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FR–KDE: A Hybrid Fuzzy Rule-Based Information Fusion Method with its Application in Biomedical Classification

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Abstract

Granular computing (GrC) is an essential tool to solve human real problem since the information granules is close to human perception schemes. In GrC, both classification accuracy and interpretability play significant roles. Fuzzy rule (FR) based classification systems are effective methods solving this problem. However, the accuracy of FR may be decreased when solving some complex application. In this paper, a novel model called FR–KDE integrating the FR and kernel density estimation (KDE) in the framework of Dempster–Shafer evidence theory is proposed to deal with the classification problem. By fusing the result of FR and KDE via the Dempster’s combination rule, it can reduce the uncertainty of FR and obtain better accuracy. To illustrate the effect of the FR–KDE approach, it is applied to the medical data classification problem. Experimentally, the results demonstrate that the FR–KDE method is effective in handling biomedical data classification problems.

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References

  1. Fujita, H., Gaeta, A., Loia, V., Orciuoli, F.: Resilience analysis of critical infrastructures: a cognitive approach based on granular computing. IEEE Trans. Cybern. (2018). https://doi.org/10.1109/TCYB.2018.2815178

    Article  Google Scholar 

  2. Pedrycz, W., Al-Hmouz, R., Balamash, A.S., Morfeq, A.: Modeling with linguistic entities and linguistic descriptors: a perspective of granular computing. Soft Comput. 21(7), 1833–1845 (2017)

    Article  MATH  Google Scholar 

  3. Pedrycz, W.: Granular bidirectional and multidirectional associative memories: Towards a collaborative buildup of granular mappings. J. Inform. Process. Syst. 13(3), 435–447 (2017)

    Google Scholar 

  4. Sun, C., Li, S., Deng, Y.: Determining weights in multi-criteria decision making based on negation of probability distribution under uncertain environment. Mathematics 8(2), 191 (2020)

    Article  MathSciNet  Google Scholar 

  5. Zhou, M., Liu, X.B., Chen, Y.W., Qian, X.F., Yang, J.B., Wu, J.: Assignment of attribute weights with belief distributions for MADM under uncertainties. Knowledge Based Syst. 189, 105110 (2020)

    Article  Google Scholar 

  6. Song, Y., Fu, Q., Wang, Y.F., Wang, X.: Divergence-based cross entropy and uncertainty measures of Atanassov’s intuitionistic fuzzy sets with their application in decision making. Appl. Soft Comput. 84, 105703 (2019)

    Article  Google Scholar 

  7. Li, Y., Garg, H., Deng, Y.: A new uncertainty measure of discrete Z-numbers. Int. J. Fuzzy Syst. 22(3), 760–776 (2020)

    Article  MathSciNet  Google Scholar 

  8. Pan, Y., Zhang, L., Li, Z., Ding, L.: Improved fuzzy Bayesian network-based risk analysis with interval-valued fuzzy sets and D-S evidence theory. IEEE Transactions on Fuzzy Systems p (2019). https://doi.org/10.1109/TFUZZ.2019.2929024

  9. Yang, J., Li, S., Xu, Z., Liu, H., Yao, W.: An understandable way to extend the ordinary linear order on real numbers to a linear order on interval numbers. In: IEEE Transactions on Fuzzy Systems p (2020). https://doi.org/10.1109/TFUZZ.2020.3006557

  10. Zhou, M., Liu, X., Yang, J.: Evidential reasoning approach for MADM based on incomplete interval value. J. Intell. Fuzzy Syst. 33(6), 3707–3721 (2017)

    Article  Google Scholar 

  11. Xue, Y., Deng, Y.: Refined expected value decision rules under orthopair fuzzy environment. Mathematics 8(3), 442 (2020)

