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Multi-granulation Rough Sets and Uncertainty Measurement for Multi-source Fuzzy Information System

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Abstract

Rough set theory is an effective mathematical tool to deal with uncertain information. With the arrival of the information age, we need to handle not only single-source data sets, but also multi-source data sets. In real life; most of the data we face are fuzzy multi-source data sets. However, the rough set model has not been found for multi-source fuzzy information systems. This paper aims to study how to use the rough set model in multi-source fuzzy environment. Firstly, we define a distance formula between two objects in an information table and further propose a tolerance relation through this formula. Secondly, the supporting characteristic function is proposed by the inclusion relation between tolerance classes and concept set X. And then, from the perspective of multi-granulation, each information source is regarded as a granularity. The optimistic, pessimistic, generalized multi-granulation rough set model and some important properties are discussed in multi-source fuzzy information systems. At the same time, the uncertainty measurement are considered for the different models. Finally, some experiments are carried out to interpret and evaluate the validity and significance of the approach.

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References

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

    Article  MATH  Google Scholar 

  2. Pawlak, Z.: Rough set theory and its applications to data analysis. J. Cybernet. 29(7), 661–688 (1998)

    MATH  Google Scholar 

  3. Peng, X.S., Wen, J.Y., Li, Z.H., Yang, G.Y., Zhou, C.K., Reid, A., Hepburn, D.M., Judd, M.D., Siew, W.H.: Rough set theory applied to pattern recognition of Partial Discharge in noise affected cable data. IEEE Trans. Dielectr. Electr. Insul. 24(1), 147–156 (2017)

    Article  Google Scholar 

  4. Zhu, W.: Generalized rough sets based on relations. Inf. Sci. 177(22), 4997–5011 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Macparthalain, N., Shen, Q.: On rough sets, their recent extensions and applications. Knowl. Eng. Rev. 25(4), 365–395 (2010)

    Article  Google Scholar 

  6. Morsi, N.N., Yakout, M.M.: Axiomatics for fuzzy rough sets. Fuzzy Sets Syst. 100(1–3), 327–342 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  7. Yeung, D.S., Chen, D.G., Tsang, E.C.C., Lee, J.W.T., Wang, X.Z.: On the generalization of fuzzy rough sets. IEEE Trans. Fuzzy Syst. 13(3), 343–361 (2005)

    Article  Google Scholar 

  8. Cornelis, C., Cock, M.D., Radzikowska, A.M.: Vaguely quantified rough sets. In: Rough Sets, Fuzzy Sets, Data Mining Granular Computing, International Conference, RSFDGrC, Toronto, Canada (2007)

  9. Bonikowski, Z., Bryniarski, E., Wybraniec-Skardowska, U.: Rough pragmatic description logic. Intell. Syst. Ref. Libr. 43, 157–184 (2013)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  11. Xu, W.H., Li, W.T.: Granular computing approach to two-way learning based on formal concept analysis in fuzzy datasets. IEEE Trans. Cybernet. 46(2), 366–379 (2016)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  13. Wang, G.Y., Feng, H.U., Huang, H., Yu, W.U.: A granular computing model based on tolerance relation. J. China Univ. Posts Telecommun. 12(3), 86–90 (2005)

    Google Scholar 

  14. Qian, Y.H., Liang, J.Y., Dang, C.Y.: Incomplete multigranulation rough set. IEEE Trans. Syst. Man Cybernet. Part A Syst. Hum. 40(2), 420–431 (2010)

    Article  Google Scholar 

  15. Qian, Y.H., Liang, J.Y., Yao, Y.Y., Dang, C.Y.: MGRS: a multi-granulation rough set. Inf. Sci. Int. J. 180(6), 949–970 (2010)

    MathSciNet  MATH  Google Scholar 

  16. Lin, G.P., Liang, J.Y., Li, J.J.: A fuzzy multigranulation decision-theoretic approach to multi-source fuzzy information systems. Knowl. Based Syst. 91, 102–113 (2016)

