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Double-quantitative multigranulation rough fuzzy set based on logical operations in multi-source decision systems

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Abstract

Fuzzy phenomena exist widely in real life, and with the rapid development of big data technology we may gather information from multiple sources. So it is extremely meaningful to study fuzzy concepts in the context of multiple information sources. In this study, six novel kinds of double-quantitative multigranulation rough fuzzy set models are proposed. Both absolute and relative information are taken into account by utilizing the logical conjunction and disjunction operators to define the lower and upper approximations. Four decision regions can be computed based on the results of approximations, and the corresponding four decision rules are established. Some basic propositions of these models are discussed. The relationships among the six double-quantitative multigranulation rough fuzzy set models are analysed. The corresponding algorithms of obtaining four decision regions are given and the time complexity of them are analysed. Later a weather example is employed to illustrate that our models can divide data sets to the positive region, the negative region, the lower boundary region, and the upper boundary region, where the samples in the positive region completely support the concept set, the samples in the negative region completely oppose the concept set, and the samples in the lower and upper boundary may support or oppose the concept set. Finally, an experiment is conducted to demonstrate that our models perform better than the mean fusion method in terms of decision-making.

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References

  1. Chen Z, Bagherinia A, Minaei-Bidgoli B, Parvin H, Pho K-H (2021) Fuzzy Clustering Ensemble Considering Cluster Dependability. International Journal of Artificial Intelligence Tools

  2. Cornelis C, Cock MD, Kerre EE (2010) Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge. Expert System 20(5):260–270

    Article  Google Scholar 

  3. Dubois D, Prade H (2007) Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems 17(2):191–209

    MATH  Google Scholar 

  4. Fan BJ, Tsang ECC, Xu WH, Yu JH (2017) Double-quantitative rough fuzzy set based decisions: A logical operations method. Information Sciences 378(C):264–281

    Article  MATH  Google Scholar 

  5. Ferraro MB, Giordani P, Vichi M (2021) A class of two-mode clustering algorithms in a fuzzy setting. Econometrics and Statistics 18:63–78

    Article  MathSciNet  Google Scholar 

  6. Guo YT, Tsang ECC, Xu WH, Chen DG (2019) Local logical disjunction double-quantitative rough sets, Information. Science 500:87–112

    MATH  Google Scholar 

  7. Gupta A, Datta S, Das S (2021) Fuzzy Clustering to Identify Clusters at Different Levels of Fuzziness: An Evolutionary Multiobjective Optimization Approach. IEEE Transactions on Cybernetics 51(5):2601–2611

    Article  Google Scholar 

  8. Huang B, Guo CX, Zhuang YL, Li HX, Zhou XZ (2014) Intuitionistic fuzzy multigranulation rough sets. Information Sciences 277:299–320

    Article  MathSciNet  MATH  Google Scholar 

  9. http://archive.ics.uci.edu/ml/index.php

  10. https://sci2s.ugr.es/keel/datasets.php

  11. Jensen R, Tuson A, Shen Q (2014) Finding rough and fuzzy-rough set reducts with SAT, Information. Science 255:100–120

    MATH  Google Scholar 

  12. Kanzawa Y, Miyamoto S (2021) Generalized Fuzzy c-Means Clustering and its Property of Fuzzy Classification Function. Journal of Advanced Computational Intelligence and Intelligent Informatics 25(1):73–82

    Article  Google Scholar 

  13. Khammar AH, Arefi M, Akbari MG (2021) A general approach to fuzzy regression models based on different loss functions. Soft Computing 25:835–849

    Article  Google Scholar 

  14. Kong QZ, Zhang XW, Xu WH, Xie ST (2020) Attribute reducts of multi-granulation information system. Artificial Intelligence Review 53(2):1353–1371

    Article  Google Scholar 

  15. Li MM, Chen MH, Xu WH (2019) Double-quantitative multigranulation decision-theoretic rough fuzzy set model. International Journal of Machine Learning and Cybernetics 10:3225–3244

    Article  Google Scholar 

  16. Li WT, Pedrycz W, Xue XP, Xu WH, Fan BJ (2018) Distance-based double-quantitative rough fuzzy sets with logic operations. International Journal of Approximate Reasoning 101:206–233

    Article  MathSciNet  MATH  Google Scholar 

  17. Li WT, Xu WH (2015) Double-quantitative decision-theoretic rough set. Information Sciences 316:54–67

    Article  MathSciNet  MATH  Google Scholar 

  18. Li WT, Xu WH, Zhang XY, Zha J (2021) Updating approximaitons with dynamic objects based on local multigranulation rough sets in ordered information systems. Artificial Intelligence Review. https://doi.org/10.1007/s10462-021-10053-9

