A survey on granular computing and its uncertainty measure from the perspective of rough set theory

Abstract

Granular computing is an umbrella term to cover a series of theories, methodologies, techniques, and tools that make use of information granules in complex problem solving. Rough sets, as one of the main concrete models of granular computing, has attracted considerable attention and has been successfully applied to numerous kinds of fields. To show the basic ideas and principles of granular computing from the perspective of rough sets, the main models, uncertainty measures and applications of rough sets are surveyed in the paper.

This is a preview of subscription content, access via your institution.

References

  1. Antonelli M, Ducange P, Lazzerini B, Marcelloni F (2016) Multi-objective evolutionary design of granular rule-based classifiers. Granul Comput 1(1):37–58

    Article  Google Scholar 

  2. Azam N (2013) Formulating three-way decision making with game-theoretic rough sets. In: 2013 26th IEEE Canadian conference on electrical and computer engineering (CCECE), pp 1–4

  3. Azam N, Yao J (2012a) Classifying attributes with game-theoretic rough sets. Intelligent Decision Technologies. Springer, New York, pp 175–184

    Google Scholar 

  4. Azam N, Yao J (2012b) Multiple criteria decision analysis with game-theoretic rough sets. In: International conference on rough sets and knowledge technology, pp 399–408

  5. Azam N, Yao J (2013) Game-theoretic rough sets for feature selection. In: Rough sets and intelligent systems-professor Zdzisław pawlak in memoriam, pp 61–78

  6. Azam N, Yao J (2014a) Analyzing uncertainties of probabilistic rough set regions with game-theoretic rough sets. Int J Approx Reason 55(1):142–155

    MathSciNet  MATH  Article  Google Scholar 

  7. Azam N, Yao J (2014b) Game-theoretic rough sets for recommender systems. Knowl Based Syst 72:96–107

    Article  Google Scholar 

  8. Beaubouef T, Petry F, Arora G (1998) Information-theoretic measures of uncertainty for rough sets and rough relational databases. Inf Sci 109(1–4):185–195

    Article  Google Scholar 

  9. Blanco-Fernández Y, Pazos-Arias J, Gil-Solla A, Ramos-Cabrer M, López-Nores M, García-Duque J, Fernández-Vilas A, Díaz-Redondo R, Bermejo-Muñoz J (2008) A flexible semantic inference methodology to reason about user preferences in knowledge-based recommender systems. Knowl Based Syst 21(4):305–320

    Article  Google Scholar 

  10. Bonikowski Z, Bryniarski E, Wybraniec-Skardowska U (1998) Extensions and intentions in the rough set theory. Inf Sci 107(1–4):149–167

    MathSciNet  MATH  Article  Google Scholar 

  11. Chakhar S, Ishizaka A, Labib A, Saad I (2016) Dominance-based rough set approach for group decisions. Eur J Oper Res 251(1):206–224

    MathSciNet  MATH  Article  Google Scholar 

  12. Chakrabarty K, Biswas R, Nanda S (2000) Fuzziness in rough sets. Fuzzy Sets Syst 110(2):247–251

    MathSciNet  MATH  Article  Google Scholar 

  13. Chakraborty D, Pal S (2017) Neighborhood rough filter and intuitionistic entropy in unsupervised tracking. IEEE Trans Fuzzy Syst 26(4):2188–2200

    Article  Google Scholar 

  14. Chen D, Wang C, Hu Q (2007) A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets. Inf Sci 177(17):3500–3518

    MathSciNet  MATH  Article  Google Scholar 

  15. Chen H, Zhou L, Han B (2011) On compatibility of uncertain additive linguistic preference relations and its application in the group decision making. Knowl Based Syst 24(6):816–823

    Article  Google Scholar 

  16. 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 

  17. Chen H, Li T, Fan X, Luo C (2019a) Feature selection for imbalanced data based on neighborhood rough sets. Inf Sci 483:1–20

    Article  Google Scholar 

  18. Chen T, Liu J, Zhu F, Wang Y, Liu J, Chen J (2018) A novel multi-radius neighborhood rough set weighted feature extraction method for remote sensing image classification. Geomat Inf Sci Wuhan Univ 43(2):311–317

