In 2020, r-near topological spaces on Near Approximation Spaces were introduced by Atmaca [1]. In this study, we introduce the concept of continuity on r-near topological spaces and examine some properties of it.
AtmacaS., r-Near topologies on nearness approximation spaces, Journal of Intelligent & Fuzzy Systems39-5 (2020), 6849–6855.
2.
BorkowskiM. and PetersJ.F., Matching 2D image segments withgenetic algorithms and approximation spaces, Transactions onRough Sets, V, LNCS4100 (2006), 63–101.
3.
HenryC., Near Sets: Theory and Applications (Ph.D. Thesis (supervisor J.F. Peters), Department of Electrical & Computer Engineering, University of Manitoba (2010).
4.
HenryC. and PetersJ.F., Image Pattern Recognition Using Approximation Spaces and Near Sets, In: Proceedings of Eleventh International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC 2007), Joint Rough Set Symposium (JRS 2007), Lecture Notes in Artificial Intelligence4482 (2007), 475–482.
5.
İnanE. and ÖztürkM.A., Erratum and notes for neargroups on nearness approximation spaces, Hacet. J. Math. Stat.43(2) (2014), 279–281.
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İnanE. and ÖztürkM.A., Near groups on nearnessapproximation spaces, Hacet. J. Math. Stat.41(4) (2012), 545–558.
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İnanE. and ÖztürkM.A., Near semigroups on nearnessapproximation spaces, Ann. Fuzzy Math. Inform.10(2) (2015), 287–297.
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LockeryD. and PetersJ.F., Robotic target tracking with approximation space-based feedback during reinforcement learning, Springer Best Paper Award, In: Proceedings of Eleventh International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC 2007), Joint Rough Set Symposium (JRS 2007), Lecture Notes in Artificial Intelligence4482 (2007), 483–490.
9.
PawlakZ., Rough sets, Int. J. of Information and ComputerSciences11(5) (1982), 341–356.
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PetersJ.F., Near sets. General theory about nearness of objects, Applied Mathematical Sciences1(53–56) (2007), 2609–2629.
11.
PetersJ.F., Near sets, special theory about nearness of objects, Fund. Inform.75(1-4) (2007), 407–433.
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PetersJ.F. and RamannaS., Feature Selection: Near Set Approach. In: Z.W. Ras, S. Tsumoto, D.A. Zighed (Eds.), 3rd Int. Workshop on Mining Complex Data (MCD’08), ECML/PKDD-2007, LNAI, Springer (2007).
13.
PetersJ.F., Near Sets. Toward Approximation Space-Based Object Recognition. In: Yao, Y., Lingras, P., Wu, W.-Z, Szczuka, M., Cercone, N., Slezak, D., Eds., Proc. of the Second Int. Conf. on Rough Sets and Knowledge Technology (RSKT07), Joint Rough Set Symposium (JRS07), Lecture Notes in Artificial Intelligence, 4481, Springer, Berlin (2007), 22–33.
14.
PetersJ.F., Perceptual granulation in ethology-based reinforcement learning. In: Pedrycz, W., Skowron, A., Kreinovich, V. (Eds.), Handbook on Granular Computing, Wiley, NY (2007).
15.
PetersJ.F., Toward approximate adaptive learning. In: Int. Conf. Rough Sets and Emerging Intelligent Systems Paradigms in Memoriam Zdzislaw Pawlak, Lecture Notes in Artificial Intelligence, 4585, Springer, Berlin Heidelberg (2007), 57–68.
16.
PetersJ.F., Granular computing in approximate adaptive learning, International Journal of Information Technology and Intelligent Computing (2007), in press.
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PetersJ.F., Sufficiently near sets of neighbourhoods, in: J. Yao, S. Ramanna, G. Wang, Z. Suraj (eds.), Rough Sets and Knowledge Technology (2011), LNCS 6954, Springer, Berlin, 17–24.
18.
PetersJ.F. and HenryC., Reinforcement learning with approximationspaces, Fundamenta Informaticae71(2–3) (2006), 323–349.
19.
PetersJ.F., BorkowskiM., HenryC., LockeryD.Int. J. Info. Technol Intell. Comput.3(2) (2008), 1–35Monocular visionsystem that learns with approximation spaces, Ella, A., Lingras,, Slezak, Peters, J. F. Classification of perceptual objects bymeans of features.
20.
PetersJ.F., BorkowskiM., HenryC., LockeryD. and GundersonD.S., LineCrawling Bots that Inspect Electric Power Transmission Line Equipment. In: Proc. Third Int. Conference on Autonomous Robots and Agents (ICARA 2006), Palmerston North, New Zealand (2006), 39–44.
21.
PetersJ.F. and NaimpallyS., Approach spaces for near filters, Gen. Math. Notes 2(1) (2011), 159–164.
22.
PetersJ.F., ShahfarS., RamannaS. and SzturmT., Biologically-inspired adaptive learning: A near set approach, In: Proc. Frontiers in the Convergence of Bioscience and Information Technologies (FBIT07), IEEE, NJ, 11 October (2007), in press.
23.
PetersJ.F. and TiwariS., Approach merotopies and near filters, Gen. Math. Notes3(1) (2011), 1–15.
SinghP.K. and TiwariS., Topological structures in rough settheory: A survey, Hacet. J. Math. Stat.49(4) (2020), 1270–1294.
26.
SkowronA. and PetersJ.F., Rough granular computing. In: Pedrycz,W.,Skowron, A., Kreinovich, V. (Eds.), Handbook on Granular Computing, Wiley, NY (2007).
