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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
http://www.rapidtables.com/math/symbols/Basic_Math_Symbols.htm. Access 30 Mar 2017
Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic, Dordrecht
Pal SK, Skowron A (1999) Rough-fuzzy hybridization: a new trend in decision making. Springer, New York Inc
Krysiński J (1990) Rough sets approach to the analysis of the structure-activity relationship of quaternary imidazolium compounds. Arzneimittelforschung 40(7):795–799
Podsiadło M, Rybiński H (2014) Rough sets in economy and finance. Transactions on Rough Sets XVII. Springer, Berlin Heidelberg, pp 109–173
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
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
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
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
Fibak J et al (1986) Rough sets based decision algorithm for treatment of duodenal ulcer by HSV. Biol Sci 34:227–249
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
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
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
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
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
Grzymala-Busse JW (1998) Applications of the rule induction system LERS. Rough Sets in Knowledge Discovery 1, pp 366–375
Paterson GI (1994) Rough classification of pneumonia patients using a clinical database. Rough Sets, Fuzzy Sets and Knowledge Discovery. Springer, London, pp 412–419
Tsumoto S, Tanaka H (1995) PRIMEROSE: probabilistic rule induction method based on rough sets and resampling methods. Comput Intell 11(2):389–405
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
Kandulski M, Marciniec J, Tukałło K (1992) Surgical wound infection—conducive factors and their mutual dependencies. Intelligent decision support. Springer, Netherlands, pp 95–110
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
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
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
Ziarko W (1998) Rough sets as a methodology for data mining. Rough Sets Knowl Discov 1:554–576
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
Slowinski K, Stefanowski J (1996) On limitations of using rough set approach to analyse non-trivial medical information systems
Paszek P, Wakulicz Deja A (1996) Optimalization diagnose in progressive encephalopathy applying the rough set theory. Zimmermann 557.1:192–196
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
Wakulicz-Deja A, Paszek P (1997) Diagnose progressive encephalopathy applying the rough set theory. Int J Med Informatics 46(2):119–127
Czyzewski A (1998) Speaker-independent recognition of isolated words using rough sets. Inf Sci 104(1-2):3–14
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
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
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
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
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
Tanaka H, Maeda Y (1998) Reduction methods for medical data. Rough Sets in Knowledge Discovery 2. Physica-Verlag HD, pp 295–306
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
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
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
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
Mrózek A, Skabek K (1998) Rough sets in economic applications. Rough Sets in Knowledge Discovery 2. Physica-Verlag HD, pp 238–271
Piasta Z, Lenarcik A (1998) Learning rough classifiers from large databases with missing values. Rough Sets Knowl Discov 1:483–499
Van den Poel D (1998) Rough sets for database marketing. Rough Sets in Knowledge Discovery 2. Physica-Verlag HD, pp 324–335
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
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
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
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
Kowalczyk W (1996) Analyzing temporal patterns with rough sets. Zimmermann 557:139
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
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
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
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
Reinhard A et al (1992) An application of rough set theory in the control conditions on a polder. S lowi nski 428:331
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
Gunn JD, Grzymala-Busse JW (1994) Global temperature stability by rule induction: an interdisciplinary bridge. Human Ecology 22(1):59–81
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
Roy B, Slowinski R, Treichel W (1992) “Multicriteria programming of water supply systems for rural AREAS1, 13–31
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
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
Czyzewski A (1996) Mining knowledge in noisy audio data. KDD
Czyżewski A (1998) Soft processing of audio signals. Rough Sets in Knowledge Discovery 2. Physica-Verlag HD, pp 147–165
Czyzewski A, Krolikowski R (1997) New methods of intelligent filtration and coding of audio. Audio Engineering Society Convention 102. Audio Engineering Society
Kostek B (1998) Soft computing-based recognition of musical sounds. Rough Sets in Knowledge Discovery 2. Physica-Verlag HD, pp 193–213
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
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
Kostek B, Szczerba M (1996) Parametric representation of musical phrases. Audio Engineering Society Convention 101. Audio Engineering Society
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
Bazan JG et al (1998) Synthesis of decision rules for object classification. Incomplete Information: Rough Set Analysis. Physica-Verlag HD, pp 23–57
Ruhe G (1996) Qualitative analysis of software engineering data using rough sets. Tsumoto, Kobayashi, Yokomori, Tanaka, and Nakamura 484:292
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
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
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
Srinivasan P (1989) Intelligent information retrieval using rough set approximations. Inf Process Manage 25(4):347–361
Skowron A, Suraj Z (1993) Rough sets and concurrency. Bull Polish Acad Sci. Technical sciences 41.3:237–254
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
Beaubouef T, Petry FE (1994) A rough set model for relational databases. Rough Sets, Fuzzy Sets and Knowledge Discovery. Springer, London, pp 100–107
Ras ZW (1996) Cooperative knowledge-based systems. Intell Autom Soft Comput 2(2):193–201
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
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this chapter
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)