  19. Li JH, Ren Y, Mei CL, Qian YH, Yang XB (2016) A comparative study of multigranulation rough sets and concept lattices via rule acquisition. Knowledge-Based Systems 91:152–164

    Article  Google Scholar 

  20. Li JH, Wang F, Wu WZ, Xu WH, Yang XB, Zhe YH (2021) Review of Multi-granularity Data Analysis Methods Based on Granular Computing. Journal of Data Acquisition and Processing 36(3):418–435

    Google Scholar 

  21. Liang JY, Wang F, Dang CY, Qian YH (2012) An efficient rough feature selection algorithm with a multi-granulation view. International journal of approximate reasoning 53:912–926

    Article  MathSciNet  Google Scholar 

  22. Liang XY, Guo Q, Qian Y H, Ding WP, Zhang QF, Evolutionary Deep Fusion Method and Its Application in Chemical Structure Recognition, IEEE Transactions on Evolutionary Computation, https://doi.org/10.1109/TEVC.2021.3064943

  23. Lin BY, Xu WH (2018) Multi-granulation rough set for incomplete interval-valued decision information systems based on multi-threshold tolerance relation. Symmetry 10(6):208–229

    Article  MATH  Google Scholar 

  24. Liu CH, Wang MZ (2011) Covering fuzzy rough set based on multigranulations, Proceedings of International Conference on Uncertainty Reasoning and Knowledge. Engineering 146–149

  25. Pawlak Z (1982) Rough sets. International Journal of Computer and Information Sciences 11(5):341–356

    Article  MathSciNet  MATH  Google Scholar 

  26. Pawlak Z (1998) Rough set theory and its applications to data analysis. Cybernetics and Systems 29(7):661–688

    Article  MATH  Google Scholar 

  27. Pei DW (2005) A generalized model of fuzzy rough sets. International Journal of General Systems 34(5):603–613

    Article  MathSciNet  MATH  Google Scholar 

  28. Qian YH, Liang JY, Yao YY, Dang CY (2010) MGRS: A multi-granulation rough set. Information sciences 180:949–970

    Article  MathSciNet  MATH  Google Scholar 

  29. Qian YH, Liang JY, Dang CY (2010) Incomplete multigranulation rough set. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 40(2):420–431

    Article  Google Scholar 

  30. Qian YH, Zhang H, Sang YL, Liang JY (2014) Multigranulation decision-theoretic rough sets. International Journal of Approximate Reasoning 55(1):225–237

    Article  MathSciNet  MATH  Google Scholar 

  31. Qian J, Liu CH, Yue XD (2019) Multigranulation sequential three-way decisions based on multiple thresholds. International journal of approximate reasoning 105:396–416

    Article  MathSciNet  MATH  Google Scholar 

  32. Qian YH, Liang XY, Lin GP, Guo Q, Liang JY (2017) Local multigranulation decision-theoretic rough sets. International Journal of Approximate Reasoning 82:119–137

    Article  MathSciNet  MATH  Google Scholar 

  33. Spiliotis M, Garrote L (2021) Unit hydrograph identification based on fuzzy regression analysis. Evolving Systems 1–22

  34. Sanz JA, Bustince H (2021) A wrapper methodology to learn interval-valued fuzzy rule-based classification systems. Applied Soft Computing 104(3):107249

    Article  Google Scholar 

  35. Sang BB, Guo YT, Shi DR, Xu WH (2018) Decision-theoretic rough set model of multi-source decision systems. International Journal of Machine Learning Cybernetics 9(11):1941–1954

    Article  Google Scholar 

  36. Sang BB, Yang L, Chen HM, Xu WH, Guo YT, Yuan Z (2019) Generalized multi-granulation double-quantitative decision-theoretic rough set of multi-source information system. International Journal of Approximate Reasoning 115:157–179

    Article  MathSciNet  MATH  Google Scholar 

  37. Shen S, Cui J (2012) Estimation and inference of the fuzzy linear regression model with L fuzzy observations. Fifth International Joint Conference on Computational Sciences and Optimization. IEEE 354–358

  38. Sun BZ, Ma WM, Zhao HY (2014) Decision-theoretic rough fuzzy set model and application, Information. Science 283:180–196

    MATH  Google Scholar 

  39. Tabakov M, Chlopowiec A, Dlubak A (2021) Classification with Fuzzification Optimization Combining Fuzzy Information Systems and Type-2 Fuzzy Inference. Applied Sciences 11(8):3484

