Uncertain Fuzzy Time Series: Technical and Mathematical Review

Subject Areas : Journal of Computer & Robotics

Aref  Safari ¹ (Department of Computer Engineering, Islamic Azad University, Shahr-e-Qods Branch, Iran, Tehran)

Received: 2020-08-20 Accepted : 2021-04-19 Published : 2020-06-01

Keywords: fuzzy logic, Time-Series, Type-2 Fuzzy Time Series,

Abstract :

Time series consists of a sequence of observations, measured at moments in time, sorted chronologically, and evenly spaced from each other, so the data are usually dependent on each other. Uncertainty is the consequence of imperfection of knowledge about a state or a process. The time series is an important class of time-based data objects and it can be easily obtained from scientific and financial applications. Main carrier of time series forecasting is which constitutes the level of uncertainty human knowledge, with its intrinsic ambiguity and vagueness in complex and non-stationary criteria. In this study, a comprehensive revision on the existing time series pattern analysis research is given. They are generally categorized into representation and indexing, similarity measure, uncertainty modeling, visualization and mining. Various Fuzzy Time Series (FTS) models have been proposed in scientific literature during the past decades or so. Among the most accurate FTS models found in literature are the high order models. However, three fundamental issues need to be resolved with regards to the high order models. The primary objective of this paper is to serve as a glossary for interested researchers to have an overall depiction on the current time series prediction and fuzzy time-series models development.

References:

[1] Song Q, Chissom B S, Forecasting enrollments with
fuzzy time series-part I, Fuzzy sets and systems,
Vol.54, No.1, 1-9, 1993.
[2] Song Q, Chissom B S, Fuzzy time series and its
models, Fuzzy sets and systems, Vol.54, No.3, 269-
277, 1993.
[3] Song Q, Chissom B S, Forecasting enrollments with
fuzzy time series-part II, Fuzzy sets and systems,
Vol.62, No.1, 1- 8, 1994.
[4] Chen S M, Forecasting enrollments based on fuzzy
time series, Fuzzy sets and systems, Vol.81, No.3,
311-319, 1996.
[5] Huarng K, Effective lengths of intervals to improve
forecasting in fuzzy time series, Fuzzy sets and
systems, Vol.123, No.3, 387-394, 2017.
[6] Kuo I H, Horng S J, Kao TW, et al, An improved
method for forecasting enrollments based on fuzzy
time series and particle swarm optimization, Expert
Systems with Applications, Vol.36, No.3, 6108-6117,
2017.
[7] Kuo I H, Horng S J, Chen Y H, et al, Forecasting
TAIFEX based on fuzzy time series and particle
swarm optimization, Expert Systems with
Applications, Vol.37, No.2, 1494-1502, 2020.
[8] Chen S M, Chung N Y, forecasting enrollments using
high order fuzzy time series and genetic algorithms,
International Journal of Intelligent Systems, Vol.21,
No.5, 485-501, 2016.
[9] Wang L, Liu X, PedryczW, Effective intervals
determined by information granules to improve
forecasting in fuzzy time series, Expert Systems with
Applications, Vol.40, No.14, 5673- 5679, 2013.
[10] LuW, Chen X, PedryczW, Liu X, Yang J. Using
interval information granules to improve forecasting in
fuzzy time series, International Journal of
Approximate Reasoning, Vol.57, 1-18, 2019.
[11] Wang L, Liu X, Pedrycz W, et al, Determination of
temporal information granules to improve forecasting
in fuzzy time series,Expert Systems with Applications,
Vol.41, No.6, 3134-3142, 2019.
[12] Huarng K, Yu H K, A type 2 fuzzy time series model
for stock index forecasting, Physica A: Statistical
Mechanics and its Applications, Vol.353, 445-462,
2015.
[13] Bajestani N S, Zare A, Application of optimized type
2 fuzzy time series to forecast Taiwan stock index, In
2009 2nd International Conference on Computer,
Control and Communication, 2018.
[14] Bajestani N S, Zare A, Forecasting TAIEX using
improved type 2 fuzzy time series, Expert Systems
with Applications, Vol.38, No.5, 5816-5821, 2011.
[15] Singh P, Borah B, Forecasting stock index price based
on Mfactors fuzzy time series and particle swarm
optimization, International Journal of Approximate
Reasoning, Vol.55, No.3, 2014.
[16] Aref Safari, Danial Barazandeh, Seyed Ali Khalegh
Pour. A Novel Fuzzy-C Means Image Segmentation
Model for MRI Brain Tumor Diagnosis. J. ADV
COMP ENG TECHNOL, 6(1) Winter 2020 : 19-2
[17] J. Kennedy, R. Eberhart and Y. Shi, Swarm
intelligence, ISBN: 1-55860-595-9, Morgan Kaufman,
2001. [48] Q. Song and B.S. Chissom, Fuzzy time
series and its models, Fuzzy Sets and Systems 54
[18] S.N. Sivanandam, S. Sumathi and S.N. Deepa,
Introduction to fuzzy logic using MATHLAB, ISBN:
103-540-35780-7, Springer-Verlag, 2007.
[19] A. Safari, R. Hosseini, M. Mazinani, A Novel Type-2
Adaptive Neuro Fuzzy Inference System Classifier for
Modelling Uncertainty in Prediction of Air Pollution
Disaster, IJE Transactions B: Applications, Vol 30,
No. 11, Pages 1746-1751, (2017).
[20] J.C. Dunn, A fuzzy relative of the ISODATA process
and its use in detecting compact well-separated
clusters, J. Cybernet. 3 (2019) 32–57.
[21] X. Golay, S. Kollias, G. Stoll, D. Meier, A. Valavanis,
P. Boesiger, A new correlation-based fuzzy logic
clustering algorithm for fMRI, Mag. Resonance Med.
40 (2018) 249–260.
[22] C.S. Muller-Levet, F. Klawonn, K.-H. Cho, O.
Wolkenhauer, Fuzzy clustering of short time series
and unevenly distributed sampling points, Proceedings
of the 5th International Symposium on Intelligent Data
Analysis, Berlin, Germany, August 28–30, 2018.

