Abstract
Partial nature of real–life problems requires working out partial approximation schemes. Partial approximation of sets is based on classical set theory. Its generalization for multisets gives a plausible opportunity to introduce an abstract concept of “to be close enough to a membrane” in membrane computing. The paper presents important features of general (maybe partial) multiset approximation spaces, their lattice theory properties, and shows how partial multiset approximation spaces can be applied to membrane computing.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11(5), 341–356 (1982)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Girish, K.P., John, S.J.: Relations and functions in multiset context. Information Sciences 179(6), 758–768 (2009)
Grzymala-Busse, J.: Learning from examples based on rough multisets. In: Proceedings of the Second International Symposium on Methodologies for Intelligent Systems, pp. 325–332. North-Holland Publishing Co., Amsterdam (1987)
Csajbók, Z.E.: Approximation of sets based on partial covering. In: Peters, J.F., Skowron, A., Ramanna, S., Suraj, Z., Wang, X. (eds.) Transactions on Rough Sets XVI. LNCS, vol. 7736, pp. 144–220. Springer, Heidelberg (2013)
Csajbók, Z., Mihálydeák, T.: Partial approximative set theory: A generalization of the rough set theory. International Journal of Computer Information Systems and Industrial Management Applications 4, 437–444 (2012)
Mihálydeák, T., Csajbók, Z.: Membranes with local environments. In: Csuhaj-Varjú, E., Gheorghe, M., Vaszil, G. (eds.) Proceedings of the 13th International Conference on Membrane Computing, CMC13, Budapest, Hungary, August 28-31, pp. 311–322. MTA SZTAKI, The Computer and Automation Research Institute of the Hungarian Academy of Sciences (2012)
Mihálydeák, T., Csajbók, Z.E.: Membranes with boundaries. In: Csuhaj-Varjú, E., Gheorghe, M., Rozenberg, G., Salomaa, A., Vaszil, G. (eds.) CMC 2012. LNCS, vol. 7762, pp. 277–294. Springer, Heidelberg (2013)
Păun, G.: Computing with membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000)
Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)
Păun, G., Rozenberg, G., Salomaa, A. (eds.): The Oxford Handbook of Membrane Computing. Oxford Handbooks. Oxford University Press, Inc., New York (2010)
Birkhoff, G.: Lattice theory, 3rd edn. Colloquium Publications, vol. 25. American Mathematical Society, Providence (1967)
Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, Cambridge (2002)
Grätzer, G.: General Lattice Theory. Birkhäuser Verlag, Basel und Stuttgart (1978)
Kudlek, M., Martín-Vide, C., Păun, G.: Toward a formal macroset theory. In: Calude, C.S., Pun, G., Rozenberg, G., Salomaa, A. (eds.) Multiset Processing. LNCS, vol. 2235, pp. 123–134. Springer, Heidelberg (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mihálydeák, T., Csajbók, Z.E. (2013). Partial Approximation of Multisets and Its Applications in Membrane Computing. In: Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds) Rough Sets and Knowledge Technology. RSKT 2013. Lecture Notes in Computer Science(), vol 8171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41299-8_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-41299-8_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41298-1
Online ISBN: 978-3-642-41299-8
eBook Packages: Computer ScienceComputer Science (R0)