tolerance Approximation Spaces. Fundamenta Informaticae 27, 245–253 (1996)
Wong, S.K.M., Ziarko, W.: Comparison of the Probabilistic Approximate Classification and Fuzzy Set Model. Fuzzy Sets and Systems 21, 357–362 (1986)
Wong, S.K.M.: A Rough Set Model for Reasoning about Knowledge. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery 1: Methodology and Applications, pp. 276–285. Physica-Verlag, New York (1998)
Yao, Y.Y., Wong, S.K.M., Lin, T.Y.: A Review of Rough Set Models. In: Lin, T.Y., Cercone, N. (eds.) Rough Sets and Data Mining, pp. 47–75. Kluwer Academic Publishers, Boston (1997)
Ziarko, W.: Variable Precision Rough Set Model. J. Computer and System Sciences 46, 39–59 (1993)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Khan, M.A., Banerjee, M. (2008). Multiple-Source Approximation Systems: Membership Functions and Indiscernibility. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds) Rough Sets and Knowledge Technology. RSKT 2008. Lecture Notes in Computer Science(), vol 5009. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79721-0_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-79721-0_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79720-3
Online ISBN: 978-3-540-79721-0
eBook Packages: Computer ScienceComputer Science (R0)