Skip to main content
SpringerLink
Log in

A novel multivariate fuzzy time series based forecasting algorithm incorporating the effect of clustering on prediction

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Forecasting has often played predominant roles in daily life as necessary measures can be taken to bypass the undesired and detrimental future prompted by this fact, the issue of forecasting becomes one of the most important topics of research for the modern scientists and as a result several innovative forecasting techniques have been developed. Amongst various well-known forecasting techniques, fuzzy time series-based methods are successfully used, though they are suffering from some serious drawbacks, viz., fixed sized intervals, using some fixed membership values (0, 0.5, and 1) and moreover, the defuzzification process only deals with the factor that is to be predicted. Additionally, most of the existing and widely used fuzzy time series-based forecasting algorithms employ their own clustering techniques that may be data-dependent and in turn the predictive accuracy decrease. Prompted by the fact, the present author developed a novel multivariate fuzzy forecasting algorithm that is able to remove all the drawbacks as also can predict the future occurrences with better predictive accuracy. Moreover, the comparisons with the thirteen other existing frequently used forecasting algorithms (viz., conventional, fuzzy time series-based algorithms and ANN) were performed to demonstrate its better efficiency and predictive accuracy. Towards the end, the applicability and predictive accuracy of the developed algorithm has been demonstrated using three different data sets collected from three different domains, such as: oil agglomeration process (coal washing technique), frequently occurred web error prediction and the financial forecasting. The real dataset related to oil agglomeration was collected from CIMFER, Dhanbad, India, that regarding the frequently occurred web error codes of www.ismdhanbad.ac.in, the official website of ISM Dhanbad, was collected from the Indian School of Mines (ISM) Dhanbad, India server and the finance data set was collected from the Ministry of Statistical and Program Implementation (Govt. of India).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Abbreviations

\(\mathrm{Z}^{+}\) :

The set of positive integers

\(cl(r)({r\in \text{ Z }^+})\) :

Cluster \(r\) generated by the chosen clustering algorithm

\(a_i ({i\in \text{ Z }^+})\) :

The \(i\)th \(({i\in \text{ Z }^+})\) cluster or interval related to the main factor

\(A_i ({i\in \text{ Z }^+})\) :

The linguistic variables corresponding to \(a_i \)

\(b_{j,i} ({i,j\in \mathrm{Z}^+})\) :

The \(i\)th cluster or interval of the \(j\)th secondary factor

\(B_{j,i} ({i,j\in \mathrm{Z}^+})\) :

The linguistic variables corresponding to \(b_{j,i} \)

\(M(i,j)\) :

The \(j\)th\(({i\in \mathrm{Z}^+})\) element of the \(i\)th\(({i\in \mathrm{Z}^+})\) cluster of the main factor

\(S(i)_{p,q} (i,p,q\in \mathrm{Z}^+)\) :

The \(q\)th element of the \(p\)th cluster of the \(i\)th secondary factor

Predicted \((i)\) :

The predicted value of \(i\)

References

  • Aladag H, Basaran MA, Egrioglu E, Yolcu U, Uslu VR (2008) Forecasting in high order fuzzy time series by using neural networks to define fuzzy relations. Expert Syst Appl 3:4228–4231

    Google Scholar 

  • Aliev RA, Fazlollahi B, Aliev RR, Guirimov B (2008) Linguistic time series forecasting using fuzzy recurrent neural network. Soft Comput 12:183–190

    Article  Google Scholar 

  • Bezdek JC, Ethrlich R, Full W (1984) FCM: the fuzzy c-means clustering algorithm. Comput Geosci 10:191–203

    Article  Google Scholar 

  • Bulut E, Duru O, Yoshida S (2012) A fuzzy integrated logical forecasting (FILF) model of time charter rates in dry bulk shipping: a vector autoregressive design of fuzzy time series with fuzzy C-means clustering. Marit Econ Logist 14(3):300–318

    Article  Google Scholar 

  • Bulut E (2014) Modeling seasonality using the fuzzy integrated logical forecasting (FILF) approach. Expert Syst Appl 41(4):1806–1812

    Article  Google Scholar 

  • Chatterjee S, Roy A (2014a) Web software fault prediction under fuzzy environment using MODULO-M multivariate fuzzy clustering algorithm and newly proposed revised prediction algorithm. Appl Soft Comput 22:372–396

    Article  Google Scholar 

  • Chatterjee S, Roy A (2014b) Novel algorithms for web software fault prediction. Qual Reliab Eng Int. doi:10.1002/qre.1687

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

    Article  Google Scholar 

  • Chen SM, Tanuwijaya K (2011) Multivariate fuzzy forecasting based on fuzzy time series and automatic clustering techniques. Expert Syst Appl 38:10594–10605

    Article  Google Scholar 

  • Chen LS, Hsueh CC, Chang CJ (2013) A two-stage approach for formulating fuzzy regression models. Knowl Based Syst 52:302–310

    Article  Google Scholar 

  • Dunn JC (1973) A fuzzy relative of the ISODATA process and its use in detecting compact well- separated clusters. J Cybern 3(3):32–57

    Article  MathSciNet  MATH  Google Scholar 

  • Duru O (2010) Fuzzy integrated logical forecasting model for dry bulk shipping index forecasting: an improved fuzzy time series approach. Expert Syst Appl 37:5372–5380