    Article  Google Scholar 

  17. Yu, J.H., Zhang, B., Chen, M.H., Xu, W.H.: Double-quantitative decision-theoretic approach to multigranulation approximate space. Int. J. Approx. Reason. 98, 236–258 (2018)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  19. Xu, W.H., Guo, Y.T.: Generalized multigranulation double-quantitative decision-theoretic rough set. Knowl. Based Syst. 105, 190–205 (2016)

    Article  Google Scholar 

  20. She, Y.H., He, X.L., Shi, H.X., Qian, Y.H.: A multiple-valued logic approach for multigranulation rough set model. Int. J. Approx. Reason. 82(3), 270–284 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  21. Li, Z.W., Liu, X.F., Zhang, G.Q., Xie, N.X., Wang, S.C.: A multi-granulation decision-theoretic rough set method for distributed fc -decision information systems: an application in medical diagnosis. Appl. Soft Comput. 56, 233–244 (2017)

    Article  Google Scholar 

  22. Wei, W., Liang, J.: Information fusion in rough set theory: an overview. Inf. Fusion 48, 107–118 (2019)

    Article  Google Scholar 

  23. Che, X.Y., Mi, J.S., Chen, D.G.: Information fusion and numerical characterization of a multi-source information system. Knowl. Based Syst. 145, 121–133 (2018)

    Article  Google Scholar 

  24. Guo, Y.T., Xu, W.H.: Attribute reduction in multi-source decision systems. Lect Notes. Comput Sci. 9920, 558–568 (2016). 

    Article  Google Scholar 

  25. Sang, B.B., Guo, Y.T., Shi, D.R., Xu, W.H.: Decision-theoretic rough set model of multi-source decision systems. Int. J. Mach. Learn. Cybernet. 9(1), 1–14 (2017)

    Google Scholar 

  26. Xu, W.H., Li, M.M., Wang, X.Z.: Information fusion based on information entropy in fuzzy multi-source incomplete information system. Int. J. Fuzzy Syst. 19(4), 1200–1216 (2017b)

    Article  MathSciNet  Google Scholar 

  27. Xu, W.H., Yu, J.H.: A novel approach to information fusion in multi-source datasets: a granular computing viewpoint. Inf. Sci. 378, 410–423 (2017)

    Article  Google Scholar 

  28. Li, M.M., Zhang, X.Y.: Information fusion in a multi-source incomplete information system based on information entropy. Entropy 19(11), 570–586 (2017)

    Article  Google Scholar 

  29. Huang, Y.Y., Li, T.R., Luo, C., Fujita, H., Horng, S.J.: Dynamic fusion of multi-source interval-valued data by fuzzy granulation. IEEE Trans. Fuzzy Syst. 26(6): 3403–3417 (2018)  

    Article  Google Scholar 

  30. Wu, J., Su, Y.H., Cheng, Y.W., Shao, X.Y., Chao, D., Cheng, L.: Multi-sensor information fusion for remaining useful life prediction of machining tools by adaptive network based fuzzy inference system. Appl. Soft Comput. 68, 13–23 (2018)

    Article  Google Scholar 

  31. Elmadany, N.E.D., He, Y.F., Ling, G.: Information fusion for human action recognition via biset/multiset globality locality preserving canonical correlation analysis. IEEE Trans. Image Process. 27(11), 5275–5287 (2018)

    Article  MathSciNet  Google Scholar 

  32. Xiao, G.Q., Li, K.L., Li, K.Q., Xu, Z.: Efficient top-(k, l) range query processing for uncertain data based on multicore architectures. Distrib. Parallel Databases 33(3), 381–413 (2015)

    Article  Google Scholar 

  33. Brunetti, A., Weder, B.: Investment and institutional uncertainty: a comparative study of different uncertainty measures. Weltwirtschaftliches Archiv 134(3), 513–533 (1998)

