Abstract
Active cell components involved in real biological processes have to be close enough to a membrane in order to be able to pass through it. Rough set theory gives a plausible opportunity to model boundary zones around cell-like formations. However, this theory works within conventional set theory, and so to apply its ideas to membrane computing, first, we have worked out an adequate approximation framework for multisets. Next, we propose a two–component structure consisting of a P system and an approximation space for multisets. Using the approximation technique, we specify the closeness around membranes, even from inside and outside, via boundaries in the sense of multiset approximations. Then, we define communication rules within the P system in such a way that they operate in the boundary zones solely. The two components mutually cooperate.
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References
Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Pardini, G., Tesei, L.: Spatial P systems. Natural Computing 10(1), 3–16 (2011)
Blizard, W.D.: Multiset theory. Notre Dame Journal of Formal Logic 30(1), 36–66 (1989)
Blizard, W.D.: The development of multiset theory. Modern Logic 1, 319–352 (1991)
Blizard, W.D.: Dedekind multiset and function shells. Theoretical Computer Science 110(1), 79–98 (1993)
Calude, C.S., Pun, G., Rozenberg, G., Salomaa, A. (eds.): Multiset Processing. LNCS, vol. 2235. Springer, Heidelberg (2001)
Cardelli, L., Gardner, P.: Processes in Space. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds.) CiE 2010. LNCS, vol. 6158, pp. 78–87. Springer, Heidelberg (2010)
Csajbók, Z.: Partial approximative set theory: A generalization of the rough set theory. In: Martin, T., Muda, A.K., Abraham, A., Prade, H., Laurent, A., Laurent, D., Sans, V. (eds.) Proceedings of SoCPaR 2010, Cergy Pontoise / Paris, December 7-10, pp. 51–56. IEEE (2010)
Csajbók, Z.: Approximation of sets based on partial covering. Theoretical Computer Science 412(42), 5820–5833 (2011); rough Sets and Fuzzy Sets in Natural Computing
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)
Csuhaj-Varjú, E., Gheorghe, M., Stannett, M.: P Systems Controlled by General Topologies. In: Durand-Lose, J., Jonoska, N. (eds.) UCNC 2012. LNCS, vol. 7445, pp. 70–81. Springer, Heidelberg (2012)
Cyran, M., et al.: Oracle Database Concepts, 10g Release 2 (10.2). Oracle (2005), http://docs.oracle.com/cd/B19306_01/server.102/b14220.pdf
Dedekind, R.: Essays on the Theory of Numbers. Dover, New York (1963); translated by Beman, W.W
Girish, P., John, S.J.: Rough multisets and information multisystems. Advances in Decision Sciences 2011, 17 pages (2011)
Knuth, D.E.: The Art of Computer Programming. Seminumerical Algorithms, 2nd edn., vol. 2. Addison-Wesley, Reading (1981)
Kudlek, M., Martín-Vide, C., Păun, G.: Toward a formal macroset theory. In: Calude, et al. (ed.) [5], pp. 123–134
Mihálydeák, T.: Partial First-order Logic with Approximative Functors Based on Properties. In: Li, T., Nguyen, H.S., Wang, G., Grzymala-Busse, J., Janicki, R., Hassanien, A.E., Yu, H. (eds.) RSKT 2012. LNCS(LNAI), vol. 7414, pp. 514–523. Springer, Heidelberg (2012)
Mihálydeák, T., Csajbók, Z.: Membranes with Boundaries. In: Csuhaj-Varjú, E., Gheorghe, M., Rozenberg, G., Salomaa, A., Vaszi, G. (eds.) CMC 2012. LNCS, vol. 7762, pp. 277–294. Springer, Heidelberg (2013)
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)
Pawlak, Z.: Hard and soft sets. In: Ziarko, W. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, Proceedings of the International Workshop on Rough Sets and Knowledge Discovery (RSKD 1993), October 12-15, pp. 130–135. Springer, Banff (1994)
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)
Singh, D., Ibrahim, A.M., Yohanna, T., Singh, J.N.: An overview of the applications of multisets. Novi Sad J. Math. 37(2), 73–92 (2007)
Syropoulos, A.: Mathematics of multisets. In: Calude, et al. (ed.) [5], pp. 347–358
Yager, R.R.: O, the theory of bags. International Journal of General Systems 13(1), 23–37 (1986)
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Mihálydeák, T., Csajbók, Z.E. (2013). Membranes with Boundaries. In: Csuhaj-Varjú, E., Gheorghe, M., Rozenberg, G., Salomaa, A., Vaszil, G. (eds) Membrane Computing. CMC 2012. Lecture Notes in Computer Science, vol 7762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36751-9_19
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DOI: https://doi.org/10.1007/978-3-642-36751-9_19
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