    Article  Google Scholar 

  • Duru O (2012) A multivariate model of fuzzy integrated logical forecasting method (M-FILF) and multiplicative time series clustering: A model of time-varying volatility for dry cargo freight market. Expert Syst Appl 39(4):4135–4142

    Article  Google Scholar 

  • Duru O, Bulut E (2014) A non-linear clustering method for fuzzy time series: histogram damping partition under the optimized cluster paradox. Appl Soft Comput. doi:10.1016/j.asoc.2014.08.038

  • Hartingan JA, Wong MA (1979) A K-means clustering algorithm. J Royal Stat Soc Ser C 28(1):100–108

    Google Scholar 

  • Huarng K (2001b) Heuristic models of fuzzy time series for forecasting. Fuzzy Sets Syst 123:369–386

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Huarng K, Yu THK (2005) A type 2 fuzzy time series model for stock index forecasting. Phys A 353:445–462

    Article  Google Scholar 

  • Huarng K, Yu THK (2006) Ratio-based lengths of intervals to improve fuzzy time series forecasting. IEEE Trans Syst Man Cybern Part B Cybern 32:328–340

    Article  Google Scholar 

  • Huynh T, Miller J (2009) Another viewpoint on evaluating web software reliability based on workload and failure data extracted from server logs. Empir Softw Eng 14:371–396

    Article  Google Scholar 

  • Hyndman RJ (2006) Another look at forecast-accuracy metrics for intermittent demand. Foresight Int J Appl Forecast 4:43–46

  • Khashei M, Bijari M, Hejazi SR (2012) Combining seasonal ARIMA models with computational intelligence techniques for time series forecasting. Soft Comput 16:1091–1105

    Article  MATH  Google Scholar 

  • Knuth DE (1973) The art of computer programing, vol 1. Addison-Wesley Publishing Company, USA

  • Lutkepohl H (2005) New introduction to multiple time series analysis. Springer, Berlin

    Book  MATH  Google Scholar 

  • Mamdani, E. H. (1977) Application of fuzzy logic to approximate reasoning using linguistic synthesis. IEEE Trans. On ComputersC-26, 1182–1191

  • Rabiei MR, Arghami NR, Taheri M (2014) Least-squares approach to regression modeling in full interval-valued fuzzy environment. Soft Comput 18(10):2043–2059

    Article  MATH  Google Scholar 

  • Ross TJ (2010) Fuzzy logic with engineering Applications, Wiley, India

  • Sahinoglu E, Uslu T (2011) Increasing coal quality by oil agglomeration after ultrasonic treatment. Fuel Process Technol 116:332–338

    Article  Google Scholar 

  • Shen J, Chang Lee ES, Deng Y, Brown SJ (2005) Determination of cluster number in clustering microarray data. Appl Math Comput 169(2):1172–1185

  • Song Q, Chissom BS (1993b) Fuzzy time series and its model. Fuzzy Sets Syst 54:269–277

  • Song Q, Chissom BS (1993a) Forecasting enrollments with fuzzy time series-Part I. Fuzzy Sets Syst 54:1–9

    Article  MathSciNet  Google Scholar 

  • Song Q, Chissom BS (1994) Forecasting enrollments with fuzzy time series-Part II. Fuzzy Sets Syst 62:1–8

    Article  Google Scholar 

  • Tanaka K (1996) An introduction to fuzzy logic for practical applications, Springer

  • Tsaur RC (2008) Forecasting analysis by using fuzzy grey regression model for solving limited time series data. Soft Comput 12:1105–1113

    Article  MATH  Google Scholar 

  • Tseng FM, Tzeng GH, Yu HC, Yaun B (2001) Fuzzy ARIMA model for forecasting the foreign exchange market. Fuzzy Sets Syst 118:9–19

    Article  MathSciNet  Google Scholar 

  • Zadeh LA (1975) The concept of linguistic variable and its application to approximate reasoning, parts 1–3. Inform Sci 8(3):199–249, 301–357, 9, 43–80

Download references

Acknowledgments

The author is thankful to Dr. Henry Lieberman, Massachusetts Institute of Technology, Cambridge, Massachusetts,USA, for his thorough checking and wonderful suggestions for the betterment of this paper. The author is also thankful to Mr. Rajesh Mishra, system administrator, ISM Dhanbad, India, for providing the log files of www.ismdhanbad.ac.in Last, the author shows his gratitude to Dr. V. K. Kalyani, Scientist, CIMFER, a CSIR Lab (run by the Govt. of India), for providing the data related to the oil agglomeration process. The author is very much thankful to the reviewers for their valuable suggestions.

Author information

Authors and Affiliations

  1. Intelligent Security Systems Research Lab, Department of Computer Science, University of Memphis, Memphis, TN, 38111, USA

    Arunava Roy

Authors
  1. Arunava Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arunava Roy.

Additional information

Communicated by V. Loia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Roy, A. A novel multivariate fuzzy time series based forecasting algorithm incorporating the effect of clustering on prediction. Soft Comput 20, 1991–2019 (2016). https://doi.org/10.1007/s00500-015-1619-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-015-1619-3

Keywords

Search

Navigation