Sage Journals: Discover world-class research

Abstract

In many data-driven modeling, prediction or identification applications to unknown systems, linguistic (fuzzy) results described by fuzzy sets are more preferable than the crisp results described by numbers owing to the uncertainties and/or noises existed in the observed data. On the other hand, fuzzy neural network (FNN) provides a powerful tool for providing accurate crisp results, but does not have the ability to achieve linguistic outputs due to its crisp weights. This study extends the crisp weights of FNN to fuzzy ones to obtain linguistic outputs. And, a data-driven design method is proposed to construct this kind of fuzzily weighted FNN (FW-FNN). The proposed data-driven method includes four steps. Firstly, a fully connected FNN is generated. Then, the SVD-QR method based pruning strategy is presented to realize the structure reduction of the initial FW-FNN. Thirdly, the centers of the Gaussian fuzzy weights in the structure reduced FW-FNN are learned by the least square method. Fourthly, the multi-objective algorithm is utilized to optimize the widths of the Gaussian fuzzy weights to achieve the maximum of the average membership grades of the output fuzzy sets and the minimum of the coverage intervals of the linguistic outputs. To evaluate the proposed FW-FNN and the data-driven method, applications to the nonlinear dynamic system identification, the chaotic time series prediction and the traffic flow prediction are given. Simulation results demonstrate that the linguistic outputs can effectively capture the uncertainties and/or noises in the observed data. It provides us a very useful tool for system modeling, prediction and identification especially when uncertainties and/or noises should be taken into account.

Keywords

Data-driven method fuzzy neural network multi-objective optimization structure reduction

Get full access to this article

View all access options for this article.

References

Zadeh

L.A.

, Fuzzy sets, Information and Control 8(3) (1965), 338–353.

Zadeh

L.A.

, Fuzzy logic and approximate reasoning, Synthese 30(3-4) (1975), 407–428.

Yager

R.R.

and Zadeh

L.A.

, An introduction to fuzzy logic applications in intelligent systems, Springer International 165 (1992).

Jafarzadeh

, Fadali

M.S.

and Livani

, Stability analysis of electricity markets using TSK fuzzy modeling, IEEE Transactions on Power Systems 31(2) (2016), 1161–1169.

Zhao

, Yin

, Niu

and Zheng

, Stabilization for a class of switched nonlinear systems with novel average dwell time switching by T-S fuzzy modeling, IEEE Transactions on Cybernetics 46(8) (2016), 1952–1957.

, Yi

and Zhang

, On the monotonicity of interval type-2 fuzzy logic systems, IEEE Transactions on Fuzzy Systems 22(5) (2014), 1197–1212.

Hong

M.O.

and Wang

, Linguistic dynamic systems based on computing with words and their stabilities, Science in China Series F 52(5) (2009), 780–796.

Horikawa

S.I.

, Furuhashi

and Uchikawa

, On fuzzy modeling using fuzzy neural networks with the back-propagation algorithm, IEEE Transactions on Neural Networks 3(5) (1992), 801–806.

Chen

Y.C.

and Teng

C.C.

, A model reference control structure using a fuzzy neural network, Fuzzy Sets and Systems 73(3) (1995), 291–312.

10.

Jang

J.S.R.

, ANFIS: Adaptive-network-based fuzzy inference systems, IEEE Transactions on Systems Man and Cybernetics 23(3) (1993), 665–685.

11.

Lin

C.T.

and Lee

C.G.

, Neural Fuzzy Systems, PTR Prentice Hall, 1996.

12.

Dong

, Sun

and Li

, A novel forecasting model based on a hybrid processing strategy and an optimized local linear fuzzy neural network to make wind power forecasting: A case study of wind farms in China, Renewable Energy 102 (2017), 241–257.

13.

Zhang

and Ge

, Freeway travel time prediction using takagi-sugeno-kang fuzzy neural network, Computer-Aided Civil and Infrastructure Engineering 28(8) (2013), 594–603.

14.

Zahedi

, Azizi

, Bahadori

, Elkamel

and Alwi

S.R.W.

, Electricity demand estimation using an adaptive neuro-fuzzy network: A case study from the Ontario province-Canada, Energy 49(1) (2013), 323–328.

15.

Wai

R.J.

, Lin

Y.F.

and Liu

Y.K.

, Design of adaptive control and fuzzy neural network control for single-stage boost inverter, IEEE Transactions on Industrial Electronics 62(9) (2015), 5434–5445.

16.

, Ding

, Zhao

, Yi

and Zhang

, Building energy consumption prediction: An extreme deep learning approach, Energies 10(10) (2017), 1–20.

17.

Yin

, Ding

S.X.

, Xie

and Luo

, A review on basic data-driven approaches for industrial process monitoring, IEEE Transactions on Industrial Electronics 61(11) (2014), 6418–6428.

18.

Deng

and Wang

, Incremental learning of dynamic fuzzy neural networks for accurate system modeling, Fuzzy Sets and Systems 160(7) (2009), 972–987.

