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

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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).

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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 \(i\)

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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.

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Authors and Affiliations

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

    Arunava Roy

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  1. Arunava Roy
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Correspondence to Arunava Roy.

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Communicated by V. Loia.

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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

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