Hesitant probabilistic fuzzy set based time series forecasting method

Abstract

Uncertainties due to randomness and fuzziness coexist in the system simultaneously. Recently probabilistic fuzzy set has gained attention of researchers to handle both types of uncertainties simultaneously in a single framework. In this paper, we introduce hesitant probabilistic fuzzy sets in time series forecasting to address the issues of non-stochastic non-determinism along with both types of uncertainties and propose a hesitant probabilistic fuzzy set based time series forecasting method. We also propose an aggregation operator that uses membership grades, weights and immediate probability to aggregate hesitant probabilistic fuzzy elements to fuzzy elements. Advantages of the proposed forecasting method are that it includes both type of uncertainties and non-stochastic hesitation in a single framework and also enhance the accuracy in forecasted outputs. The proposed method has been implemented to forecast the historical enrolment student’s data at University of Alabama and share market prizes of State Bank of India (SBI) at Bombay stock exchange (BSE), India. The effectiveness of the proposed method has been examined and tested using error measures.

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References

  1. Almeida RJ, Kaymak U (2009) Probabilistic fuzzy systems in value-at-risk estimation. Intell Syst Account Finance Manag 16(1-2):49–70

    Article  Google Scholar 

  2. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    MathSciNet  MATH  Article  Google Scholar 

  3. Bas E, Egrioglu E, Yolcu U, Grosan C (2018) Type 1 fuzzy function approach based on ridge regression for forecasting. Granul Comput 3:1–9

    Article  Google Scholar 

  4. Bisht K, Kumar S (2016) Fuzzy time series forecasting method based on hesitant fuzzy sets. Expert Syst Appl 64:557–568

    Article  Google Scholar 

  5. Chen SM (1996) Forecasting enrolments based on fuzzy time series. Fuzzy Sets Syst 81(3):311–319

    MathSciNet  Article  Google Scholar 

  6. Chen MY (2014) A high-order fuzzy time series forecasting model for internet stock trading. Future Gen Comput Syst 37:461–467

    Article  Google Scholar 

  7. Chen SM, Chen CD (2011) Handling forecasting problems based on high-order fuzzy logical relationships. Expert Syst Appl 38(4):3857–3864

    Article  Google Scholar 

  8. Chen MY, Chen BT (2014) Online fuzzy time series analysis based on entropy discretization and a fast Fourier transform. Appl Soft Comput 14:156–166

    Article  Google Scholar 

  9. Chen MY, Chen BT (2015) A hybrid fuzzy time series model based on granular computing for stock price forecasting. Inf Sci 294:227–241

    MathSciNet  Article  Google Scholar 

  10. Chen SM, Hong JA (2014) Multicriteria linguistic decision making based on hesitant fuzzy linguistic term sets and the aggregation of fuzzy sets. Inf Sci 286:63–74

    Article  Google Scholar 

  11. Chen SM, Hwang JR (2000) Temperature prediction using fuzzy time series. IEEE Trans Syst Man Cybern Part B (Cybern) 30(2):263–275

    Article  Google Scholar 

  12. Chen SM, Phuong BDH (2017) Fuzzy time series forecasting based on optimal partitions of intervals and optimal weighting vectors. Knowl Based Syst 118:204–216

    Article  Google Scholar 

  13. Chen SM, Tanuwijaya K (2011) Fuzzy forecasting based on high-order fuzzy logical relationships and automatic clustering techniques. Expert Syst Appl 38(12):15425–15437

    Article  Google Scholar 

  14. Chen SM, Wang NY, Pan JS (2009) Forecasting enrollments using automatic clustering techniques and fuzzy logical relationships. Expert Syst Appl 36(8):11070–11076

    Article  Google Scholar 

  15. Cheng CH, Chang JR, Yeh CA (2006) Entropy-based and trapezoid fuzzification-based fuzzy time series approaches for forecasting IT project cost. Technol Forecast Soc Change 73(5):524–542

    Article  Google Scholar 

  16. Cheng CH, Cheng GW, Wang JW (2008) Multi-attribute fuzzy time series method based on fuzzy clustering. Expert Syst Appl 34(2):1235–1242

    Article  Google Scholar 

  17. Cheng SH, Chen SM, Jian WS (2016) Fuzzy time series forecasting based on fuzzy logical relationships and similarity measures. Inf Sci 327:272–287

    MathSciNet  MATH  Article  Google Scholar 

  18. D’Aniello G, Gaeta A, Loia V, Orciuoli F (2017) A granular computing framework for approximate reasoning in situation awareness. Granul Comput 2(3):141–158

    Article  Google Scholar 

  19. Deng W, Wang G, Zhang X, Xu J, Li G (2016) A multi-granularity combined prediction model based on fuzzy trend forecasting and particle swarm techniques. Neuro Comput 173:1671–1682

    Google Scholar 

  20. Ding J, Xu Z, Zhao N (2017) An interactive approach to probabilistic hesitant fuzzy multi-attribute group decision making with incomplete weight information. J Intell Fuzzy Syst 32(3):2523–2536