    Article  Google Scholar 

  12. Yager, R.R.: Interval valued entropies for Dempster-Shafer structures. Knowledge Based Syst. 161, 390–397 (2018)

    Article  Google Scholar 

  13. Fujita, H., Gaeta, A., Loia, V., Orciuoli, F.: Improving awareness in early stages of security analysis: a zone partition method based on GrC. Appl. Intell. 49, 1063–1077 (2018)

    Article  Google Scholar 

  14. Pedrycz, W., Wang, X.: Designing fuzzy sets with the use of the parametric principle of justifiable granularity. IEEE Trans. Fuzzy Syst. 24(2), 489–496 (2016)

    Article  Google Scholar 

  15. Liao, H., Mi, X., Xu, Z.: A survey of decision-making methods with probabilistic linguistic information: Bibliometrics, preliminaries, methodologies, applications and future directions. Fuzzy Optimiz. Decis. Mak. (2019). https://doi.org/10.1007/s10700-019-09309-5

    Article  MATH  Google Scholar 

  16. Fernández, A., Altalhi, A., Alshomrani, S., Herrera, F.: Why linguistic fuzzy rule based classification systems perform well in big data applications? Int. J. Comput. Intell. Syst. 10(1), 1211–1225 (2017)

    Article  Google Scholar 

  17. Pelusi, D., Mascella, R., Tallini, L., Nayak, J., Naik, B., Abraham, A.: Neural network and fuzzy system for the tuning of gravitational search algorithm parameters. Exp. Syst. Appl. 102, 234–244 (2018)

    Article  Google Scholar 

  18. Jiang, W., Zhang, Z., Deng, X.: A novel failure mode and effects analysis method based on fuzzy evidential reasoning rules. IEEE Access 7, 113605–113615 (2019)

    Article  Google Scholar 

  19. Morente-Molinera, J., Wu, X., Morfeq, A., Al-Hmouz, R., Herrera-Viedma, E.: A novel multi-criteria group decision-making method for heterogeneous and dynamic contexts using multi-granular fuzzy linguistic modelling and consensus measures. Inform. Fusion 53, 240–250 (2020)

    Article  Google Scholar 

  20. Liu, P., Zhang, X.: A new hesitant fuzzy linguistic approach for multiple attribute decision making based on Dempster-Shafer evidence theory. Appl. Soft Comput. 86, 105897 (2020)

    Article  Google Scholar 

  21. Xiao, F., Zhang, Z., Abawajy, J.: Workflow scheduling in distributed systems under fuzzy environment. J. Intell. Fuzzy Syst. 37(4), 5323–5333 (2019)

    Article  Google Scholar 

  22. Fei, L., Feng, Y., Liu, L.: On Pythagorean fuzzy decision making using soft likelihood functions. Int. J. Intell. Syst. 34(12), 3317–3335 (2019)

    Article  Google Scholar 

  23. Cl, Fan, Song, Y., Fu, Q., Lei, L., Wang, X.: New operators for aggregating intuitionistic fuzzy information with their application in decision making. IEEE Access 6, 27214–27238 (2018)

    Article  Google Scholar 

  24. Fei, L., Deng, Y.: Multi-criteria decision making in Pythagorean fuzzy environment. Appl. Intell. 50(2), 537–561 (2020)

    Article  Google Scholar 

  25. Garg, H., Rani, D.: Novel exponential divergence measure of complex intuitionistic fuzzy sets with an application to decision-making process. Scientia Iranica (2019). https://doi.org/10.24200/sci.2019.53194.3103

    Article  Google Scholar 

  26. Liao, H., Wu, X.: DNMA: A double normalization-based multiple aggregation method for multi-expert multi-criteria decision making. Omega (2019). https://doi.org/10.1016/j.omega.2019.04.001

    Article  Google Scholar 

  27. Xiao, F.: EFMCDM: Evidential fuzzy multicriteria decision making based on belief entropy. IEEE Trans. Fuzzy Syst. 28(7), 1477–1491 (2020)