    Google Scholar 

  19. Chen Y, Wu K, Chen X, Tang C, Zhu Q (2014) An entropy-based uncertainty measurement approach in neighborhood systems. Inf Sci 279:239–250

    MathSciNet  MATH  Article  Google Scholar 

  20. Chen Y, Zhang Z, Zheng J, Ma Y, Xue Y (2017) Gene selection for tumor classification using neighborhood rough sets and entropy measures. J Biomed Inf 67:59–68

    Article  Google Scholar 

  21. Chen Y, Qin N, Li W, Xu F (2019b) Granule structures, distances and measures in neighborhood systems. Knowl Based Syst 165:268–281

    Article  Google Scholar 

  22. Cui Y (2009) Optimization research on the energy-conserving generation dispatch based on rough sets. In: 2009 International conference on machine learning and cybernetics, vol 3, pp 1405–1409

  23. Dagdia Z, Zarges C, Beck MG, Lebbah M (2018) A distributed rough set theory based algorithm for an efficient big data pre-processing under the spark framework. In: IEEE international conference on big data

  24. Dai J, Wang W, Tian H, Liang L (2013a) Attribute selection based on a new conditional entropy for incomplete decision systems. Knowl Based Syst 39(2):207–213

    Article  Google Scholar 

  25. Dai J, Wang W, Xu Q (2013b) An uncertainty measure for incomplete decision tables and its applications. IEEE Trans Cybern 43(4):1277–1289

    Article  Google Scholar 

  26. Du W, Hu B (2018) A fast heuristic attribute reduction approach to ordered decision systems. Eur J Oper Res 264(2):440–452

    MathSciNet  MATH  Article  Google Scholar 

  27. Dubois D, Prade H (1992) Putting rough sets and fuzzy sets together. Intelligent decision support. Springer, New York, pp 203–232

    Google Scholar 

  28. Durai M, Acharjya D, Kannan A, Iyengar N (2012) An intelligent knowledge mining model for kidney cancer using rough set theory. Int J Bioinform Res Appl 8(5–6):417–435

    Article  Google Scholar 

  29. Fan T, Liau C, Liu D (2011) Dominance-based fuzzy rough set analysis of uncertain and possibilistic data tables. Int J Approx Reason 52(9):1283–1297

    MathSciNet  MATH  Article  Google Scholar 

  30. Fang B, Hu B (2016) Probabilistic graded rough set and double relative quantitative decision-theoretic rough set. Int J Approx Reason 74:1–12

    MathSciNet  MATH  Article  Google Scholar 

  31. Ghimire R, Zhang C, Pattipati K (2018) A rough set-theory-based fault-diagnosis method for an electric power-steering system. IEEE/ASME Trans Mechatron 23(5):2042–2053

    Article  Google Scholar 

  32. Gong Z, Shi Z, Yao H (2012) Variable precision rough set model for incomplete information systems and its \(\beta \)-reducts. Comput Inform 31:1385–1399

    MathSciNet  MATH  Google Scholar 

  33. Greco S, Matarazzo B, Slowinski R (1999) Rough approximation of a preference relation by dominance relations. Eur J Oper Res 117(1):63–83

    MATH  Article  Google Scholar 

  34. Greco S, Matarazzo B, Slowinski R (2001) Rough sets theory for multicriteria decision analysis. Eur J Oper Res 129(1):1–47

    MATH  Article  Google Scholar 

  35. Greco S, Matarazzo B, Slowinski R (2002) Rough sets methodology for sorting problems in presence of multiple attributes and criteria. Eur J Oper Res 138(2):247–259

    MathSciNet  MATH  Article  Google Scholar 

  36. Hamidzadeh J, Zabihimayvan M, Sadeghi R (2018) Detection of web site visitors based on fuzzy rough sets. Soft Comput 22(7):2175–2188

    Article  Google Scholar 

  37. Hamouda S, Wahed M, Alez R, Riad K (2018) Robust breast cancer prediction system based on rough set theory at National Cancer Institute of Egypt. Comput Methods Programs Biomed 153:259–268

