As an emerging technology, the efficient and energy conserving process of permanent magnetic drive (PMD) presents high uncertainties. This paper designs a type of Begian–Melek–Mendel (BMM) structure interval type-2 fuzzy logic systems (IT2 FLSs) for PMD process uncertain parameters forecasting. The antecedent, consequent, and input measurements of systems are all selected as the Gaussian type-2 primary membership functions with uncertain standard deviations. Then the backpropagation algorithms are used to tune the parameters of IT2 FLSs. According to the Monte Carlo simulation studies and convergence analysis, the proposed IT2 FLSs are proved to be superior to two corresponding T1 FLSs in generalization ability.
BarbounisTGTheocharisJB (2007) Locally recurrent neural networks for wind speed prediction using spatial correlation. Information Sciences177(24): 5775–5797.
2.
BarkatSTlemcaniANouriH (2011) Noninteracting adaptive control of PMSM using interval type-2 fuzzy logic systems. IEEE Transactions on Fuzzy Systems19(5): 925–936.
3.
BernardoDHagrasHTsangE (2013) A genetic type-2 fuzzy logic based system for the generation of summarized linguistic predictive models for financial applications. Soft Computing17(12): 2185–2201.
4.
BiglarbegianMMelekWWMendelJM (2010) On the stability of interval type-2 TSK fuzzy logic systems. IEEE Transactions on Systems, Man and Cybernetics. Part B, Cybernetics40(3): 798–818.
5.
BiglarbegianMMelekWWMendelJM (2011a) Design of novel interval type-2 fuzzy controllers for modular and reconfigurable robots: Theory and experiments. IEEE Transactions on Industrial Electronics58(4): 1371–1384.
6.
BiglarbegianMMelekWWMendelJM (2011b) On the robustness of type-1 and interval type-2 fuzzy logic systems in modeling. Information Sciences181(7): 1325–1347.
7.
CastilloOAmador-AnguloLCastroJR, et al. (2016) A comparative study of type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and generalized type-2 fuzzy logic systems in control problems. Information Sciences354(c): 257–274.
8.
CastilloOMelinP (2012) A review on the design and optimization of interval type-2 fuzzy controllers. Applied Soft Computing12(4): 1267–1278.
9.
CastilloOMelinPOntiverosE, et al. (2019) A high-speed interval type 2 fuzzy system approach for dynamic parameter adaptation in metaheuristics. Engineering Applications of Artificial Intelligence85: 666–680.
10.
CervantesLCastilloO (2015) Type-2 fuzzy logic aggregation of multiple fuzzy controllers for airplane flight control. Information Sciences324: 247–256.
11.
ChenY (2019a) Study on centroid type-reduction of interval type-2 fuzzy logic systems based on noniterative algorithms. Complexity2019: 7325053.
12.
ChenY (2019b) Study on sampling based discrete Nie-Tan algorithms for computing the centroids of general type-2 fuzzy sets. IEEE Access7(1): 156984–156992.
13.
ChenYWangDZ (2017) Forecasting by general type-2 fuzzy logic systems optimized with QPSO algorithms. International Journal of Control, Automation and Systems15(6): 2950–2958.
14.
ChenYWangDZ (2018) Study on centroid type-reduction of general type-2 fuzzy logic systems with weighted enhanced Karnik-Mendel algorithms. Soft Computing22(4): 1361–1380.
15.
ChenYWangDZ (2019) Forecasting by designing Mamdani general type-2 fuzzy logic systems optimized with quantum particle swarm optimization algorithms. Transactions of the Institute of Measurement and Control41(10): 2886–2896.
16.
ChenYWangDZNingW (2018) Forecasting by TSK general type-2 fuzzy logic systems optimized with genetic algorithms. Optimal Control Applications & Methods39(1): 393–409.
17.
ChenYWangDZTongSC (2016) Forecasting studies by designing Mamdani interval type-2 fuzzy logic systems: With the combination of BP algorithms and KM algorithms. Neurocomputing174(b): 1133–1146.
18.
ChenYWuJXLanJ (2020) Study on reasonable initialization enhanced Karnik-Mendel algorithms for centroid type-reduction of interval type-2 fuzzy logic systems. AIMS Mathematics5(6): 6149–6168.
19.
GaoXJHuangTWWangZY, et al. (2014) Exploiting a modified gray model in back propagation neural networks for enhanced forecasting. Cognitive Computation6(3): 331–337.
20.
GaxiolaFMelinPValdezF, et al. (2016) Optimization of type-2 fuzzy weights in backpropagation learning for neural networks using GAs and PSO. Applied Soft Computing38: 860–871.
21.
GonzalezCICastroJRMelinP, et al. (2016) An edge detection method based on generalized type-2 fuzzy logic. Soft Computing20(2): 773–784.
22.
GreenfieldSChiclanaF (2013) Accuracy and complexity evaluation of defuzzification strategies for the discretised interval type-2 fuzzy set. International Journal of Approximate Reasoning54(8): 1013–1033.
23.
GusevKYBurkovskiiVL (2013) A neural network forecasting model for integrated economic indicators. Automation and Remote Control74(9): 1567–1572.
24.
HagrasH (2007) Type-2 FLSs: A new generation of fuzzy controllers. IEEE Computational Intelligence Magazine2(1): 30–43.
25.
HagrasHWagnerC (2012) Towards the wide spread use of type-2 fuzzy logic systems in real world applications. IEEE Computational Intelligence Magazine7(3): 14–24.
