Skip to main content

Abstract

This chapter discusses the basic preliminaries of rough set theory (RST). Since its inception, RST has been a prominent tool for data analysis due to its analysis-friendly nature. RST provides a range of data structures, e.g. Information Systems, Decision Systems and Approximations to represent the real-world data. Furthermore, it provides various methods to help analyse this data. This chapter discusses the basic concepts of RST with an example to set a strong foundation of RST to be used as feature selection.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. http://www.rapidtables.com/math/symbols/Basic_Math_Symbols.htm. Access 30 Mar 2017

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

    Book  MATH  Google Scholar 

  3. Pal SK, Skowron A (1999) Rough-fuzzy hybridization: a new trend in decision making. Springer, New York Inc

    MATH  Google Scholar 

  4. Krysiński J (1990) Rough sets approach to the analysis of the structure-activity relationship of quaternary imidazolium compounds. Arzneimittelforschung 40(7):795–799

    Google Scholar 

  5. Podsiadło M, Rybiński H (2014) Rough sets in economy and finance. Transactions on Rough Sets XVII. Springer, Berlin Heidelberg, pp 109–173

    Chapter  MATH  Google Scholar 

  6. Prasad V, Srinivasa Rao T, Surendra Prasad Babu M (2016) Thyroid disease diagnosis via hybrid architecture composing rough data sets theory and machine learning algorithms. Soft Comput 20(3):1179–1189

    Article  Google Scholar 

  7. Xie C-H, Liu Y-J, Chang J-Y (2015) Medical image segmentation using rough set and local polynomial regression. Multimed Tools Appl 74(6):1885–1914

    Article  Google Scholar 

  8. Montazer GA, ArabYarmohammadi S (2015) Detection of phishing attacks in Iranian e-banking using a fuzzy–rough hybrid system. Appl Soft Comput 35:482–492

    Article  Google Scholar 

  9. Pawlak Z, Słowiński K, Słowiński R (1986) Rough classification of patients after highly selective vagotomy for duodenal ulcer. Int J Man Mach Stud 24(5):413–433

    Article  Google Scholar 

  10. Fibak J et al (1986) Rough sets based decision algorithm for treatment of duodenal ulcer by HSV. Biol Sci 34:227–249

    Google Scholar 

  11. Fibak J, Slowinski K, Slowinski R (1986) The application of rough set theory to the verification of indications for treatment of duodenal ulcer by HSV. In: Proceedings 6th internat, workshop on expert systems and their applications, Avignon, France, Vol 1, pp 587–599

    Google Scholar 

  12. Slowinski R, Slowi_nski K (1989) An expert system for treatment of duodenal ulcer by highly selective vagotomy (in Polish). Pamietnik 54. Jubil. ZjazduTowarzystwaChirurgow Polskich, Krakow I, 223–228

    Google Scholar 

  13. Slowinski K (1992) Rough classification of HSV patients. In: Intelligent decision support-handbook of applications and advances of the rough sets theory, pp 77–94

    Chapter  Google Scholar 

  14. Słowiński K (1994) Rough sets approach to analysis of data of diagnostic peritoneal lavage applied for multiple injuries patients. In: Rough sets, fuzzy sets and knowledge discovery. Springer, London, pp 420–425

    Chapter  Google Scholar 

  15. Slowiński K, Slnowiński R, Stefanowski J (1988) Rough sets approach to analysis of data from peritoneal lavage in acute pancreatitis. Med Inform 13(3):143–159

    Article  Google Scholar 

  16. Grzymala-Busse JW (1998) Applications of the rule induction system LERS. Rough Sets in Knowledge Discovery 1, pp 366–375

    Google Scholar 

  17. Paterson GI (1994) Rough classification of pneumonia patients using a clinical database. Rough Sets, Fuzzy Sets and Knowledge Discovery. Springer, London, pp 412–419

    Chapter  Google Scholar 

  18. Tsumoto S, Tanaka H (1995) PRIMEROSE: probabilistic rule induction method based on rough sets and resampling methods. Comput Intell 11(2):389–405

    Article  Google Scholar 

  19. Jelonek J et al (1994) Neural networks and rough sets—comparison and combination for classification of histological pictures. Rough Sets, Fuzzy Sets and Knowledge Discovery. Springer, London, pp 426–433