[23] M. Kumar, N.R. Patel, J. Woo, Clustering seasonality
patterns in the presence of errors, Proceedings of KDD
’02, Edmonton, Alberta, Canada.
[24] Y. Kakizawa, R.H. Shumway, N. Taniguchi,
Discrimination and clustering for multivariate time
series, J. Amer. Stat. Assoc. 93 (441) (2018) 328–340.
[25] R. Dahlhaus, On the Kullback–Leibler information
divergence of locally stationary processes, Stochastic
Process. Appl. 62 (2019) 139–168.
[26] R.H. Shumway, Time–frequency clustering and
discriminant analysis, Stat. Probab. Lett. 63 (2013)
307–314.
[27] J.C. Bezdek, N.R. Pal, Some new indexes of cluster
validity, IEEE Trans. Syst. Man Cybernet. B:
Cybernet. 28 (3) (2018) 301–315.
[28] C H López-Caraballo1, I Salfate1, J A Lazzús1, P
Rojas1, M Rivera1 and L Palma-Chilla1, Mackey-
Glass noisy chaotic time series prediction by a swarmoptimized
neural network, Journal of Physics:
Conference Series, Volume 720, XIX Chilean Physics
Symposium 201426–28 November, (2014)
Concepción, Chile
[29] P. C. de Lima Silva, H. J. Sadaei, R. Ballini and F. G.
Guimarães, "Probabilistic Forecasting With Fuzzy
Time Series," in IEEE Transactions on Fuzzy
Systems, vol. 28, no. 8, pp. 1771-1784, Aug (2020).
[30] Mackey, Michael C., and Leon Glass. "Oscillation
and chaos in physiological control systems." Science
197.4300 (1977): 287-289.