26.
HernandezMdlAMelinPMéndezGM, et al. (2015) A hybrid learning method composed by the orthogonal least-squares and the back-propagation learning algorithms for interval A2-C1 type-1 non-singleton type-2 TSK fuzzy logic systems. Soft Computing19(3): 661–678.
27.
HsuCHJuangCF (2013) Evolutionary robot wall-following control using type-2 fuzzy controller with species-de-activated continuous ACO. IEEE Transactions on Fuzzy Systems21(1): 100–112.
28.
KaufmanAGuptaMM (1985) Introduction to Fuzzy Arithmetic Theory and Applications. New York: Van Nostrand Reinhold.
29.
KhanesarMAJalalianAKaynakO (2017) Improving the speed of center of set type-reduction in interval type-2 fuzzy systems by eliminating the need for sorting. IEEE Transactions on Fuzzy Systems25(5): 1193–1206.
30.
KhosraviANahavandiS (2014) Load forecasting using interval type-2 fuzzy logic systems: Optimal type reduction. IEEE Transactions on Industrial Informatics10(2): 1055–1063.
31.
KhosraviANahavandiSCreightonD, et al. (2012) Interval type-2 fuzzy logic systems for load forecasting: A comparative study. IEEE Transactions on Power Systems27(3): 1274–1282.
32.
LeesCWangMHHagrasH (2010) Type-2 fuzzy ontology and its application to personal diabetic-diet recommendation. IEEE Transactions on Fuzzy Systems18(2): 316–328.
33.
LiJWJohnRCouplandS, et al. (2018) On Nie-Tan operator and type-reduction of interval type-2 fuzzy sets. IEEE Transactions on Fuzzy Systems26(2): 1036–1039.
34.
LiuXWMendelJM (2011) Connect Karnik-Mendel algorithms to root-finding for computing the centroid of an interval type-2 fuzzy set. IEEE Transactions on Fuzzy Systems19(4): 652–665.
35.
MehdiRAlfredSJonathanPC (2016) Drought forecasting using Markov chain model and artificial neural networks. Water Resources Management30(7): 2245–2259.
36.
MendelJM (2001) Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Englewood Cliffs, NJ: Prentice Hall.
37.
MendelJM (2004) Computing derivatives in interval type-2 fuzzy logic systems. IEEE Transactions on Fuzzy Systems12(1): 84–98.
38.
MendelJM (2013) On KM algorithms for solving type-2 fuzzy set problems. IEEE Transactions on Fuzzy Systems21(3): 426–446.
MéndezGMHernandezMdlA (2013) Hybrid learning mechanism for interval A2-C1 type-2 non-singleton Takagi-Sugeno-Kang fuzzy logic systems. Information Sciences220(1): 149–169.
41.
MendozaOMelinPCastilloO (2009) Interval type-2 fuzzy logic and modular networks for face recognition applications. Applied Soft Computing9(4): 1377–1387.
42.
NiewiadomskiA (2010) On finity, countability, cardinalities, and cylindric extensions of type-2 fuzzy sets in linguistic summarization of databases. IEEE Transactions on Fuzzy Systems18(3): 532–545.
43.
Ontiveros-RoblesEMelinPCastilloO (2017) New methodology to approximate type-reduction based on a continuous root-finding Karnik Mendel algorithm. Algorithms10(3): 77–96.
44.
Ontiveros-RoblesEMelinPCastilloO (2018) Comparative analysis of noise robustness of type 2 fuzzy logic controllers. Kybernetika54(1): 175–201.
45.
PanyPKGhoshalSP (2015) Dynamic electricity price forecasting using local linear wavelet neural network. Neural Computing and Applications26(8): 2039–2047.
46.
RezaieKAmalnikMSGereieA, et al. (2007) Using extended Monte Carlo simulation method for the improvement of risk management: Consideration of relationships between uncertainties. Applied Mathematics and Computation190(2): 1492–1501.
47.
SafarinejadianBGhanePMonirvaghefiH (2015) Fault detection in non-linear systems based on type-2 fuzzy logic. International Journal of Systems Sciences45(3): 394–404.
48.
TaoCWTaurJSChangCW, et al. (2012) Simplified type-2 fuzzy sliding controller for wing rocket system. Fuzzy Sets and Systems207(16): 111–129.
49.
TongSCLiYM (2010) Robust adaptive fuzzy backstepping output feedback tracking for nonlinear system with dynamic uncertainties. Science China Information Sciences53(2): 307–324.
50.
TongSCLiYM (2014) Observer-based adaptive fuzzy backstepping control of uncertain pure-feedback systems. Science China Information Sciences57(1): 1–14.
51.
WangDZChenY (2018) Study on permanent magnetic drive forecasting by designing Takagi Sugeno Kang type interval type-2 fuzzy logic systems. Transactions of the Institute of Measurement and Control40(6): 2011–2023.
52.
WuDR (2013) Approaches for reducing the computational cost of interval type-2 fuzzy logic systems: Overview and comparisons. IEEE Transactions on Fuzzy Systems21(1): 80–99.
53.
ZhangHWangJ (2015) State estimation of discrete-time Takagi-Sugeno fuzzy systems in a network environment. IEEE Transactions on Cybernetics45(8): 1525–1536.
54.
ZhangHShiYWangJ (2014) On energy-to-peak filtering for nonuniformly sampled nonlinear systems: A Markovian jump system approach. IEEE Transactions on Fuzzy Systems22(1): 212–222.