    Article  Google Scholar 

  38. Herbert J, Yao J (2011a) Analysis of data-driven parameters in game-theoretic rough sets. In: International conference on rough sets and knowledge technology, pp 447–456

  39. Herbert J, Yao J (2011b) Game-theoretic rough sets. Fundam Inform 108(3–4):267–286

    MathSciNet  MATH  Article  Google Scholar 

  40. Hobbs J (1985) Granularity. In: International joint conference on artificial intelligence, pp 432–435

  41. Hong T, Wang T, Wang S (2007) Mining fuzzy \(\beta \)-certain and \(\beta \)-possible rules from quantitative data based on the variable precision rough-set model. Expert Syst Appl 32(1):223–232

    Article  Google Scholar 

  42. Hu C, Zhang L, Wang B, Zhang Z, Li F (2019) Incremental updating knowledge in neighborhood multigranulation rough sets under dynamic granular structures. Knowl Based Syst 163:811–829

    Article  Google Scholar 

  43. Hu J, Wang G, Zhang Q (2006) Uncertainty measure of covering generated rough set. In: International conference on web intelligence and intelligent agent technology workshops. https://doi.org/10.1109/WI-IATW.2006.139

  44. Hu J, Wang G, Zhang Q (2010) Covering based generalized rough fuzzy set model. J Softw 21(5):968–977

    MathSciNet  MATH  Article  Google Scholar 

  45. Hu Q, Pedrycz W, Yu D, Lang J (2009) Selecting discrete and continuous features based on neighborhood decision error minimization. IEEE Trans Syst Man Cybern B 40(1):137–150

    Google Scholar 

  46. Hu Q, Chakhar S, Siraj S, Labib A (2017) Spare parts classification in industrial manufacturing using the dominance-based rough set approach. Eur J Oper Res 262(3):1136–1163

    MATH  Article  Google Scholar 

  47. Huang B (2011) Graded dominance interval-based fuzzy objective information systems. Knowl Based Syst 24(7):1004–1012

    Article  Google Scholar 

  48. Huang B, He X, Zhou X (2004) Rough entropy based on generalized rough sets covering reduction. J Softw 15(2):215–220

    MathSciNet  MATH  Google Scholar 

  49. Huang Y, Li T, Luo C, Fujita H, Horng S (2017) Dynamic variable precision rough set approach for probabilistic set-valued information systems. Knowl Based Syst 122:131–147

    Article  Google Scholar 

  50. Inuiguchi M, Yoshioka Y, Kusunoki Y (2009) Variable-precision dominance-based rough set approach and attribute reduction. Int J Approx Reason 50(8):1199–1214

    MathSciNet  MATH  Article  Google Scholar 

  51. Jiang Y, Li W, Zhao Y, Yu F (2015) Evaluation of power quality performance based on rough set and evidence theory. Power Syst Prot Control 43:1–7

    Google Scholar 

  52. Klir G, Wierman M (1999) Uncertainty-based information. Physic-Verlag, Heidelberg

    Google Scholar 

  53. Li W, Pedrycz W, Xue X, Zhang X, Fan B, Long B (2018) Information measure of absolute and relative quantification in double-quantitative decision-theoretic rough set model. J Eng 16:1436–1441

    Google Scholar 

  54. Li W, Jia X, Wang L, Zhou B (2019) Multi-objective attribute reduction in three-way decision-theoretic rough set model. Int J Approx Reason 105:327–341

    MathSciNet  MATH  Article  Google Scholar 

  55. Li Y, Zhang G, Zhang H (2017) Image segmentation based on the fuzzy c-means clustering and rough sets. In: IEEE international conference on computer communications

  56. Li Z, Zhang P, Ge X, Xie N, Zhang G (2018b) Uncertainty measurement for a covering information system. Soft Comput 23(14):1–19

    MATH  Google Scholar 

  57. Liang J, Shi Z (2004) The information entropy, rough entropy and knowledge granulation in rough set theory. Int J Uncertain Fuzziness Knowl Based Syst 12(01):37–46