    Article  Google Scholar 

  40. Wu MF, Kou GX, Notice of Retraction, (2010) Fuzzy rough set model based on multi-granulations. 2010 2nd International Conference on Computer Engineering and Technology, pp 271–275

  41. Wu WZ, Mi JS, Zhang WX (2003) Generalized fuzzy rough sets. Information Science 151(3):263–282

    Article  MathSciNet  MATH  Google Scholar 

  42. Xu WH, Wang QR, Zhang XT (2013) Multi-granulation rough sets based on tolerance relations. Soft Computing 17:1241–1252

    Article  MATH  Google Scholar 

  43. Xu WH, Wang QR, Luo SQ (2014) Multi-granulation fuzzy rough sets. Journal of Intelligent and Fuzzy Systems 26:1323–1340

    Article  MathSciNet  MATH  Google Scholar 

  44. Xu WH, Zhang XT, Wang QR (2012) A generalized multi-granulation rough set approach. International Conference on Intelligent Computing 681–689

  45. Xu WH, Li MM, W XZ (2017) Information Fusion Based on Information Entropy in Fuzzy Multi-source Incomplete Information System. International Journal of Fuzzy Systems 19:1200–1216

    Article  Google Scholar 

  46. Xu WH, Yu JH (2017) A novel approach to information fusion in multi-source datasets: A granular computing viewpoint. Information Sciences 378:410–423

    Article  MATH  Google Scholar 

  47. Xu WH, Li WT (2016) Granular computing approach to two-way learning based on formal concept analysis in fuzzy datasets. IEEE Transactions on Cybernetics 46(2):366–379

    Article  MathSciNet  Google Scholar 

  48. Xu WH, Guo YT (2016) Generalized multigranulation double-quantitative decision-theoretic rough set. Knowledge-based systems 105:190–205

    Article  Google Scholar 

  49. Yang L, Xu WH, Zhang XY, Sang BB (2020) Multi-granulation method for information fusion in multi-source decision information system. International Journal of Approximate Reasoning 122:47–65

    Article  MathSciNet  MATH  Google Scholar 

  50. Yang L, Zhang XY, Xu WH, Sang BB (2019) Multi-granulation Rough Sets and Uncertainty Measurement for Multi-source Fuzzy Information System. International Journal of Fuzzy Systems 21(6):1919–1937

    Article  MathSciNet  Google Scholar 

  51. Yao YY, Lin TY (1996) Generalization of rough sets using modal logics. Intelligent Automation and Soft Computing 2(2):103–120

    Article  Google Scholar 

  52. Yao YY (2007) Decision-theoretic rough set models. Lecture Notes in Computer Science 4481:1–12

    Article  Google Scholar 

  53. Yu JH, Zhang B, Chen MH, Xu WH (2018) Double-quantitative decision-theoretic approach to multigranulation approximate space. International Journal of Approximate Reasoning 98:236–258

    Article  MathSciNet  MATH  Google Scholar 

  54. Zadeh LA (1965) Fuzzy sets. Inf. Control 8(3):338–353

    Article  MATH  Google Scholar 

  55. Zadeh LA (1979). In: Gupta N, Ragade R, Yager R (eds) Fuzzy Sets and Information Granularity, Advances in Fuzzy Set Theory and Applications. North-Holland, Amsterdam, pp 3–18

    Google Scholar 

  56. Zhang XY, Gou HY, Lv ZY, Miao DQ (2021) Double-quantitative distance measurement and classification learning based on the tri-level granular structure of neighborhood system. Knowledge-Based Systems 217(1C4):106799

    Article  Google Scholar 

  57. Zhang XY, Yao H, Lv ZY, Miao DQ (2021) Class-specific information measures and attribute reducts for hierarchy and systematicness. Information Sciences 563:196–225

    Article  MathSciNet  Google Scholar 

  58. Zhu W, Wang FY (2003) Reduction and axiomization of covering generalized rough sets. Information Sciences 152(1):217–230

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This paper is supported by the National Natural Science Foundation of China (Nos. 61976245, 61772002).

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  1. College of Artificial Intelligence, Southwest University, Chongqing, 400715, People’s Republic of China

    Xiuwei Chen & Weihua Xu

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  1. Xiuwei Chen
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Chen, X., Xu, W. Double-quantitative multigranulation rough fuzzy set based on logical operations in multi-source decision systems. Int. J. Mach. Learn. & Cyber. 13, 1021–1048 (2022). https://doi.org/10.1007/s13042-021-01433-2

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