    Google Scholar 

  28. Yager, R.R.: Generalized Dempster-Shafer Structures. IEEE Trans. Fuzzy Syst. 27(3), 428–435 (2019)

    Article  MathSciNet  Google Scholar 

  29. Fei, L., Feng, Y., Liu, L.: Evidence combination using OWA-based soft likelihood functions. Int. J. Intell. Syst. 34(9), 2269–2290 (2019)

    Article  Google Scholar 

  30. Fu, C., Xu, D.L., Xue, M.: Determining attribute weights for multiple attribute decision analysis with discriminating power in belief distributions. Knowledge Based Syst. 143, 127–141 (2018)

    Article  Google Scholar 

  31. Liu, Q., Tian, Y., Kang, B.: Derive knowledge of Z-number from the perspective of Dempster-Shafer evidence theory. Eng. Appl. Artif. Intell. 85, 754–764 (2019)

    Article  Google Scholar 

  32. Jiang, W., Cao, Y., Deng, X.: A novel Z-network model based on Bayesian network and Z-number. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2918999

    Article  Google Scholar 

  33. Kang, B., Zhang, P., Gao, Z., Chhipi-Shrestha, G., Hewage, K., Sadiq, R.: Environmental assessment under uncertainty using Dempster-Shafer theory and Z-numbers. J. Ambient Intell. Human. Comput. (2019). https://doi.org/10.1007/s12652-019-01228-y

    Article  Google Scholar 

  34. Kang, B., Deng, Y.: The maximum Deng entropy. IEEE Access 7(1), 120758–120765 (2019)

    Article  Google Scholar 

  35. Cao, Z., Ding, W., Wang, Y.K., Hussain, F.K., Al-Jumaily, A., Lin, C.T.: Effects of repetitive SSVEPs on EEG complexity using multiscale inherent fuzzy entropy. Neurocomputing 389, 198–206 (2019)

    Article  Google Scholar 

  36. Gao, X., Deng, Y.: The pseudo-pascal triangle of maximum Deng entropy. Int. J. Comput. Commun. Contr. 15(1), 1006 (2020)

    Google Scholar 

  37. Xiao, F.: GIQ: A generalized intelligent quality-based approach for fusing multi-source information. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.2991296

    Article  Google Scholar 

  38. Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. The annals of mathematical statistics pp 325–339, (1967)

  39. Shafer, G.: A mathematical theory of evidence, vol. 42. Princeton University Press, Princeton (1976)

    Book  MATH  Google Scholar 

  40. Qin, B., Xiao, F.: A non-parametric method to determine basic probability assignment based on Kernel Density Estimation. IEEE Access 6, 73509–73519 (2018)

    Article  Google Scholar 

  41. Song, Y., Deng, Y.: Divergence measure of belief function and its application in data fusion. IEEE Access 7(1), 107465–107472 (2019)

    Article  Google Scholar 

  42. Xiao, F.: Evidence combination based on prospect theory for multi-sensor data fusion. ISA Trans. (2020). https://doi.org/10.1016/j.isatra.2020.06.024

    Article  Google Scholar 

  43. Xiao, F., Cao, Z., Jolfaei, A.: A novel conflict measurement in decision making and its application in fault diagnosis. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.3002431

    Article  Google Scholar 

  44. Cao, Z., Chuang, C.H., King, J.K., Lin, C.T.: Multi-channel EEG recordings during a sustained-attention driving task. Scientific Data (2019). https://doi.org/10.1038/s41597-019-0027-4

    Article  Google Scholar 

  45. Meng, D., Liu, M., Yang, S., Zhang, H., Ding, R.: A fluid-structure analysis approach and its application in the uncertainty-based multidisciplinary design and optimization for blades. Adv. Mech. Eng. 10(6), 1687814018783410 (2018)

    Article  Google Scholar 

  46. Deng, Y.: Uncertainty measure in evidence theory. Sci. China Inform. Sci. (2021). https://doi.org/10.1007/s11432-020-3006-9