    MathSciNet  MATH  Article  Google Scholar 

  58. Liang J, Chin K, Dang C, Yam R (2002) A new method for measuring uncertainty and fuzziness in rough set theory. Int J Gen Syst 31(4):331–342

    MathSciNet  MATH  Article  Google Scholar 

  59. Lin G, Qian Y, Li J (2012) NMGRS: neighborhood-based multigranulation rough sets. Int J Approx Reason 53(7):1080–1093

    MathSciNet  MATH  Article  Google Scholar 

  60. Lin G, Liang J, Qian Y (2013) Multigranulation rough sets: from partition to covering. Inf Sci 241:101–118

    MathSciNet  MATH  Article  Google Scholar 

  61. Lin T (1988) Neighborhood systems and relational database. In: ACM sixteenth conference on computer science, p 725

  62. Lin T (1997) Granular computing: from rough sets and neighborhood systems to information granulation and computing in words. In: European congress on intelligent techniques and soft computing, pp 1602–1606

  63. Lin T (2001) Granulation and nearest neighborhoods: rough set approach. Granul Comput. https://doi.org/10.1007/978-3-7908-1823-9_6

  64. Lin T, Yao Y (1996) Neighborhoods systems: measure, probability and belief functions. In: Proceedings of the 4th international workshop on rough sets, fuzzy sets and machine discovery, pp 202–207

  65. Lin T et al (1998) Granular computing on binary relations i: data mining and neighborhood systems. Rough Sets Knowl Discov 1:107–121

    MathSciNet  MATH  Google Scholar 

  66. Liu C, Miao D, Qian J (2014) On multi-granulation covering rough sets. Int J Approx Reason 55(6):1404–1418

    MathSciNet  MATH  Article  Google Scholar 

  67. Liu D, Li J (2019) Safety monitoring data classification method based on wireless rough network of neighborhood rough sets. Saf Sci 118:103–108

    Article  Google Scholar 

  68. Liu D, Yao Y, Li T (2011) Three-way investment decisions with decision-theoretic rough sets. Int J Comput Intell Syst 4(1):66–74

    Article  Google Scholar 

  69. Liu J, Lin Y, Li Y, Weng W, Wu S (2018) Online multi-label streaming feature selection based on neighborhood rough set. Pattern Recogn 84:273–287

    Article  Google Scholar 

  70. Luca A, Termini S (1972) A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Inf Control 20(4):301–312

    MathSciNet  MATH  Article  Google Scholar 

  71. Luo C, Li T, Yao Y (2017) Dynamic probabilistic rough sets with incomplete data. Inf Sci 417:39–54

    Article  Google Scholar 

  72. Luo G, Yang X (2009) Attribute reduction optimal selection algorithms based on variable precision dominance-based rough sets. Chin J Manag Sci 17(2):169–175

    Google Scholar 

  73. Lv J, Hui Z, Fan W, Du X (2013) Uncertainty measures in interval ordered information systems. J Appl Sci 13(17):3522–3527

    Article  Google Scholar 

  74. Ma J, Zhang H, Qian Y (2019) Three-way decisions with reflexive probabilistic rough fuzzy sets. Granul Comput 4(3):363–375

    Article  Google Scholar 

  75. Ma W, Sun B (2012) Probabilistic rough set over two universes and rough entropy. Int J Approx Reason 53(4):608–619

    MathSciNet  MATH  Article  Google Scholar 

  76. Ma X, Li D (2017) A hybrid fault diagnosis method based on fuzzy signed directed graph and neighborhood rough set. In: 2017 6th data driven control and learning systems (DDCLS), pp 253–258

  77. Mandal P, Ranadive A (2018) Multi-granulation fuzzy decision-theoretic rough sets and bipolar-valued fuzzy decision-theoretic rough sets and their applications. Granul Comput 4(3):483–509

    Article  Google Scholar 

  78. Mckee T (2000) Developing a bankruptcy prediction model via rough sets theory. Intell Syst Acc Finance Manag 9(3):159–173