    Article  Google Scholar 

  34. Wu, D.R., Mendel, J.M.: Uncertainty measures for interval type-2 fuzzy sets. Inf. Sci. 177(23), 5378–5393 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  35. Dai, J.H., Xu, Q.: Approximations and uncertainty measures in incomplete information systems. Inf. Sci. 198(3), 62–80 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  36. Xiao, G.Q., Li, K.L., Xu, Z., Li, K.Q.: Efficient monochromatic and bichromatic probabilistic reverse top-k query processing for uncertain big data. J. Comput. Syst. Sci. 89, 92–113 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  37. Teng, S.H., Fan, L., Ma, Y.X., Mi, H., Nian, Y.J.: Uncertainty measures of rough sets based on discernibility capability in information systems. Soft Comput. 21(4), 1081–1096 (2017)

    Article  MATH  Google Scholar 

  38. Chen, Y.M., Yu, X., Ying, M., Xu, F.F.: Measures of uncertainty for neighborhood rough sets. Knowl. Based Syst. 120, 226–235 (2017)

    Article  Google Scholar 

  39. Hu, Q., Lei, Z., Chen, D., Pedrycz, W., Yu, D.: Gaussian kernel based fuzzy rough sets: model, uncertainty measures and applications. Int. J. Approx. Reason. 51(4), 453–471 (2010)

    Article  MATH  Google Scholar 

  40. Wei, C.P., Rodriguez, R.M., Martinez, L.: Uncertainty measures of extended hesitant fuzzy linguistic term sets. IEEE Trans. Fuzzy Syst. 26(3), 1763–1768 (2018)

    Article  Google Scholar 

  41. Huang, B., Guo, C.X., Li, H.X., Feng, G.F., Zhou, X.Z.: Hierarchical structures and uncertainty measures for intuitionistic fuzzy approximation space. Inf. Sci. 336, 92–114 (2016)

    Article  MATH  Google Scholar 

  42. Xiao, G .Q., Wu, F., Zhou, X., Li, K .Q.: Probabilistic top-k range query processing for uncertain databases. J. Intell. Fuzzy Syst. 31(2), 1109–1120 (2016)

    Article  MATH  Google Scholar 

  43. Xiao, G.Q., Li, K.L., Zhou, X., Li, K.Q.: Queueing analysis of continuous queries for uncertain data streams over sliding windows. Int. J. Pattern Recognit. Artif. Intell. 30(9), 1–16 (2016)

    Google Scholar 

  44. Xiao, G.Q., Li, K.L., Li, K.Q.: Reporting l most influential objects in uncertain databases based on probabilistic reverse top-k queries. Inf. Sci. 405, 207–226 (2017)

    Article  Google Scholar 

  45. Lin, G.P., Liang, J.Y., Qian, Y.H.: An information fusion approach by combining multigranulation rough sets and evidence theory. Inf. Sci. 314, 184–199 (2015)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

We would like to express our thanks to the Editor-in-Chief, handling associate editor and anonymous referees for his/her valuable comments and constructive suggestions. This paper is supported by the National Natural Science Foundation of China (Nos. 61472463, 61772002) and the Fundamental Research Funds for the Central Universities (No. XDJK2019B029).

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Authors and Affiliations

  1. School of Science, Chongqing University of Technology, Chongqing, 400054, People’s Republic of China

    Lei Yang

  2. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Xiaoyan Zhang & Weihua Xu

  3. School of Information Science and Technology, Southwest Jiaotong University, Chengdu, 611756, People’s Republic of China

    Binbin Sang

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  1. Lei Yang
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  2. Xiaoyan Zhang
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  3. Weihua Xu
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Correspondence to Xiaoyan Zhang.

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Yang, L., Zhang, X., Xu, W. et al. Multi-granulation Rough Sets and Uncertainty Measurement for Multi-source Fuzzy Information System. Int. J. Fuzzy Syst. 21, 1919–1937 (2019). https://doi.org/10.1007/s40815-019-00667-1

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