Universal approximation by hierarchical fuzzy system with constraints on the fuzzy rule

Joo, Moon G.; Lee, Jin S.

doi:10.1016/s0165-0114(01)00176-2

Cited by 70 publications

(37 citation statements)

References 11 publications

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“…An aggregate operation might also exist in order to combine the outputs of one layer (Holve 1998;Joo and Lee 1999;Alimi 2005, 2010; Lee et al 2003;Salgado 2008;Zhang and Zhang 2006; Aja-Fernández and Alberola-López 2008; Joo and Sudkamp 2009). • Hybrid HFS (HHFS): This type of HFS is a mixture of the two previous ones (Joo and Lee 2002;Wang et al 2006;Chen et al 2004Chen et al , 2007; Aja-Fernández and Alberola-López 2008) (Fig. 2c).…”

Section: Introductionmentioning

confidence: 99%

Multi-objective genetic learning of serial hierarchical fuzzy systems for large-scale problems

Benítez

Casillas

2012

Soft Comput

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When we face a problem with a high number of variables using a standard fuzzy system, the number of rules increases exponentially and the obtained fuzzy system is scarcely interpretable. This problem can be handled by arranging the inputs in hierarchical ways. This paper presents a multi-objective genetic algorithm that learns serial hierarchical fuzzy systems with the aim of coping with the curse of dimensionality. By means of an experimental study, we have observed that our algorithm obtains good results in interpretability and accuracy with problems in which the number of variables is relatively high.

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Section: Introductionmentioning

confidence: 99%

Multi-objective genetic learning of serial hierarchical fuzzy systems for large-scale problems

Benítez

Casillas

2012

Soft Comput

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“…To overcome the difficulty resulting from high dimensional input spaces, hierarchical fuzzy systems were proposed in the early 1990s [17] and [27], and have attracted considerable attention. Work includes function approximation [8], [9] and [25], fuzzy-neural modeling [4], control [17]- [19] and [26], pattern classification [5] and [7], robotics [6] and [23], and linguistic modeling [3]. A review on hierarchical fuzzy systems is given in [22].…”

Section: Introductionmentioning

confidence: 99%

“…To our knowledge, the only available results about their representative capabilities are those given in [25] and [8], [9]. In [25], based on the linear hierarchical structure in [17] in which the number of rules increases linearly with the number of input variables, it was proved that hierarchical fuzzy systems are universal approximators.…”

Section: Introductionmentioning

confidence: 99%

Approximation Capabilities of Hierarchical Fuzzy Systems

Zeng

Keane

2005

IEEE Trans. Fuzzy Syst.

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Derived from practical application in location analysis and pricing, and based on the approach of hierarchical structure analysis of continuous functions, this paper investigates the approximation capabilities of hierarchical fuzzy systems. By first introducing the concept of the natural hierarchical structure, it is proved that continuous functions with natural hierarchical structure can be naturally and effectively approximated by hierarchical fuzzy systems to overcome the curse of dimensionality in both the number of rules and parameters. Then, based on Kolmogorov's theorem, it is shown that any continuous function can be represented as a superposition of functions with the natural hierarchical structure and can then be approximated by hierarchical fuzzy systems to achieve the universal approximation property. Further, the conditions under which the hierarchical fuzzy approximation is superior to the standard fuzzy approximation in overcoming the curse of dimensionality are analyzed.

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“…Kallel (ilhem.kallelgieee.org) and N. Baklouti designed by decomposing behaviors with regards to their interactivity and also by decomposing control laws [6,7,9,11].…”

mentioning

confidence: 99%

“…With each pair, a complete rule base is associated. The rules have the form:if Xkl = dkl and Xk2 = dk2 then hk = Ck k 1= .,9 There are no fuzzy sets associated to the hidden fuzzy variables hk in the consequences. They are fully of membership for fuzzy terms Ck are evaluated by inference of rule base obtained by the fuzzy logic unit BFSk.Degree of membership u(B,j) for output variables Yi is obtained by inference of the overall rule base obtained by BFSo such as: if h1 = C1 and ....andh = Cg then Y1 = VI and Y2 =Vr and Y3= P After automatic training of all BFSi (i=l,..,l0) by MAGAD-BFS, a zeroth order fuzzy Sugeno model allowing the robot to avoid any possible collision is generated.…”

mentioning

confidence: 99%

Accuracy Preserving Interpretability with Hybrid Hierarchical Genetic Fuzzy Modeling: Case of Motion Planning Robot Controller

Kallel

Baklouti

Alimi

2006

2006 International Symposium on Evolving Fuzzy Systems

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Design of robot controller for motion planning, using fuzzy logic control, requires formulation of rules that are collectively responsible for necessary levels of intelligent behaviors. To ensure the model interpretability, this collection of rules can be naturally decomposed and efficiently implemented as a hierarchical fuzzy model. This paper describes how this can be done using Hybrid Hierarchical Genetic Fuzzy modeling. The idea is to combine, in a hierarchical design, "mapping" for sub-goal behavior (SGB), and "reactivity" for local avoiding obstacles behavior (LAOB), to have at the same time, an interpretable and precise communicating system for robot motion planning controller. The design of each fuzzy unit of the hierarchical model is automatically ensured by MAGAD-BFS method (Multi-Agent Genetic Algorithm for the Design of Beta Fuzzy Systems), promoting itself as an interpretability-accuracy trade-off. A proposed reduced version of Generalized Local Voronoi Diagram (RGL VD) comes to guarantee a high degree of precision for robot motion to attempt destinations (sub-goals). Compared to the navigation using only fuzzy rules controller, the hybrid hierarchical model is more efficient in terms of saving time and optimizing path.

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Universal approximation by hierarchical fuzzy system with constraints on the fuzzy rule

Cited by 70 publications

References 11 publications

Multi-objective genetic learning of serial hierarchical fuzzy systems for large-scale problems

Multi-objective genetic learning of serial hierarchical fuzzy systems for large-scale problems

Approximation Capabilities of Hierarchical Fuzzy Systems

Accuracy Preserving Interpretability with Hybrid Hierarchical Genetic Fuzzy Modeling: Case of Motion Planning Robot Controller

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