    Chapter  Google Scholar 

  20. Kandulski M, Marciniec J, Tukałło K (1992) Surgical wound infection—conducive factors and their mutual dependencies. Intelligent decision support. Springer, Netherlands, pp 95–110

    Google Scholar 

  21. Grzymala-Busse JW, Linda KG (1996) A comparison of less specific versus more specific rules for preterm birth prediction. In: Proceedings of the first online workshop on soft computing WSC1 on the internet, Japan

    Google Scholar 

  22. Slowinski K et al (1995) Rough set approach to the verification of indications for treatment of urinary stones by extracorporeal shock wave lithotripsy (ESWL). Soft Computing, Society for Computer Simulation, San Diego, California, pp 142–145

    Google Scholar 

  23. Tsumoto S, Ziarko W (1996) The application of rough sets-based data mining technique to differential diagnosis of meningoenchepahlitis. International Symposium on Methodologies for Intelligent Systems. Springer, Berlin, Heidelberg

    Book  Google Scholar 

  24. Ziarko W (1998) Rough sets as a methodology for data mining. Rough Sets Knowl Discov 1:554–576

    MATH  Google Scholar 

  25. Rubin S, Michalowski W, Slowinski R (1996) Developing an emergency room diagnostic check list using rough sets-a case study of appendicitis. Simul Med Sci, 19–24

    Google Scholar 

  26. Slowinski K, Stefanowski J (1996) On limitations of using rough set approach to analyse non-trivial medical information systems

    Google Scholar 

  27. Paszek P, Wakulicz Deja A (1996) Optimalization diagnose in progressive encephalopathy applying the rough set theory. Zimmermann 557.1:192–196

    Google Scholar 

  28. Wakulicz-Deja A, Boryczka M, Paszek P (1998) Discretization of continuous attributes on decision system in mitochondrial encephalomyopathies. In: International conference on rough sets and current trends in computing. Springer, Berlin, Heidelberg

    Chapter  Google Scholar 

  29. Wakulicz-Deja A, Paszek P (1997) Diagnose progressive encephalopathy applying the rough set theory. Int J Med Informatics 46(2):119–127

    Article  Google Scholar 

  30. Czyzewski A (1998) Speaker-independent recognition of isolated words using rough sets. Inf Sci 104(1-2):3–14

    Article  Google Scholar 

  31. Stefanowski J, Slowiński K (1997) Rough set theory and rule induction techniques for discovery of attribute dependencies in medical information systems. European Symposium on Principles of Data Mining and Knowledge Discovery. Springer, Berlin, Heidelberg

    Book  Google Scholar 

  32. Ohrn A et al (1997) Modelling cardiac patient set residuals using rough sets. In: Proceedings of the AMIA annual fall symposium. American medical informatics association

    Google Scholar 

  33. Słowiński K, Stefanowski J (1998) Multistage rough set analysis of therapeutic experience with acute pancreatitis. Rough Sets in Knowledge Discovery 2. Physica-Verlag HD, pp 272–294

    Google Scholar 

  34. Swiniarski RW (1998) Rough sets and bayesian methods applied to cancer detection. In: International conference on rough sets and current trends in computing. Springer, Berlin, Heidelberg

    Chapter  Google Scholar 

  35. Carlin US, Komorowski J, Øhrn A (1998) Rough set analysis of patients with suspected acute appendicitis. Traitement d’information et gestion d’incertitudes dans les systèmes à base de connaissances. Conférence internationale

    Google Scholar 

  36. Tanaka H, Maeda Y (1998) Reduction methods for medical data. Rough Sets in Knowledge Discovery 2. Physica-Verlag HD, pp 295–306

    Google Scholar 

  37. Wojdyłło P (1998) Wavelets, rough sets and artificial neural networks in EEG analysis. In: International conference on rough sets and current trends in computing. Springer, Berlin, Heidelberg

    Chapter  Google Scholar 

  38. Slowinski R, Zopounidis C (1995) Application of the rough set approach to evaluation of bankruptcy risk. Intell Syst Account Finance Manag 4(1):27–41

    Article  Google Scholar 

  39. Slowinski R, Zopounidis C (1994) Rough-set sorting of firms according to bankruptcy risk. Applying Multiple Criteria Aid for Decision to Environmental Management. Springer, Netherlands, pp 339–357

