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Generalized Rough Sets Applied to Graphs Related to Urban Problems

Authors: Mihai Rebenciuc, Simona Mihaela Bibic


Branch of modern mathematics, graphs represent instruments for optimization and solving practical applications in various fields such as economic networks, engineering, network optimization, the geometry of social action, generally, complex systems including contemporary urban problems (path or transport efficiencies, biourbanism, & c.). In this paper is studied the interconnection of some urban network, which can lead to a simulation problem of a digraph through another digraph. The simulation is made univoc or more general multivoc. The concepts of fragment and atom are very useful in the study of connectivity in the digraph that is simulation - including an alternative evaluation of k- connectivity. Rough set approach in (bi)digraph which is proposed in premier in this paper contribute to improved significantly the evaluation of k-connectivity. This rough set approach is based on generalized rough sets - basic facts are presented in this paper.

Keywords: (Bi)digraphs, rough set theory, systems of interacting agents, complex systems.

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[1] M. Rebenciuc, Binary relations - addenda 1 (kernel, restrictions and inducing, relational morphisms), UPB, Sci. Bulll. Series A, vol. 70, no. 3, pp. 11–22, 2008.
[2] M. Rebenciuc, Binary relations - addenda 2 (sections, composabilities), UPB, Sci. Bulll. Series A, vol. 71, no. 1, pp. 21–32, 2009.
[3] M. Rebenciuc, Rough sets - generalizations and applications, (manuscript available), 2011.
[4] M. Rebenciuc, Rough sets in (weak) nonhomogeneous relational approximation spaces and in generalized topological approximation spaces with applications, IEEE Transactions on Fuzzy Systems, FUZZ (under review), 2017.
[5] Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, vol. 5, no. 11, pp. 341–356, 1982.
[6] Z. Pawlak and A. Skowron Rudiments of rough sets, Information Sciences, vol. 177, no. 1, pp. 3–27, 2007.
[7] R. Slowinski (ed.), Intelligent decision support: handbook of applications and advances of the rough sets theory, Kluwer Academic Publishers, 1992.
[8] J. Peters and A. Skowron (eds.), Transactions on rough sets XX, 1st ed., LNCS 10020, Springer, 2016.
[9] V. Flores et al. (eds.), Rough sets and knowledge technology, LNAI 9920, Springer, 2016.
[10] Z. Pawlak and A. Skowron, Rough sets: some extensions, Information Sciences, vol. 177, no. 1, pp. 28–40, 2007.
[11] L. D’eer et al., Neighborhood operators for covering - based rough sets, Information Sciences, vol. 336, pp. 21–44, 2016.
[12] B. Tripathy and D. Acharjya, Approximation of classification and measures of uncertainty in rough sets on two universal sets, International Journal Advanced Science and Technology, vol. 40, pp. 77–90, 2012.
[13] N. Thuan, Covering rough sets from a topological point of view, International Journal of Computer Theory and Engineering, vol. 1, no. 5, pp. 606–609, 2009.
[14] H. Mustafa and F. Sleim, Generalized closed sets in ditopological texture spaces with application in rough set theory, Journal of Advances in Mathematics, vol. 4, no. 2, pp. 394–407, 2013.
[15] M. Diker, A category approach to relation preserving functions in rough set theory, International Journal of Approximate Reasoning, vol. 56, pp. 71–86, 2015.
[16] D. Dubois and H. Prade et al., Articles written on the occasion of the 50th anniversary of rough set theory, Rapport Interne IRIT, 2015.
[17] E. Kerre et al., An overview of the fuzzy axiomatic systems and characterization proposed at Ghent University, Axioms, vol. 5, no. 2, pp. 1–13, 2016.
[18] L. A. Zadeh, Fuzzy sets, Information and Control, vol. 8, no. 3, pp. 338–353, 1965.
[19] D. Dubois and H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General System, vol. 17, no. 2-3, pp. 191–209, 1990.
[20] D. Miao et al. (eds.), Rough sets and knowledge technology, LNAI 8818, Springer, pp. 3–76, 2014.
[21] D. Ciucci et al. (eds.), Rough sets and knowledge technology, LNAI 9436, Springer, pp. 191–254, 2015.
[22] A. Das et al., A profit maximizing solid transportation model under rough interval approach, IEEE Transactions on Fuzzy Systems, vol. 25, no. 3, pp. 485–498, 2017.
[23] D. Hu et al., Statistical inference in rough set theory based on Kolmogorov - Smirnov goodness-of-fit test, IEEE Transactions on Fuzzy Systems, vol. PP, no. 99, 2017.
[24] J. Dai et al., Neighbor inconsistent pair selection for attribute reduction by rough set approach, IEEE Transactions on Fuzzy Systems, vol. PP, no. 99, 2017.
[25] M. Aggarwal, Rough information set and its applications in decision making, IEEE Transactions on Fuzzy Systems, vol. 25, no. 2, pp. 265– 276, 2017.
[26] Y. Yang et al., Incremental perspective for feature selection based on fuzzy rough sets, IEEE Transactions on Fuzzy Systems, vol. PP, no. 99, 2017.
[27] J. Gross et al. (eds.), Handbook of graph theory, 2nd ed., CRC Press, 2014.
[28] L. H. Harper, Optimal assignment of numbers to vertices, Journal of SIAM, vol. 12, pp. 131–135, 1964.
[29] G. Chaty, On critically and minimally k-vertex (arc) strongly connected digraphs, Proc., Keszthely, pp. 193–203, 1976.
[30] Y. O. Hamidoune, Sur les atomes d’un graphe orient´e, CR Acad. Sci. Paris A, vol. 284, pp. 1253–1256, 1977.
[31] Y. O. Hamidoune, A property of a-fragments of a digraph, Discrete Mathematics, vol. 31, no. 1, pp. 105–106, 1980.
[32] Y. O. Hamidoune, Quelques problemes de connexit´e dans les graphes orient´es, Journal of Combinatorial Theory, Series B, vol. 30, no. 1, pp. 1–10, 1981.
[33] R. Milner, The space and motion of communicating agents, Cambridge University Press, 2009.
[34] M. Sevegnani and M. Calder, Bigraphs with sharing, Theoretical Computer Science, vol. 577, pp. 43–73, 2015.
[35] J. Webb et al., Graph theory applications in network security, Grin Publishing, 2016.
[36] E. Tracada and A. Caperna, A new paradigm for deep sustainability: biourbanism, Proc. Application of Efficient & Renewable Energy Technologies in Low Cost Buildings and Construction, pp. 367–381, 2013.
[37] B. Ak and E. Koc, A guide for genetic algorithm based on parallel machine scheduling and flexible job-shop scheduling, Procedia-Social and Behavioral Sciences, vol. 62, pp. 817–823, 2012.
[38] R. Capello, The City Network Paradigm: Measuring Urban Network Externalities, Urban Studies, vol. 37, no. 11, pp. 1925–1945, 2000.