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Textures and dynamic relational systems

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Abstract

Dynamic relational systems have different forms in literature of rough set theory. They are divided into two parts by Pagliani as synchronic and diachronic dynamics. Synchronic dynamic case is related to the presence of a multi-sources. In the case of diachronic dynamics, it is supposed that changes occur in time. These changes are related to new objects, attributes or attribute values entered into the system. Here, we consider the dynamic systems which are related to the both of these types of dynamics. In a recent paper, the author studied on the results about reduct, definability and quasi-uniformity in dynamic relational systems. Here, the natural generalizations of these results are given. In particular, it is proved that weak and strong definabilities are preserved under pre-images with respect to direlation preserving difunctions between textural dynamic relational systems. Further, the connections between definable sets and the ditopology are determined by ditopologies of reflexive direlations. Then it is given some basic results on ditopologies induced by direlations and direlational quasi-uniformities. Morover, it is discussed on the connections between textural approximation spaces and direlational-quasi uniformities.

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References

  1. Brown LM, Diker M (1998) Ditopological texture spaces and intuitionistic sets. Fuzzy Sets Syst 98:217–224

    Article  MathSciNet  MATH  Google Scholar 

  2. Brown LM, Ertürk R, Dost Ş (2004) Ditopological texture spaces and fuzzy topology, I. Basic concepts. Fuzzy Sets Syst 171–199

  3. Brown LM, Ertürk R, Dost Ş (2004) Ditopological texture spaces and fuzzy topology, II. Topological considerations. Fuzzy Sets Syst 147:201–231

    Article  MathSciNet  MATH  Google Scholar 

  4. Brown LM, Ertürk R (2000) I. Representation theorems, Fuzzy sets as texture spaces. Fuzzy Sets Syst 110(2):227–236

    Article  MATH  Google Scholar 

  5. Chen H, Li T, Ruan D, Lin J, Hu C (2013) A rough-set-based incremental approach for updating approximations under dynamic maintenance environments. IEEE Trans Knowl Data Eng 25(2):274–284

    Article  Google Scholar 

  6. Chen H, Li T, Luo C, Horng S, Wang G (2015) A decision-theoretic rough set approach for dynamic data mining. IEEE Trans Fuzzy Syst 23(6):1958–1970

    Article  Google Scholar 

  7. Ciucci D (2010) Classification of dynamics in rough sets. RSCTC LNAI 6086:257–266

    Google Scholar 

  8. Ciucci D (2012) Temporal dynamics in information tables. Fundam Inform 115:57–74

    MathSciNet  MATH  Google Scholar 

  9. Demirci M (2007) Textures and C-spaces. Fuzzy Sets Syst 855:1237–1245

    Article  MathSciNet  MATH  Google Scholar 

  10. Diker M (2010) Textural approach to generalized rough sets based on relations. Inf Sci 180(8):1418–1433

    Article  MathSciNet  MATH  Google Scholar 

  11. Diker M (2011) Textures and fuzzy rough sets. Fundam Inform 108:305–336

    MathSciNet  MATH  Google Scholar 

  12. Diker M (2012) Definability and textures. Int J Approx Reason 53:558–572

    Article  MathSciNet  MATH  Google Scholar 

  13. Diker M (2013) Categories of rough sets and textures. Theor Comput Sci 488:46–65

    Article  MathSciNet  MATH  Google Scholar 

  14. Diker M (2015) A category approach to relation preserving functions in rough set theory. Int J Approx Reason 56:71–86

    Article  MathSciNet  MATH  Google Scholar 

  15. Diker M, Altay Uğur A (2012) Textures and covering based rough sets. Inf Sci 184:44–63

    Article  MathSciNet  MATH  Google Scholar 

  16. Diker M, Altay Uğur A, Bayhan S (2015) Rough sets and textural neigbourhoods. In: Ciucci D, Wang G, Mitra S, Wu WZ (eds) Rough sets and knowledge technology: 10th international conference, RSKT 2015, held as part of the international joint conference on rough sets, IJCRS 2015, Tianjin, China, November 20–23, 2015. Lecture notes in computer science, vol 9436. Springer International Publishing, Cham, pp 202–213

  17. Dost Ş (2015) A textural view of soft fuzzy rough sets. J Intell Fuzzy Syst 28(6):2519–2535

    Article  MathSciNet  MATH  Google Scholar 

  18. Dost Ş (2015) A categorical view of textural approximation spaces. Quaest Math 38(3):385–402

    Article  MathSciNet  MATH  Google Scholar 

  19. Järvinen J, Kortelainen J (2004) A note on definability in rough set theory. In: De Baets B, De Caluwe R, De Tr G, Fodor J, Kacpryzk J, Zadrozny S (eds) Current issues in data and knowledge engineering. Academicka Oficyna Wydawnicza EXIT, Warsaw, pp 272–277

    Google Scholar 

  20. Khan MA, Banerjee M (2010) A study of multiple-source approximation systems. In: Peters JF et al (eds) Transactions on rough sets XII, LNCS. vol 6190, Springer, Berlin, pp 46–75

  21. Khan MA, Banerjee M (2008) Formal reasoning with rough sets in multiple-source approximation systems. Int J Approx Reason 49(2):466–477

