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A Modified Weighted Fuzzy Time Series Model for Forecasting Based on Two-Factors Logical Relationship

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Abstract

In this paper, we present a modified weighted fuzzy time series model for forecasting based on two-factors fuzzy logical relationship groups. The proposed method define a new technique to partition the universe of discourse into different length of intervals to different factors. Also, the proposed method fuzzifies the historical data sets of the main factor and second factor to their maximum membership grades, obtained by their corresponding triangular fuzzy sets and further constructs the fuzzy logical relationship groups which is based on the two factors to increase in the forecasting accuracy rates. This study also introduces a new defuzzification technique based on the weighted function define on two-factors fuzzy logical relationship groups. The implementation of the proposed method is verified in forecasting on Bombay stock exchange Sensex historical data and compares the forecasted accuracy rate in terms of root mean square and average forecasting error which indicates that the proposed method can achieve more accurate forecasted output over the existing models on fuzzy time series.

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Abbreviations

\( \tilde{A} \) :

Fuzzy set

\( \tilde{A}_{i} \) :

Triangular fuzzy sets in the main factor

\( \tilde{B}_{i} \) :

Triangular fuzzy sets in the second factor

\( U \) :

Universe of discourse on the main factor

\( V \) :

Universe of discourse on the second factor

\( u_{i} \) :

Linguistic intervals define for the main factor

\( v_{i} \) :

Linguistic intervals define for the second factor

\( u \) :

Length of interval in the main factor

\( v \) :

Length of interval in the second factor

\( w_{i} \) :

Weight function

\( F\left( t \right) \) :

Fuzzy time series at time \( t \)

\( \alpha \) :

Define parameter and it value set as \( - 1, 0, 1 \)

\( m_{i} \) :

Midpoints of the linguistic intervals \( u_{i} \) define for the main factor

FLR:

Fuzzy logical relationships

FLRGs:

Fuzzy logical relationship groups

TFN:

Triangular fuzzy numbers

RMSE:

Root mean square error

AFE:

Average forecasting error

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Acknowledgements

The authors are very thankful to the editor and the anonymous reviewers for their constructive suggestions to improve the quality of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Abhishekh & Sanjay Kumar

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  1. Abhishekh
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  2. Sanjay Kumar
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Correspondence to Abhishekh.

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Abhishekh, Kumar, S. A Modified Weighted Fuzzy Time Series Model for Forecasting Based on Two-Factors Logical Relationship. Int. J. Fuzzy Syst. 21, 1403–1417 (2019). https://doi.org/10.1007/s40815-019-00652-8

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