    Article  Google Scholar 

  79. Mehdizadeh M (2019) Integrating ABC analysis and rough set theory to control the inventories of distributor in the supply chain of auto spare parts. Comput Ind Eng. https://doi.org/10.1016/j.cie.2019.01.047

  80. Miao D (1999) An information representation of the concepts and operations in rough set theory. J Softw 22:113–116

    Google Scholar 

  81. Miao D, Wang J (1998) On the relationships between information entropy and roughness of knowledge in rough set theory. Pattern Recognit Artif Intell 11(1):34–40

    Google Scholar 

  82. Min F, Zhang Z, Zhai W, Shen R (2020) Frequent pattern discovery with tri-partition alphabets. Inf Sci 507:715–732

    MathSciNet  Article  Google Scholar 

  83. Mustafa N, Li J (2017) Medical data classification scheme based on hybridized smote technique (hst) and rough set technique (rst). In: 2017 IEEE 2nd international conference on cloud computing and big data analysis (ICCCBDA), pp 49–55

  84. Neuman J, Morgenstern O (1953) Theory of games and economic behavior. Princeton University Press, Princeton. https://doi.org/10.1038/157172a0

    Google Scholar 

  85. Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):341–356

    MATH  Article  Google Scholar 

  86. Pawlak Z, Skowron A (2007) Rough sets: some extensions. Inf Sci 177(1):28–40

    MathSciNet  MATH  Article  Google Scholar 

  87. Pawlak Z, Wong S, Ziarko W (1988) Rough sets: probabilistic versus deterministic approach. Int J Man Mach Stud 29(1):81–95

    MATH  Article  Google Scholar 

  88. Peters G, Poon S (2011) Analyzing IT business values—a dominance based rough sets approach perspective. Expert Syst Appl 38(9):11120–11128

    Article  Google Scholar 

  89. Qian Y, Liang J (2008) Combination entropy and combination granulation in rough set theory. Int J Uncertain Fuzziness Knowl Based Syst 16(02):179–193

    MathSciNet  MATH  Article  Google Scholar 

  90. Qian Y, Dang C, Liang J, Tang D (2009) Set-valued ordered information systems. Inf Sci 179(16):2809–2832

    MathSciNet  MATH  Article  Google Scholar 

  91. Qian Y, Liang J, Dang C (2010) Incomplete multigranulation rough set. IEEE Trans Syst Man Cybern A 40(2):420–431

    Article  Google Scholar 

  92. Qian Y, Xu H, Liang J, Liu B, Wang J (2015) Fusing monotonic decision trees. IEEE Trans Knowl Data Eng 27(10):2717–2728

    Article  Google Scholar 

  93. Qian Y, Liang X, Lin G, Qian G, Liang J (2017) Local multigranulation decision-theoretic rough sets. Int J Approx Reason 82:119–137

    MathSciNet  MATH  Article  Google Scholar 

  94. Qian Y, Liang X, Wang Q, Liang J, Liu B, Skowron A, Yao Y, Ma J, Dang C (2018) Local rough set: a solution to rough data analysis in big data. Int J Approx Reason 97:38–63

    MathSciNet  MATH  Article  Google Scholar 

  95. Rajesh T, Malar RSM, Geetha MR (2018) Brain tumor detection using optimisation classification based on rough set theory. Cluster Comput. https://doi.org/10.1007/s10586-018-2111-5

  96. Rehman N, Ali A, ASS I, IA M, Park C (2019) Variable precision multi decision \(\lambda \)-soft dominance based rough sets and their applications in conflict problems. J Intell Fuzzy Syst 36(6):5345–5360

    Article  Google Scholar 

  97. Ren M, Qu Y, Deng A (2018) Covering rough set-based three-way decision feature selection. In: Tenth international conference on advanced computational intelligence, pp 782–787

  98. Sebastián M, Georg P, Richard W (2020) Credit scoring using three-way decisions with probabilistic rough sets. Inf Sci 507:700–714

    Article  Google Scholar 

  99. Sen D, Pal S (2008) Generalized rough sets, entropy, and image ambiguity measures. IEEE Trans Syst Man Cybern B 39(1):117–128