    Article  MathSciNet  MATH  Google Scholar 

  22. Khan MA, Banerjee M (2008) Multiple-source approximation systems: membership functions and indiscernibility. Springer, Berlin

    MATH  Google Scholar 

  23. Li T, Ruan D, Wets G, Song J, Xu Y (2007) A rough sets based characteristic relation approach for dynamic attribute generalization in data mining. Knowl Based Syst 20(5):485–494

    Article  Google Scholar 

  24. Li S, Li T, Liu D (2013) Dynamic maintenance of approximations in dominance-based rough set approach under the variation of the object set. Int J Intell Syst 28(8):729–751

    Article  Google Scholar 

  25. Liang J, Wang F, Dang C, Qian Y (2014) A group incremental approach to feature selection applying rough set technique. IEEE Trans Knowl Data Eng 26(2) 9: 1–31.

  26. Lu J, Li S-G, Yang X-F, Fu W-Q (2011) Categorical properties M-indiscernibility spaces. Theor Comput Sci 412(42):5902–5908

    Article  MathSciNet  MATH  Google Scholar 

  27. Luo C, Li T, Chen H (2014) Dynamic maintenance of approximations in set-valued ordered decision systems under the attribute generalization. Inf Sci 257:210–228

    Article  MathSciNet  MATH  Google Scholar 

  28. Özçağ S, Brown LM (2003) Di-uniform texture spaces. Appl Gen Topol 4(1):157–192

  29. Pagliani P (2004) Pretopologies and dynamic spaces. Fundam Inform 59(23):221–239

    MathSciNet  MATH  Google Scholar 

  30. Pagliani P, Chakraborty M (2008) A geometry of approximation. Springer, Berlin

    Book  MATH  Google Scholar 

  31. Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer, Dordrecht

    Book  MATH  Google Scholar 

  32. Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 5:341–356

    Article  MATH  Google Scholar 

  33. Qian Y, Liang J, Yao Y, Dang C (2010) MGRS: a multi-granulation rough set. Inf Sci 180:949–970

    Article  MathSciNet  MATH  Google Scholar 

  34. Skowron A, Stepaniuk J (1996) Tolerance approximation spaces. Fundam Inform 27:245–253

    MathSciNet  MATH  Google Scholar 

  35. Slowinski R, Vanderpooten D (2000) A generalized definition of rough approximations based on similarity. IEEE Trans Knowl Data Eng 12(2):331–336

    Article  Google Scholar 

  36. Stepaniuk J (2008) Rough-granular computing in knowledge discovery and data mining. Springer, New York

    MATH  Google Scholar 

  37. Altay Uğur A (2015) A note on dynamic relational systems. Inf Sci 293:327–337

    Article  MathSciNet  MATH  Google Scholar 

  38. Wang X (2015) Learning from big data with uncertainty editorial. J Intell Fuzzy Syst 28(5):2329–2330

    Article  MathSciNet  Google Scholar 

  39. Wang X, Ashfaq R, Fu A (2015) Fuzziness based sample categorization for classifier performance improvement. J Intell Fuzzy Syst 29(3):1185–1196

    Article  MathSciNet  Google Scholar 

  40. He Y, Wang X, Huang J (2016) Fuzzy nonlinear regression analysis using a random weight network. Inform Sci 364365:222–240

    Article  Google Scholar 

  41. He Y, Liu J, Hu Y, Wang X (2015) OWA operator based link prediction ensemble for social network. Expert Syst Appl 42(1):2150

    Article  Google Scholar 

  42. Ashfaq R, Wang X, Huang J, Abbas H, He Y (2016) Fuzziness based semi-supervised learning approach for intrusion detection system. doi:10.1016/j.ins.2016.04.019

  43. Yao YY (2007) A note on definability and approximations. LNCS Transactions on rough sets VII, vol 4400. Springer, Heidelberg, pp 274–282

    Google Scholar 

  44. Yao YY (1998) Constructive and algebraic methods of theory of rough sets. Inform Sci 109:21–47

    Article  MathSciNet  MATH  Google Scholar 

  45. Yao YY (1998) Relational interpretations of neighborhood operators and rough set approximation operators. Inform Sci 111(14):239–259

    Article  MathSciNet  MATH  Google Scholar 

  46. Zhang J, Li T, Chen H (2014) Composite rough sets for dynamic data mining. Inf Sci 257:81–100

    Article  MathSciNet  MATH  Google Scholar 

  47. Zhang J, Li T, Ruan D, Liu D (2012) Neighborhood rough sets for dynamic data mining. Int J Intell Syst 27:317–342

    Article  Google Scholar 

  48. Zhang J, Li T, Ruan D (2012) Rough sets based matrix approaches with dynamic attribute variation in set-valued information systems. Int J Approx Reason 53(4):620–635

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Secondary Science and Mathematics Education, Hacettepe University, Beytepe, 06532, Ankara, Turkey

    Ayşegül Altay Uğur

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  1. Ayşegül Altay Uğur
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Uğur, A.A. Textures and dynamic relational systems. Int. J. Mach. Learn. & Cyber. 9, 881–891 (2018). https://doi.org/10.1007/s13042-016-0616-x

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  • DOI: https://doi.org/10.1007/s13042-016-0616-x

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