    Article  Google Scholar 

  47. Alcantud, J.C., Feng, F., Yager, R.: An N-soft set approach to rough sets. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2946526

    Article  Google Scholar 

  48. Fei, L., Lu, J., Feng, Y.: An extended best-worst multi-criteria decision-making method by belief functions and its applications in hospital service evaluation. Comput. Industr. Eng. 142, 106355 (2020)

    Article  Google Scholar 

  49. Garg, H., Rani, D.: Multi-criteria decision making method based on bonferroni mean aggregation operators of complex intuitionistic fuzzy numbers. J. Industr. Manag. Optimiz. (2020). https://doi.org/10.3934/jimo.2020069

    Article  Google Scholar 

  50. Song, Y., Wang, X., Zhu, J., Lei, L.: Sensor dynamic reliability evaluation based on evidence theory and intuitionistic fuzzy sets. Appl. Intell. pp 1–13, (2018)

  51. Li, Y.F., Huang, H.Z., Mi, J., Peng, W., Han, X.: Reliability analysis of multi-state systems with common cause failures based on bayesian network and fuzzy probability. Ann. Oper. Res. (2019)

  52. Xu, X., Li, S., Song, X., Wen, C., Xu, D.: The optimal design of industrial alarm systems based on evidence theory. Control Eng. Pract. 46, 142–156 (2016)

    Article  Google Scholar 

  53. Xu, X., Xu, H., Wen, C., Li, J., Hou, P., Zhang, J.: A belief rule-based evidence updating method for industrial alarm system design. Control Eng. Pract. 81, 73–84 (2018)

    Article  Google Scholar 

  54. Zhang, H., Deng, Y.: Weighted belief function of sensor data fusion in engine fault diagnosis. Soft Comput. 24(3), 2329–2339 (2020)

    Article  MathSciNet  Google Scholar 

  55. Cao, X., Deng, Y.: A new geometric mean FMEA method based on information quality. IEEE Access 7(1), 95547–95554 (2019)

    Article  Google Scholar 

  56. Pan, L., Deng, Y.: An association coefficient of belief function and its application in target recognition system. Int. J. Intell. Syst. 35, 85–104 (2020)

    Article  Google Scholar 

  57. Fu, C., Hou, B., Chang, W., Feng, N., Yang, S.: Comparison of evidential reasoning algorithm with linear combination in decision making. Int. J. Fuzzy Syst. 22(2), 686–711 (2020)

    Article  Google Scholar 

  58. Liu, Z.G., Pan, Q., Dezert, J., Martin, A.: Combination of classifiers with optimal weight based on evidential reasoning. IEEE Trans. Fuzzy Syst. 26(3), 1217–1230 (2018)

    Article  Google Scholar 

  59. Cl, Fan, Song, Y., Lei, L., Wang, X., Bai, S.: Evidence reasoning for temporal uncertain information based on relative reliability evaluation. Exp. Syst. Appl. 113, 264–276 (2018)

    Article  Google Scholar 

  60. Zhou, M., Liu, X.B., Chen, Y.W., Yang, J.B.: Evidential reasoning rule for MADM with both weights and reliabilities in group decision making. Knowledge Based Syst. 143, 142–161 (2018)

    Article  Google Scholar 

  61. Deng, X., Jiang, W.: Evaluating green supply chain management practices under fuzzy environment: a novel method based on D number theory. Int. J. Fuzzy Syst. 21(5), 1389–1402 (2019)

    Article  Google Scholar 

  62. Liu, B., Deng, Y.: Risk evaluation in failure mode and effects analysis based on D numbers theory. Int. J. Comput. Commun. Contr. 14(5), 672–691 (2019)

    Article  Google Scholar 

  63. Deng, X., Jiang, W.: A total uncertainty measure for D numbers based on belief intervals. Int. J. Intell. Syst. 34(12), 3302–3316 (2019)