    Article  Google Scholar 

  100. Sharma S, Dua A, Singh M, Kumar N, Prakash S (2018) Fuzzy rough set based energy management system for self-sustainable smart city. Renew Sustain Energy Rev 82:3633–3644

    Article  Google Scholar 

  101. Shi Z, Gong Z (2010) The further investigation of covering-based rough sets: Uncertainty characterization, similarity measure and generalized models. Inf Sci 180(19):3745–3763

    MathSciNet  MATH  Article  Google Scholar 

  102. Singh P, Huang YP (2019) A four-way decision-making approach using interval-valued fuzzy sets, rough set and granular computing: a new approach in data classification and decision-making. Granul Comput. https://doi.org/10.1007/s41066-019-00165-7

  103. Skowron A, Jankowski A, Dutta S (2016) Interactive granular computing. Granul Comput 1(2):95–113

    MathSciNet  MATH  Article  Google Scholar 

  104. Słowiński R, Greco S, Matarazzo B (2002) Axiomatization of utility, outranking and decision rule preference models for multiple-criteria classification problems under partial inconsistency with the dominance principle. Control Cybern 31(4):1005–1035

    MATH  Google Scholar 

  105. Sun B, Ma W, Xiao X (2017) Three-way group decision making based on multigranulation fuzzy decision-theoretic rough set over two universes. Int J Approx Reason 81:87–102

    MathSciNet  MATH  Article  Google Scholar 

  106. Suo M, Zhang M, Zhou D, Zhu B, Li S (2017) Fault diagnosis of satellite power system using variable precision fuzzy neighborhood rough set. In: 2017 36th Chinese control conference (CCC), pp 7301–7306

  107. Teng S, Liu A, Pan P, Sun J, Yao W (2010) A new uncertainty measure in ordered information systems. In: 2010 2nd international conference on advanced computer control, vol 4, pp 517–521

  108. Wang C, Shao M, Sun B, Hu Q (2015a) An improved attribute reduction scheme with covering based rough sets. Appl Soft Comput 26:235–243

    Article  Google Scholar 

  109. Wang C, Qiang H, Shao M, Xu Y, Hu Q (2017) A unified information measure for general binary relations. Knowl Based Syst 135:18–28

    Article  Google Scholar 

  110. Wang G, Yang Y (2011) A novel emotion recognition method based on ensemble learning and rough set theory

  111. Wang G, Yu H (2002) Decision table reduction based on conditional information entropy. Chin J Comput 25(7):759–766

    MathSciNet  Google Scholar 

  112. Wang G, Ma X, Yu H (2015b) Monotonic uncertainty measures for attribute reduction in probabilistic rough set model. Int J Approx Reason 59:41–67

    MathSciNet  MATH  Article  Google Scholar 

  113. Wang J, Zhang X (2018) Two types of intuitionistic fuzzy covering rough sets and an application to multiple criteria group decision making. Symmetry 10(10):462

    Article  Google Scholar 

  114. Wang X, Zhang W, Liu D, Yu H, Yang X, Yang X (2019) Pseudolabel decision-theoretic rough set. Math Prob Eng. https://doi.org/10.1155/2019/6810796

  115. Wei R, Liu B, Shi K (2007) Fuzziness based on covering generalized rough sets. Comput Sci 34(1):153–155

    Google Scholar 

  116. Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. Orderd Sets D Reidel 83:314–339

    MathSciNet  MATH  Google Scholar 

  117. Xie X, Gang X, Xu X (2018) High precision image segmentation algorithm using slic and neighborhood rough set. Multimed Tools Appl 77(24):31525–31543

    Article  Google Scholar 

  118. Xu J, Miao D, Zhang Y, Zhang Z (2017a) A three-way decisions model with probabilistic rough sets for stream computing. Int J Approx Reason 88:1–22