    MATH  Article  Google Scholar 

  21. Efendi R, Arbaiy N, Deris MM (2018) A new procedure in stock market forecasting based on fuzzy random auto-regression time series model. Inf Sci 441:113–132

    MathSciNet  Article  Google Scholar 

  22. Fialho AS, Vieira SM, Kaymak U, Almeida RJ, Cismondi F, Reti SR, … Sousa JM (2016) Mortality prediction of septic shock patients using probabilistic fuzzy systems. Appl Soft Comput 42:194–203

    Article  Google Scholar 

  23. Gangwar SS, Kumar S (2014) Probabilistic and intuitionistic fuzzy sets-based method for fuzzy time series forecasting. Cybern Syst 45(4):349–361

    MATH  Article  Google Scholar 

  24. Hinojosa WM, Nefti S, Kaymak U (2011) Systems control with generalized probabilistic fuzzy-reinforcement learning. IEEE Trans Fuzzy Syst 19(1):51–64

    Article  Google Scholar 

  25. Huang WJ, Zhang G, Li HX (2012) A novel probabilistic fuzzy set for uncertainties-based integration inference. In: IEEE international conference on computational intelligence for measurement systems and applications (CIMSA). IEEE, New York, pp 58–62

  26. Huarng K (2001) Effective lengths of intervals to improve forecasting in fuzzy time series. Fuzzy Sets Syst 123(3):387–394

    MathSciNet  MATH  Article  Google Scholar 

  27. Huarng K, Yu THK (2006) Ratio-based lengths of intervals to improve fuzzy time series forecasting. IEEE Trans Syst Man Cybern Part B (Cybern) 36(2):328–340

    Article  Google Scholar 

  28. Joshi BP, Kumar S (2012a) Intuitionistic fuzzy sets based method for fuzzy time series forecasting. Cybern Syst 43(1):34–47

    MATH  Article  Google Scholar 

  29. Joshi BP, Kumar S (2012b) Fuzzy time series model based on intuitionistic fuzzy sets for empirical research in stock market. Int J Appl Evolut Comput 3(4):71–84

    Article  Google Scholar 

  30. Joshi DK, Kumar S (2018a) Trapezium cloud TOPSIS method with interval-valued intuitionistic hesitant fuzzy linguistic information. Granul Comput 20:1–14

    Google Scholar 

  31. Joshi DK, Kumar S (2018b) Entropy of interval-valued intuitionistic hesitant fuzzy set and its application to group decision making problems. Granul Comput 2:1–15

    Google Scholar 

  32. Joshi DK, Beg I, Kumar S (2018) Hesitant probabilistic fuzzy linguistic sets with applications in multi-criteria group decision making problems. Mathematics 6(4):47

    MATH  Article  Google Scholar 

  33. Kocak C (2017) ARMA (p, q) type high order fuzzy time series forecast method based on fuzzy logic relations. Appl Soft Comput 58:92–103

    Article  Google Scholar 

  34. Kumar S, Gangwar SS (2015) A fuzzy time series forecasting method induced by intuitionistic fuzzy sets. Int J Model Simul Sci Comput 6(4):1550041

    Article  Google Scholar 

  35. Kumar S, Gangwar SS (2016) Intuitionistic fuzzy time series: an approach for handling non-determinism in time series forecasting. IEEE Trans Fuzzy Syst 24(6):1270–1281

    Article  Google Scholar 

  36. Lee LW, Chen SM (2015a) Fuzzy decision making based on likelihood-based comparison relations of hesitant fuzzy linguistic term sets and hesitant fuzzy linguistic operators. Inf Sci 294:513–529

    MathSciNet  MATH  Article  Google Scholar 

  37. Lee LW, Chen SM (2015b) Fuzzy decision making and fuzzy group decision making based on likelihood-based comparison relations of hesitant fuzzy linguistic term sets 1. J Intell Fuzzy Syst 29(3):1119–1137

    MathSciNet  MATH  Article  Google Scholar 

  38. Lee HS, Chou MT (2004) Fuzzy forecasting based on fuzzy time series. Int J Comput Math 81(7):781–789

    MathSciNet  MATH  Article  Google Scholar 

  39. Li Y, Huang W (2012) A probabilistic fuzzy set for uncertainties-based modeling in logistics manipulator system. J Theor Appl Inf Technol 46(2):977–982

    MathSciNet  Google Scholar 

  40. Li J, Wang JQ (2017) Multi-criteria outranking methods with hesitant probabilistic fuzzy sets. Cognit Comput 9(5):611–625

    Article  Google Scholar 

  41. Liu HT (2007) An improved fuzzy time series forecasting method using trapezoidal fuzzy numbers. Fuzzy Optim Decis Mak 6(1):63–80

    MathSciNet  MATH  Article  Google Scholar 

  42. Liu H, Cocea M (2017) Granular computing-based approach for classification towards reduction of bias in ensemble learning. Granul Comput 2(3):131–139