    Google Scholar 

  40. Greco S, Matarazzo B, Slowinski R (1998) A new rough set approach to evaluation of bankruptcy risk. Operational tools in the management of financial risks. Springer, US, pp 121–136

    Chapter  Google Scholar 

  41. Mrózek A, Skabek K (1998) Rough sets in economic applications. Rough Sets in Knowledge Discovery 2. Physica-Verlag HD, pp 238–271

    Google Scholar 

  42. Piasta Z, Lenarcik A (1998) Learning rough classifiers from large databases with missing values. Rough Sets Knowl Discov 1:483–499

    MATH  Google Scholar 

  43. Van den Poel D (1998) Rough sets for database marketing. Rough Sets in Knowledge Discovery 2. Physica-Verlag HD, pp 324–335

    Google Scholar 

  44. Golan RH, Ziarko W (1995) A methodology for stock market analysis utilizing rough set theory. In: Computational intelligence for financial engineering, Proceedings of the IEEE/IAFE. IEEE

    Google Scholar 

  45. Ziarko W, Golan R, Edwards D (1993) An application of datalogic/R knowledge discovery tool to identify strong predictive rules in stock market data. In: Proceedings of AAAI workshop on knowledge discovery in databases, Washington, DC

    Google Scholar 

  46. Van den Poel D, Piasta Z (1998) Purchase prediction in database marketing with the ProbRough system. In: International conference on rough sets and current trends in computing. Springer, Berlin, Heidelberg

    Google Scholar 

  47. Kowalczyk AE, Eiben TJ, Euverman W, Slisser F (1999) Modelling customer retention with statistical techniques, rough data models, and genetic programming. Rough Fuzzy Hybridization: A New Trend in Decision-making

    Google Scholar 

  48. Kowalczyk W (1996) Analyzing temporal patterns with rough sets. Zimmermann 557:139

    Google Scholar 

  49. Kowalczyk W, Piasta F (1998) Rough-set inspired approach to knowledge discovery in business databases. In: Pacific-Asia conference on knowledge discovery and data mining. Springer, Berlin, Heidelberg

    Chapter  Google Scholar 

  50. Swiniarski R et al (1997) Feature selection using rough sets and hidden layer expansion for rupture prediction in a highly automated production process. Syst Sci-Wroclaw- 23:53–60

    MATH  Google Scholar 

  51. Keiser K, Szladow A, Ziarko W (1992) Rough sets theory applied to a large multispecies toxicity database. In: Proceedings of the Fifth international workshop on QSAR in environmental toxicology, Duluth, Minnesota

    Google Scholar 

  52. Teghem J, Charlet J-M (1992) Use of “Rough Sets” method to draw premonitory factors for earthquakes by Emphasing gas geochemistry: the case of a low seismic activity context, in Belgium. Intelligent Decision Support. Springer, Netherlands, pp 165–179

    Chapter  Google Scholar 

  53. Reinhard A et al (1992) An application of rough set theory in the control conditions on a polder. S lowi nski 428:331

    Google Scholar 

  54. la Busse, Grzyma JW, Gunn JD (1995) Global temperature analysis based on the rule induction system LERS. In: Proceedings of the fourth international workshop on intelligent information systems, August ow, Poland, June. Vol 5. No 9

    Google Scholar 

  55. Gunn JD, Grzymala-Busse JW (1994) Global temperature stability by rule induction: an interdisciplinary bridge. Human Ecology 22(1):59–81

    Article  Google Scholar 

  56. Greco S, Matarazzo B, Słowiński R (1998) “Rough approximation of a preference relation in a pairwise comparison table. Rough Sets in Knowledge Discovery 2. Physica-Verlag HD, pp 13–36

    Google Scholar 

  57. Roy B, Slowinski R, Treichel W (1992) “Multicriteria programming of water supply systems for rural AREAS1, 13–31

    Google Scholar 

  58. An A et al (1995) Discovering rules from data for water demand prediction. In: Proceedings of the workshop on machine learning in engineering IJCAI. Vol 95

    Google Scholar 

  59. Furuta H, Hirokane M, Mikumo Y (1998) “Extraction method based on rough set theory of rule-type knowledge from diagnostic cases of slope-failure danger levels. Rough Sets in Knowledge Discovery 2. Physica-Verlag HD, pp 178–192

