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On cluster-wise fuzzy regression analysis.

M S Yang¹, C H Ko

¹Dept. of Math., Chung Yuan Christian Univ., Chung Li.

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society

|January 1, 1997

Summary

This summary is machine-generated.

This study introduces fuzzy clustering to address data heterogeneity in fuzzy regression analysis. The one-stage generalized fuzzy regression approach is recommended for its effectiveness in cluster-wise analyses.

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Area of Science:

Fuzzy mathematics
Statistical modeling

Background:

Fuzzy regression analysis, introduced by Tanaka et al. (1982), is widely applied.
Real-world regression often involves heterogeneous observations, posing a challenge for standard models.

Purpose of the Study:

To apply fuzzy clustering techniques to fuzzy regression analysis.
To overcome data heterogeneity issues within fuzzy regression models.

Main Methods:

Development of cluster-wise fuzzy regression analysis.
Presentation of two approaches: two-stage weighted fuzzy regression and one-stage generalized fuzzy regression.
Embedding fuzzy clustering within the one-stage generalized fuzzy regression model fitting process.

Main Results:

The one-stage generalized fuzzy regression approach effectively incorporates data structure at each iteration.
Numerical results demonstrate the superiority of the one-stage procedure.
The two-stage procedure builds upon existing work by Jajuga (1986) and Diamond (1988).

Conclusions:

The one-stage generalized fuzzy regression is highly recommended for cluster-wise fuzzy regression analysis.
This method offers a more effective way to handle heterogeneous data in fuzzy regression.
Fuzzy clustering provides a robust solution for complex regression scenarios.