An Evolutionary Objective Cluster Analysis-Based Interpretable Fuzzy Identification Method - Intelligent Computing for Sustainable Energy and Environment - page 176

Tabl e 1. Comparison of different Methods in Electrical Applications

Identification Rules reduction Parameters tuning

Method

Rn Tre Tee Rn Tre Tee Tre Tee

FCM 49 508426 464130

FC[8] - -

SC 37 401998 444724

WM-TUN 13 298446 464130 - 175337 180102

WCA-TUN 20 356434 282058 - 175887 180211

MOG-UL 25 707773 311195 12 101071 908329 455210 599616

Ad-Hoc[6]

COR-WN 22 180995 497910 - -

IRL 31 179345 220320 26 175480 165046 134020 147758

EOCA-IFIM 3 347606 278778 -

Table 1. shows the performance comparison among EOCA-IFIM, Fuzzy Clus-
tering (FC) [8] and Ad-Hoc. Where the performance index is 1/2 Mean Square
Error (MSE), Rn is the number of rules, Tre is the training error, and Tee is the
test error. By EOCA-IFIM, the minimum but compact rule base, i.e., 3 rules
are got. In addition, even though the errors of training and test in our model
are not optimal, it is still in the same range of magnitude compared with the
other methods. Furthermore, the procedures of rules reduction and parameters
tuning in Ad-Hoc are avoided. Thus the computation eciency is also increased.
Generally, our model is not of well approximation and generalization ability, but
also easily to be implemented.

6 Conclusions

In this paper, based on the combination of EOCA and ES, an EOCA-IFIM ap-
proach is proposed to construct an interpretable Mamdani fuzzy model. Firstly,
an EOCA-based initial fuzzy partition strategy is presented to decrease the ef-
fect of noise and reduce the redundancy of rules. Then the semantic parameters
of rules are optimized by a (1+1) ES. By means of the CC and GNP principles,
the consistency of rules and the suitable distinguishability between fuzzy sets are
considered simultaneously by one-pass quick learning. Thus the interpretability
of the Mamdani model is enhanced properly with certain accuracy. The simula-
tion of Box-Jenkins and the electrical applications demonstrates the robustness,
the compactness and the appropriate accuracy of the presented model.

Acknowledgments. The authors would like to thank the anonymous reviewers
for their helpful comments and constructive suggestions with regard to this pa-
per. This work was supported in part by National Natural Science Foundation of
China under Grant (60974054 & 61074064), Natural Science Foundation of Tian-
jin (11JCYBJC07000) and Key Laboratory of Advanced Electrical Engineering
and Energy Technology, Tianjin Polytechnic University.