    Article  Google Scholar 

  64. Xiao, F.: Generalization of Dempster-Shafer theory: A complex mass function. Appl. Intell. 50(10), 3266–3275 (2019) 

    Article  Google Scholar 

  65. Xiao, F.: Generalized belief function in complex evidence theory. J. Intell. Fuzzy Syst. 38(4), 3665–3673 (2020)

    Article  Google Scholar 

  66. Liu, Z., Zhang, X., Niu, J., Dezert, J.: Combination of classifiers with different frames of discernment based on belief functions. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.2985332

    Article  Google Scholar 

  67. Fu, C., Chang, W., Yang, S.: Multiple criteria group decision making based on group satisfaction. Informat. Sci. 518, 309–329 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  68. Luo, Z., Deng, Y.: A matrix method of basic belief assignment’s negation in Dempster-Shafer theory. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2930027

    Article  Google Scholar 

  69. Deng, X., Jiang, W.: On the negation of a Dempster-Shafer belief structure based on maximum uncertainty allocation. Inform. Sci. 516, 346–352 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  70. Li, D., Deng, Y., Gao, X.: A generalized expression for information quality of basic probability assignment. IEEE Access 7(1), 174734–174739 (2019)

    Article  Google Scholar 

  71. Xiao, F.: CED: A distance for complex mass functions. IEEE Trans. Neural Netw. Learn. Syst. (2020). https://doi.org/10.1109/TNNLS.2020.2984918

    Article  Google Scholar 

  72. Smets, P.: Constructing the pignistic probability function in a context of uncertainty. Mach. Intell. Patt. Recogn. 10, 29–40 (1989)

    Google Scholar 

  73. Fang, R., Liao, H., Yang, J.B., Xu, D.L.: Generalised probabilistic linguistic evidential reasoning approach for multi-criteria decision-making under uncertainty. J. Oper. Res. Soc. (2019). https://doi.org/10.1080/01605682.2019.1654415

    Article  Google Scholar 

  74. Wu, X., Liao, H.: A consensus-based probabilistic linguistic gained and lost dominance score method. Eur. J. Oper. Res. 272(3), 1017–1027 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  75. Ishibuchi, H., Yamamoto, T., Nakashima, T.: Hybridization of fuzzy gbml approaches for pattern classification problems. IEEE Trans. Syst. Man Cybern. B 35(2), 359–365 (2005)

    Article  Google Scholar 

  76. Xiao, F.: A distance measure for intuitionistic fuzzy sets and its application to pattern classification problems. IEEE Trans. Syst. Man Cybern. (2019). https://doi.org/10.1109/TSMC.2019.2958635

    Article  Google Scholar 

  77. Jiang, W., Huang, K., Geng, J., Deng, X.: Multi-scale metric learning for few-shot learning. IEEE Trans Circ. Syst. Video Technol. (2020). https://doi.org/10.1109/TCSVT.2020.2995754

    Article  Google Scholar 

  78. Liu, Z., Liu, Y., Dezert, J., Cuzzolin, F.: Evidence combination based on credal belief redistribution for pattern classification. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2911915

    Article  Google Scholar 

  79. Xu, X., Zheng, J., Yang Jb, Xu, Dl, Chen Yw: Data classification using evidence reasoning rule. Knowledge Based Syst. 116, 144–151 (2017)

    Article  Google Scholar 

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Acknowledgements

The authors greatly appreciate the reviewers suggestions and the editor encouragement. This research is funded by the Research Project of Education and Teaching Reform in Southwest University (No. 2019JY053), Fundamental Research Funds for the Central Universities (No. XDJK2019C085) and Chongqing Overseas Scholars Innovation Program (No. cx2018077).

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Correspondence to Fuyuan Xiao.

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Song, X., Qin, B. & Xiao, F. FR–KDE: A Hybrid Fuzzy Rule-Based Information Fusion Method with its Application in Biomedical Classification. Int. J. Fuzzy Syst. 23, 392–404 (2021). https://doi.org/10.1007/s40815-020-00957-z

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