    MathSciNet  MATH  Article  Google Scholar 

  119. Xu W, Zhang W (2006) Fuzziness of covering generalized rough sets. Fuzzy Syst Math 20(6):115–121

    MathSciNet  MATH  Google Scholar 

  120. Xu W, Yang H, Zhang W (2007) Uncertainty measures of roughness of knowledge and rough sets in ordered information systems. In: International conference on intelligent computing, pp 759–769

  121. Xu W, Li W, Zhang X (2017b) Generalized multigranulation rough sets and optimal granularity selection. Granul Comput 2(4):271–288

    Article  Google Scholar 

  122. Xue Y, Li Z, Li S, Qiu D, Tao Y, Wang L, Yang W, Zhang K (2019) Prediction of rock burst in underground caverns based on rough set and extensible comprehensive evaluation. Bull Eng Geol Environ 78(1):417–429

    Article  Google Scholar 

  123. Yager R (2018) Decision making under measure-based granular uncertainty. Granul Comput 3(4):345–353

    Article  Google Scholar 

  124. Yang C, Qiu J, Zhang W (2013) Knowledge granulation based roughness measure for neighborhood rough sets. In: 2013 Third international conference on intelligent system design and engineering applications, pp 917–920

  125. Yang X, Yu D, Yang J, Wei L (2009) Dominance-based rough set approach to incomplete interval-valued information system. Data Knowl Eng 68(11):1331–1347

    Article  Google Scholar 

  126. Yao J, Azam N (2014) Web-based medical decision support systems for three-way medical decision making with game-theoretic rough sets. IEEE Trans Fuzzy Syst 23(1):3–15

    Article  Google Scholar 

  127. Yao Y (1998) Relational interpretations of neighborhood operators and rough set approximation operators. Inf Sci 111(1–4):239–259

    MathSciNet  MATH  Article  Google Scholar 

  128. Yao Y (1999a) Granular computing using neighborhood systems. In: Roy R, Furuhashi T, Chawdhry PK (eds) Advances in soft computing. Springer, London, pp 539–553

  129. Yao Y (1999b) Rough sets, neighborhood systems and granular computing. In: Engineering solutions for the next millennium. 1999 IEEE Canadian conference on electrical and computer engineering (Cat. No. 99TH8411), vol 3, pp 1553–1558

  130. Yao Y (2000) Granular computing: basic issues and possible solutions. In: Proceedings of the 5th joint conference on information sciences, vol 1, pp 186–189

  131. Yao Y (2004) A partition model of granular computing. In: Peters JF, Skowron A, Grzymała-Busse JW, Kostek B, Świniarski RW, Szczuka MS (eds) Transactions on rough sets I. Lecture notes in computer science, vol 3100. Springer, Berlin, Heidelberg, 232–253

  132. Yao Y (2007) Decision-theoretic rough set models. In: International conference on rough sets and knowledge technology, pp 1–12

  133. Yao Y (2008) Probabilistic rough set approximations. Int J Approx Reason 49(2):255–271

    MATH  Article  Google Scholar 

  134. Yao Y (2010) Probabilistic approaches to rough sets. Expert Syst 20(5):287–297

    Article  Google Scholar 

  135. Yao Y, Yao B (2012) Covering based rough set approximations. Inf Sci 200:91–107

    MathSciNet  MATH  Article  Google Scholar 

  136. Yu Y, Pedrycz W, Miao D (2013) Neighborhood rough sets based multi-label classification for automatic image annotation. Int J Approx Reason 54(9):1373–1387

    MATH  Article  Google Scholar 

  137. Zadeh L (1979) Fuzzy sets and information granularity. In: Gupta M, Ragade R, Yager R (eds) Advances in fuzzy set theory and applications. North-Holland Publishing Company, Amsterdam, pp 3–18

    Google Scholar 

  138. Zadeh L (1997) Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst 90(2):111–127

    MathSciNet  MATH  Article  Google Scholar 

  139. Zadeh L (1998) Some reflections on soft computing, granular computing and their roles in the conception, design and utilization of information/intelligent systems. Soft Comput 2(1):23–25