    Article  Google Scholar 

  43. Liu Z, Li HX (2005) A probabilistic fuzzy logic system for modeling and control. IEEE Trans Fuzzy Syst 13(6):848–859

    Article  Google Scholar 

  44. Livi L, Sadeghian A (2016) Granular computing, computational intelligence, and the analysis of non-geometric input spaces. Granul Comput 1(1):13–20

    Article  Google Scholar 

  45. Maciel L, Ballini R, Gomide F (2016) Evolving granular analytics for interval time series forecasting. Granul Comput 1(4):213–224

    Article  Google Scholar 

  46. Meghdadi AH, Akbarzadeh-T MR (2001) Probabilistic fuzzy logic and probabilistic fuzzy systems. In: 10th IEEE international conference on fuzzy systems, vol 3, pp 1127–1130. IEEE, New York

  47. Pathak HK, Singh P (2011) A new bandwidth interval based forecasting method for enrolments using fuzzy time series. Appl Math 2(4):504

    Article  Google Scholar 

  48. Pedrycz W, Chen SM (2011) Granular computing and intelligent systems: design with information granules of higher order and higher type. Springer, Heidelberg

    Google Scholar 

  49. Pedrycz W, Chen SM (2015a) Granular computing and decision-making: interactive and iterative approaches. Springer, Heidelberg

    Google Scholar 

  50. Pedrycz W, Chen SM (2015b) Information granularity, big data, and computational intelligence. Springer, Heidelberg

    Google Scholar 

  51. Qiu W, Liu X, Li H (2011) A generalized method for forecasting based on fuzzy time series. Expert Syst Appl 38(8):10446–10453

    Article  Google Scholar 

  52. Song Q (2003) A note on fuzzy time series model selection with sample autocorrelation functions. Cybern Syst 34(2):93–107

    MATH  Article  Google Scholar 

  53. Song Q, Chissom BS (1993a) Fuzzy time series and its models. Fuzzy Sets Syst 54(3):269–277

    MathSciNet  MATH  Article  Google Scholar 

  54. Song Q, Chissom BS (1993b) Forecasting enrolments with fuzzy time series—part I. Fuzzy Sets Syst 54(1):1–9

    Article  Google Scholar 

  55. Song Q, Chissom BS (1994) Forecasting enrolments with fuzzy time series—part II. Fuzzy Sets Syst 62(1):1–8

    Article  Google Scholar 

  56. Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539

    MATH  Google Scholar 

  57. Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision. In: 2009 IEEE international conference on fuzzy system, FUZZ-IEEE 2009, pp 1378–1382. IEEE, New York

  58. Wang W, Mishra KK (2018) A novel stock trading prediction and recommendation system. Multimed Tools Appl 77(4):4203–4215

    Article  Google Scholar 

  59. Wang YN, Lei Y, Fan X, Wang Y (2016) Intuitionistic fuzzy time series forecasting model based on intuitionistic fuzzy reasoning. Math Prob Eng 2016:1–12

    MathSciNet  MATH  Google Scholar 

  60. Wilke G, Portmann E (2016) Granular computing as a basis of human–data interaction: a cognitive cities use case. Granul Comput 1(3):181–197

    Article  Google Scholar 

  61. Xu Z, Zhou W (2017) Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment. Fuzzy Optim Decis Mak 16(4):481–503

    MathSciNet  MATH  Article  Google Scholar 

  62. Yager RR, Engemann KJ, Filev DP (1995) On the concept of immediate probabilities. Int J Intell Syst 10(4):373–397

    MATH  Article  Google Scholar 

  63. Ye F, Zhang L, Zhang D, Fujita H, Gong Z (2016) A novel forecasting method based on multi-order fuzzy time series and technical analysis. Inf Sci 367:41–57

    Article  Google Scholar 

  64. Yolcu U, Egrioglu E, Uslu VR, Basaran MA, Aladag CH (2009) A new approach for determining the length of intervals for fuzzy time series. Appl Soft Comput 9(2):647–651

    MATH  Article  Google Scholar 

  65. Yolcu OC, Yolcu U, Egrioglu E, Aladag CH (2016) High order fuzzy time series forecasting method based on an intersection operation. Appl Math Model 40(19–20):8750–8765

    MathSciNet  MATH  Article  Google Scholar 

  66. Zadeh LA (1965) Fuzzy sets. Inf control 8(3):338–353

    MATH  Article  Google Scholar 

  67. Zhou W, Xu Z (2017) Group consistency and group decision making under uncertain probabilistic hesitant fuzzy preference environment. Inf Sci 414:276–288

    Article  Google Scholar 

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Correspondence to Sanjay Kumar.

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Gupta, K.K., Kumar, S. Hesitant probabilistic fuzzy set based time series forecasting method. Granul. Comput. 4, 739–758 (2019). https://doi.org/10.1007/s41066-018-0126-1

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Keywords

  • Probabilistic and non-probabilistic uncertainties
  • Hesitant probabilistic fuzzy set
  • Fuzzy time series forecasting
  • Immediate probability