    Google Scholar 

  60. Czyzewski A (1996) Mining knowledge in noisy audio data. KDD

    Google Scholar 

  61. Czyżewski A (1998) Soft processing of audio signals. Rough Sets in Knowledge Discovery 2. Physica-Verlag HD, pp 147–165

    Google Scholar 

  62. Czyzewski A, Krolikowski R (1997) New methods of intelligent filtration and coding of audio. Audio Engineering Society Convention 102. Audio Engineering Society

    Google Scholar 

  63. Kostek B (1998) Soft computing-based recognition of musical sounds. Rough Sets in Knowledge Discovery 2. Physica-Verlag HD, pp 193–213

    Google Scholar 

  64. Czyzewski A (1995) Some methods for detection and interpolation of impulsive distortions in old audio recordings. In: IEEE ASSP workshop on applications of signal processing to audio and acoustics. IEEE

    Google Scholar 

  65. Kostek B (1998) Soft set approach to the subjective assessment of sound quality. In: Fuzzy systems proceedings, 1998. IEEE world congress on computational intelligence, The 1998 IEEE International Conference on. Vol 1. IEEE

    Google Scholar 

  66. Kostek B, Szczerba M (1996) Parametric representation of musical phrases. Audio Engineering Society Convention 101. Audio Engineering Society

    Google Scholar 

  67. Zeng H, Swiniarski R (1998) A new halftoning method based on error diffusion with rough set filtering. Rough Sets in Knowledge Discovery 2. Physica-Verlag HD, pp 336–342

    Google Scholar 

  68. Bazan JG et al (1998) Synthesis of decision rules for object classification. Incomplete Information: Rough Set Analysis. Physica-Verlag HD, pp 23–57

    Chapter  Google Scholar 

  69. Ruhe G (1996) Qualitative analysis of software engineering data using rough sets. Tsumoto, Kobayashi, Yokomori, Tanaka, and Nakamura 484:292

    Google Scholar 

  70. Peters JF, Ramanna S (1999) A rough sets approach to assessing software quality: Concepts and rough Petri net models. Rough-Fuzzy Hybridization: New Trends in Decision Making. Springer, Berlin, pp 349–380

    Google Scholar 

  71. Peters JF, Ramanna S (1998) Software deployability decision system framework: a rough set approach. Traitement d’information et gestion d’incertitudes dans les systèmes à base de connaissances. Conférence internationale

    Google Scholar 

  72. Ruhe G (1997) Knowledge discovery from software engineering data: Rough set analysis and its interaction with goal-oriented measurement. European Symposium on Principles of Data Mining and Knowledge Discovery. Springer, Berlin, Heidelberg

    Google Scholar 

  73. Srinivasan P (1989) Intelligent information retrieval using rough set approximations. Inf Process Manage 25(4):347–361

    Article  Google Scholar 

  74. Skowron A, Suraj Z (1993) Rough sets and concurrency. Bull Polish Acad Sci. Technical sciences 41.3:237–254

    Google Scholar 

  75. Nguyen SH et al (1996) Knowledge discovery by rough set methods. In: Proceedings of the international conference on information systems analysis and synthesis ISAS. Vol 96

    Google Scholar 

  76. Beaubouef T, Petry FE (1994) A rough set model for relational databases. Rough Sets, Fuzzy Sets and Knowledge Discovery. Springer, London, pp 100–107

    Chapter  Google Scholar 

  77. Ras ZW (1996) Cooperative knowledge-based systems. Intell Autom Soft Comput 2(2):193–201

    Article  Google Scholar 

  78. Tsumoto S, Tanaka H (1995) Automated discovery of functional components of proteins from amino-acid sequences based on rough sets and change of representation. KDD

    Google Scholar 

  79. Maciá-Pérez F et al (2015) Algorithm for the detection of outliers based on the theory of rough sets. Decis Support Syst 75:63–75

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Muhammad Summair Raza .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Raza, M., Qamar, U. (2019). Rough Set Theory. In: Understanding and Using Rough Set Based Feature Selection: Concepts, Techniques and Applications. Springer, Singapore. https://doi.org/10.1007/978-981-32-9166-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-981-32-9166-9_3

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-32-9165-2

  • Online ISBN: 978-981-32-9166-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics