The fuzzy system based on vague partitions and its application to path tracking control for autonomous vehicles

Abstract

As significant carriers of the application of fuzzy set theories, fuzzy systems have been widely used in many fields. However, selecting fuzzifications, fuzzy reasoning engines, and defuzzifications is subjective for Mamdani fuzzy systems, and the fuzzy rule of Takagi-Sugeno-Kang fuzzy systems is less of a linguistic interpretation. Regarding these shortcomings, this paper proposes a fuzzy system based on vague partitions processing information directly from the fuzzy rule base, in which fuzzy rules have explicit semantics. Firstly, the n-dimensional vague partition of the n-dimensional universe is defined based on 1-dimensional vague partitions and the aggregation function, and its properties are discussed. Based on these, we design the new fuzzy system, and investigate its approximation properties which is the theoretical guarantee for applying the fuzzy system. As an application, we combine the fuzzy system with PID control system to deal with autonomous vehicle path tracking control problems. A series of experiments are constructed, and experimental results indicate that the fuzzy system based on vague partitions makes the fuzzy PID control system strong robustness, and has obvious advantages compared with other traditional fuzzy systems for path tracking control problems.

Keywords

Fuzzy systems vague partitions aggregation functions fuzzy PID control path tracking

Get full access to this article

View all access options for this article.

References

Zadeh

L.A.

, Fuzzy set, Information and Control 8(1) (1965), 338–353.

Nakrani

N.M.

, Joshi

M.M.

, A human-like decision intelligence for obstacle avoidance in autonomous vehicle parking, Applied Intelligence (2022), 1–20.

Khemiri

, Naija

and Exposito

, Dispatching and rebalancingfor ride-sharing autonomous mobility-on-demand systems based on afuzzy multi-criteria approach, Soft Computing 27(4) (2023), 2041–2069.

Bonab

S.R.

, Ghoushchi

S.J.

, Deveci

et al. Logistic autonomousvehicles assessment using decision support model under sphericalfuzzy set integrated Choquet Integral approach, Expert Systemswith Applications 314 (2023), 119–205.

Zhang

, Hu

, Qiu

, Yang

, Sun

and Chen

, A novel fuzzyobserver-based steering control approach for path tracking inautonomous vehicles, IEEE Transactions on Fuzzy Systems 27(2) (2018), 278–290.

Xidias

, Zacharia

, Nearchou

, Intelligent fleet management of autonomous vehicles for city logistics, Applied Intelligence (2022), 1–19.

Mamdani

E.H.

, Application of fuzzy logic to approximate reasoningusing linguistic synthesis, IEEE Transactions on Computers 26(12) (1977), 1182–1191.

Zeng

X.J.

and Singh

M.G.

, A relationship between membershipfunctions and approximation accuracy in fuzzy systems, IEEETransactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 26(1) (1996), 176–180.

Zeng

X.J.

and Singh

M.G.

, Approximation accuracy analysis of fuzzysystems as function approximators, IEEE Transactions on FuzzySystems 4(1) (1996), 44–63.

10.

Chen

and Gang

, On approaching precisions of standard fuzzysystems with different basic functions, Acta Automatica Sinica 34(7) (2008), 823–827.

11.

Yuan

X.H.

, Li

H.X.

and Sun

K.B.

, Fuzzy systems and thier approximationcapability based on parameter singleton fuzzifier methods, ActaElectronic Sinica 39(10) (2011), 2372–2377.

12.

Jiang

and Yuan

, A new type of fuzzy systems using pyramidmembership functions (PMFs) and approximation properties, SoftComputing 22(21) (2018), 7103–7118.

13.

Zadeh

L.A.

, Outline of a new approach to the analysis of complexsystems and decision processes, IEEE Transactions on Systems,Man, and Cybernetics 3(1) (1973), 28–44.

14.

Wang

G.J.

, Fully implication triple I method for fuzzy reasoning, Science in China (Series E) 29(1) (1999), 43–53.

15.

Song

, Feng

and Lee

E.S.

, Triple I method for fuzzy reasoning, Computers and Mathematics with Applications 44 (2002), 1567–1579.

16.

Wang

G.J.

and Fu

, Unified forms of triple I method, Computers and Mathematics with Applications 49 (2005), 923–932.

17.

Liu

H.W.

and Wang

G.J.

, Unified forms of fully implicationalrestriction methods for fuzzy reasoning, Information Sciences 177(3) (2007), 956–966.

18.

Liu

H.W.

and Wang

G.J.

, Continuity of triple I methods based onseveral implications, Computers and Mathematics withApplications 56(8) (2008), 2079–2087.

19.

Zou

X.F.

and Pei

D.W.

, SIS algorithms for fuzzy reasoning, Fuzzy Systems and Mathematics 24(6) (2010), 1–7.

20.

Zhou

, Xu

and Li

, The quintuple implication principle offuzzy reasoning, Information Sciences 297 (2015), 202–215.

21.

Luo

and Zhou

, Interval-valued quintuple implication principleof fuzzy reasoning, International Journal of ApproximateReasoning 84 (2017), 23–32.

22.

Zhang

, Wang

, Bedregal

et al. Semi-overlap functions andnovel fuzzy reasoning algorithms with applications, InformationSciences 614 (2022), 104–122.

23.

Lee

M.A.

, Takagi

, Integrating design stages of fuzzy systems using genetic algorithms, In: Proceedings of the IEEE International Conference on Fuzzy Systems 1993, 612–617.

24.

Wang

L.X.

, Acourse in fuzzy systems and control, Prentice-Hall, Inc. (1997).

25.

Takagi

and Sugeno

, Fuzzy identification of systems and itsapplications to modeling and control, IEEE Transactions onSystems, Man, and Cybernetics 1 (1985), 116–132.

26.

Sugeno

and Sugeno

G.T.

, Structure identification of fuzzy model, Fuzzy Sets and Systems 28(1) (1988), 15–33.

27.

Kukolj

, Design of adaptive Takagi-Sugeno-Kang fuzzy models, Applied Soft Computing 2(2) (2002), 89–103.

28.

Rezaee

and Zarandi

M.F.

, Data-driven fuzzy modeling forTakagi-Sugeno-Kang fuzzy system, Information Sciences 180(2) (2010), 241–255.

29.

Deng

, Choi

K.S.

, Chung

F.L.

, et al. Scalable TSK fuzzy modelingfor very large datasets using minimal-enclosing-ball approximation, IEEE Transactions on Fuzzy Systems 19(2) (2010), 210–226.

30.

Khater

A.A.

, El-Nagar

A.M.

, El-Bardini

et al. Online learningof an interval type-2 TSK fuzzy logic controller for nonlinearsystems, Journal of the Franklin Institute 356(16) (2019), 9254–9285.

31.

Wai

R.J.

, Huang

Y.C.

, Yang

Z.W.

et al. Adaptivefuzzy-neural-network velocity sensorless control for robotmanipulator position tracking, IET Control Theory andApplications 4(6) (2010), 1079–1093.

32.

Jafarzadeh

, Gans

and Tadesse

, Control of TCP muscles usingTakagi-Sugeno-Kang fuzzy inference system, Mechatronics 53 (2018), 124–139.

33.

Yazid

, Garratt

and Santoso

, Position control of aquadcopter drone using evolutionary algorithms-based self-tuning forfirst-order Takagi-Sugeno-Kang fuzzy logic autopilots, AppliedSoft Computing 78 (2019), 373–392.

34.

Pan

X.D.

and Xu

, Correction to: Redefition of the concept offuzzy set based on vague partition from the perspective ofaxiomatization, Soft Computing 22(6) (2018), 2079–2079.

35.

Pan

X.D.

and Xu

, Redefition of the concept of fuzzy set based onvague partition from the perspective of axiomatization, SoftComputing 22(1) (2018), 1777–1789.

36.

Ovchinnikov

, Similarity relations, fuzzy partitions, and fuzzyorderings, Fuzzy Sets and Systems 40(1) (1991), 107–126.

37.

Zhou

, Li

and Wang

, Locally weighted factorization machinewith fuzzy partition for elderly readmission prediction, Knowledge-Based Systems 242 (2022), 108326.

38.

Zhao

X.R.

and Yao

, Three-way fuzzy partitions defined by shadowedsets, Information Sciences 497 (2019), 23–27.

39.

Torra

and Miyamoto

, A definition for I-fuzzy partitions, Soft Computing 15(2) (2011), 363–369.

40.

Marsala

, Fuzzy partitioning methods, Granular computing. Physica, Heidelberg, 2001, 163–186.

41.

Shen

, Pan

, Peng

et al. A new type of fuzzy systems interms of vague partitions, Journal of Intelligent and FuzzySystems 44(6) (2023), 9545–9563.

42.

Bustince

, Fernandez

, Mesiar

et al. Overlap functions, Nonlinear Analysis: Theory, Methods and Applications 72(3-4) (2010), 1488–1499.

43.

Klement

E.P.

, Mesiar

, Pap

et al. Triangular norms, Berlin: Springer (2000).

44.

Yager

R.R.

and Rybalov

, Uninorm aggregation operators, FuzzySets and Systems 80(1) (1996), 111–120.

45.

Zorich

V.A.

, Mathematical analysis II, Berlin: Springer. (2016).

46.

Taylor

A.E.

, Lay

D.C.

, Introduction to functional analysis, Malabar, Florida: Robert E. Krieger.

47.

Liu

J.K.

, Advanced PID ControlMATLAB Simulation (3rd Edition), Publishing House of Electronics Industry.

48.

Yolcu

O.C.

, Egrioglu

, Bas

et al. Multivariate intuitionisticfuzzy inference system for stock market prediction: The cases ofIstanbul and Taiwan, Applied Soft Computing 116(2022), 108363.

49.

Boyacioglu

M.A.

and Avci

, An adaptive network-based fuzzyinference system (ANFIS) for the prediction of stock market return:the case of the Istanbul stock exchange, Expert Systems withApplications 37(12) (2010), 7908–7912.

50.

Vechione

and Cheu

R.L.

, Comparative evaluation of adaptive fuzzyinference system and adaptive neuro-fuzzy inference system formandatory lane changing decisions on freeways, Journal ofIntelligent Transportation Systems 26(6) (2022), 746–760.

51.

Paul

S.K.

, Chowdhury

, Ahsan

, et al. An advanceddecision-making model for evaluating manufacturing plant locationsusing fuzzy inference system, Expert Systems with Applications 191 (2022), 116378.

52.

Mohiyuddin

, Javed

A.R.

, Chakraborty

et al. Secure cloudstorage for medical IoT data using adaptive neuro-fuzzy inferencesystem, International Journal of Fuzzy Systems 24(2) (2022), 1203–1215.

53.

Balasubramanian

and Ananthamoorthy

N.P.

, Improved adaptiveneuro-fuzzy inference system based on modified glowworm swarm anddifferential evolution optimization algorithm for medical diagnosis, Neural Computing and Applications 33 (2021), 7649–7660.