    Article  Google Scholar 

  140. Zakowski W (1983) Approximations in the space (u, \(\pi \)). Demonstr Math 16(3):761–770

    MATH  Google Scholar 

  141. Zhang B, Zhang L (1992) Theory and applications of problem solving. North-Holland Publishers, Amsterdam

    Google Scholar 

  142. Zhang Q, Zhang Q, Wang G (2016) The uncertainty of probabilistic rough sets in multi-granulation spaces. Int J Approx Reason 77:38–54

    MathSciNet  MATH  Article  Google Scholar 

  143. Zhang Q, Zhang P, Wang G (2017) Research on approximation set of rough set based on fuzzy similarity. J Intell Fuzzy Syst 32(3):2549–2562

    MATH  Article  Google Scholar 

  144. Zhang Q, Lv G, Chen Y, Wang G (2018a) A dynamic three-way decision model based on the updating of attribute values. Knowl Based Syst 142:71–84

    Article  Google Scholar 

  145. Zhang Q, Xie Q, Wang G (2018b) A novel three-way decision model with decision-theoretic rough sets using utility theory. Knowl Based Syst 159:321–335

    Article  Google Scholar 

  146. Zhang Q, Yang C, Wang G (2019a) A sequential three-way decision model with intuitionistic fuzzy numbers. In: IEEE transactions on systems, man, and cybernetics: systems, pp 1–13

  147. Zhang Q, Xia D, Liu K, Wang G (2020) A general model of decision-theoretic three-way approximations of fuzzy sets based on a heuristic algorithm. Inf Sci 507:522–539

    Article  Google Scholar 

  148. Zhang W (2001) Theory and methods of rough sets. Science Press, Beijing

    Google Scholar 

  149. Zhang Y, Yao J (2012) Rule measures tradeoff using game-theoretic rough sets. In: International conference on brain informatics, pp 348–359

  150. Zhang Y, Liu P, Yao J (2019b) Three-way email spam filtering with game-theoretic rough sets. In: 2019 International conference on computing, networking and communications (ICNC), pp 552–556

  151. Zhao X, Hu B (2020) Three-way decisions with decision-theoretic rough sets in multiset-valued information tables. Inf Sci 507:684–699

    MathSciNet  Article  Google Scholar 

  152. Zheng T, Zhu L (2015) Uncertainty measures of neighborhood system-based rough sets. Knowl Based Syst 86:57–65

    Article  Google Scholar 

  153. Zhong Y, Zhang X, Shan F (2018) Hybrid data-driven outlier detection based on neighborhood information entropy and its developmental measures. Expert Syst Appl 112:243–257

    Article  Google Scholar 

  154. Zhou B, Yao Y, Luo J (2010) A three-way decision approach to email spam filtering. In: Canadian conference on artificial intelligence, Springer, pp 28–39

  155. Zhu W (2007) Topological approaches to covering rough sets. Inf Sci 177(6):1499–1508

    MathSciNet  MATH  Article  Google Scholar 

  156. Zhu W (2009) Relationship between generalized rough sets based on binary relation and covering. Inf Sci 179(3):210–225

    MathSciNet  MATH  Article  Google Scholar 

  157. Zhu W, Wang F (2003) Reduction and axiomization of covering generalized rough sets. Inf Sci 152:217–230

    MathSciNet  MATH  Article  Google Scholar 

  158. Zhu W, Wang F (2006) Properties of the first type of covering-based rough sets. In: Sixth IEEE international conference on data mining-workshops (ICDMW’06), pp 407–411

  159. Ziarko W (1993) Variable precision rough set model. J Comput Syst Sci 46(1):39–59

    MathSciNet  MATH  Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 61876201), the National Key Research and Development Program of China (No. 2017YFC0 804002) and the Science and Technology Research Project of Chongqing Municipal Education Commission (No. KJQN201800624).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Qinghua Zhang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Cheng, Y., Zhao, F., Zhang, Q. et al. A survey on granular computing and its uncertainty measure from the perspective of rough set theory. Granul. Comput. 6, 3–17 (2021). https://doi.org/10.1007/s41066-019-00204-3

Download citation

Keywords

  • Granular computing
  • Rough sets
  • Granules
  • Uncertainty measure
  • Approximation sets