19.

Han

, Wu

X.L.

and Qiao

J.F.

, Nonlinear systems modeling based on self-organizing fuzzy-neural-network with adaptive computation algorithm, IEEE Trans Cybern 44(4) (2014), 554–564.

20.

, Qiao

, Han

and Yang

, A self-organizing cascade neural network with random weights for nonlinear system modeling, Applied Soft Computing 42 (2016), 184–193.

21.

Lin

Y.Y.

, Chang

J.Y.

and Lin

C.T.

, Identification and prediction of dynamic systems using an interactively recurrent selfevolving fuzzy neural network, IEEE Transactions on Neural Networks and Learning Systems 24(2) (2013), 310–321.

22.

Ishibuchi

and Nii

, Numerical analysis of the learning of fuzzified neural networks from fuzzy if-then rules, Fuzzy Sets and Systems 120(2) (2001), 281–307.

23.

, Kecman

and Ichikawa

, Fuzzified neural network based on fuzzy number operations, Fuzzy Sets and Systems 130(3) (2002), 291–304.

24.

Nii

, Kakiuchi

, Takahama

, Maenaka

and Higuchi

, Human activity monitoring using fuzzified neural networks, Procedia Computer Science 22 (2013), 960–967.

25.

G.D.

and Huang

P.H.

, A vectorization-optimization-method-based type-2 fuzzy neural network for noisy data classification, IEEE Transactions on Fuzzy Systems 21(1) (2013), 1–15.

26.

Lin

Y.Y.

, Liao

S.H.

, Chang

J.Y.

and Lin

C.T.

, Simplified interval type-2 fuzzy neural networks, IEEE Transactions on Neural Networks and Learning Systems 25(5) (2014), 959.

27.

Lin

Y.Y.

, Chang

J.Y.

and Lin

C.T.

, A TSK-type-based self-evolving compensatory interval type-2 fuzzy neural network(TSCIT2FNN) and its applications, IEEE Transactions on Industrial Electronics 61(1) (2014), 447–459.

28.

Kayacan

, Kayacan

and Khanesar

M.A.

, Identification of nonlinear dynamic systems using type-2 fuzzy neural networksąłA novel learning algorithm and a comparative study, Industrial Electronics IEEE Transactions on 62(3) (2015), 1716–1724.

29.

Hassan

, Khanesar

M.A.

, Kayacan

, Jaafar

and Khosravi

, Optimal design of adaptive type-2 neuro-fuzzy systems: A review, Applied Soft Computing 44 (2016), 134–143.

30.

, Wang

and Niu

, Exponent back propagation neural network forecasting for financial cross-correlation relationship, Expert Systems with Applications 53 (2016), 106–116.

31.

Tang

, Deng

and Huang

G.B.

, Extreme learning machine for multilayer perceptron, IEEE Transactions on Neural Networks and Learning Systems 27(4) (2016), 809–821.

32.

, Gao

, Yi

and Zhang

, Analysis and design of functionally weighted single-input-rule-modules connected fuzzy inference systems, IEEE Transactions on Fuzzy Systems (2016).

33.

, Lv

, Yi

and Zhang

, Pruned fast learning fuzzy approach for data-driven traffic flow prediction, IEEE Transactions on Fuzzy Systems 20(7) (2016), 1181–1191.

34.

Wang

, A generalized ellipsoidal basis function based online self-constructing fuzzy neural network, Neural Processing Letters 34(1) (2011), 13–37.

35.

and Mendel

J.M.

, Aggregation using the linguistic weighted average and interval type-2 fuzzy sets, IEEE Transactions on Fuzzy Systems 15(6) (2007), 1145–1161.

36.

Liu

and Mendel

J.M.

, Aggregation using the fuzzy weighted average as computed by the karnik-mendel algorithms, IEEE Transactions on Fuzzy Systems 16(1) (2008), 1–12.

37.

Wang

L.X.

and Mendel

J.M.

, Fuzzy opinion networks: A mathematical framework for the evolution of opinions and their uncertainties across social networks, IEEE Transactions on Fuzzy Systems 24(4) (2016), 880–905.

38.

Mendel

J.M.

, Uncertain rule-based fuzzy logic systems: Introduction and new directions, Ptr Upper Saddle River Nj (2001).

39.

Golub

G.H.

and Van

C.F.

, Loan, Matrix computations, JHU Press 3 (2012).

40.

Deb

, Agrawal

, Pratap

and Meyarivan

, A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization: NSGA-II. Springer Berlin Heidelberg, 2000, pp. 849–858.

41.

Chen

, Wang

, Li

, Hu

and Zhang

, The retrieval of intra-day trend and its influence on traffic prediction, Transportation Research Part C 22(5) (2012), 103–118.

Data-driven design of the extended fuzzy neural network having linguistic outputs

Abstract

Keywords

Get full access to this article

References