Hierarchical Fuzzy identification using gradient descent and recursive least square method

As is well known, Zadeh presented the compositional rule of inference to discuss complex inference modes. After that other researchers also investigated this problem. However, the classic fuzzy control systems in the application often encounter the curse of dimensionality. To overcome these difficulties in the classic fuzzy control systems with high-dimensional input variables, the entire triple-I algorithm for double fuzzy control systems and manifold learning of dimensionality reduction will be discussed in this paper. Specifically, triple-I FMP algorithm is presented for double hierarchical fuzzy control system based on Guojun Wang’s implication operator and its reversibility is proved. Using manifold learning, dimension reduction SNE algorithm is given for double-layer hierarchical fuzzy control systems to keep the distribution of peak possibly point, so as to minimize the control stability impact due to reducing dimension. Since any type of multi-layer fuzzy control system is regarded as multiple fusion of double-layer hierarchical fuzzy system, the proposed algorithms and their reversibility are universal.

In this paper an intelligent hierarchical fuzzy logic system using genetic algorithms for the prediction and modelling of interest rates in Australia is developed. The proposed system uses a hierarchical fuzzy logic system in which a genetic algorithm is used as a training method for learning the fuzzy rules knowledge bases that are used for prediction of interest rates in Australia.A hierarchical fuzzy logic system is developed to model and predict three‐month (quarterly) interest rate fluctuations. The system is further trained to model and predict interest rates for six‐month and one‐year periods. The proposed system is developed with first two, three, then four and finally five hierarchical knowledge bases to model and predict interest rates.A novel architecture called a feed forward fuzzy logic system using fuzzy logic and genetic algorithms is also developed to predict interest rates. A back‐propagation hierarchical neural network system is also developed to predict interest rates for three‐month, six‐month and one‐year periods. The results obtained from these two systems are then compared with the hierarchical fuzzy logic system results and conclusions are drown on the accuracy of all systems for prediction of interest rates in Australia. Copyright © 2004 John Wiley & Sons, Ltd.

Hierarchical fuzzy systems (HFSs) have been shown to have the potential to improve interpretability of fuzzy logic systems (FLSs). In recent years, a variety of indices have been proposed to measure the interpretability of FLSs such as the Nauck index and Fuzzy index. However, interpretability indices associated with HFSs have not so far been discussed. The structure of HFSs, with multiple layers, subsystems, and varied topologies, is the main challenge in constructing interpretability indices for HFSs. Thus, the comparison of interpretability between FLSs and HFSs — even at the index level — is still subject to open discussion. This paper begins to address these challenges by introducing extensions to the FLS Nauck and Fuzzy interpretability indices for HFSs. Using the proposed indices, we explore the concept of interpretability in relation to the different structures in FLSs and HFSs. Initial experiments on benchmark datasets show that based on the proposed indices, HFSs with equivalent function to FLSs produce higher indices, i.e. are more interpretable than their corresponding FLSs.

The quality evaluation of Semantic Web applications (SWAs) in isolation is not enough. The future shall see almost all Web applications being deployed on the cloud and available to us as services, facilitating transparency and reusability. The business model of cloud computing provides services on demand, which are paid as per their use. The Software as a Service (SaaS) delivery model of cloud computing segregates provider’s ownership from customer’s use. Since the concept of quality is crucial to services, therefore, it is plausible to build models for quality assessment of SWAs, which fit in the cloud’s SaaS paradigm. Such applications are referred to Semantic Web application as a service (SWAaaS), in the following text. In our knowledge, there are no quality factors, measures, or frameworks for tracking the quality of SWAaaS. The Semantic Web application quality framework described in Chap. 3 is not profusely appropriate for evaluation of SWAaaS, owing to the distinctive natures of Web application and service. Previously, some ways of assessing quality of SWA and SaaS have been invented, a few of which build on quality features from existing software and Web application quality models, whereas some formulate SaaS quality metrics. few works merely present quality attributes in the context of Service Level Agreement (SLA) and Quality of Service (QoS) parameters. Here, the representative quality factors influencing SWAaaS are recognized after the literature review and a Hierarchical Fuzzy System (HFS) has been developed to assess SWAaaS quality. The quality attributes of HFS have been validated using IEEE 1061 framework. Results of experiments show that our HFS handles multiple quality attributes, and may perform quality-based ranking of SWAs available as services. The hierarchical fuzzy quality model discussed here may serve as a beginning point toward an all-inclusive quality model aimed to facilitate a SWAaaS consumer to choose the best quality service among SWAs available as a service on the cloud. Additionally, HFS may act as a directive to SWAaaS provider for the betterment of quality of SWA that is being provided as a service.

Based on the approach of hierarchical structure analysis of continuous functions, this paper discusses the approximation capacities of hierarchical Takagi-Sugeno fuzzy systems. By first introducing the concept of the natural hierarchical structure, it is proved that continuous functions with the 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 the number of parameters. Then, based on the Kolmogorov's theorem, it is shown that any continuous function can be represented as a superposition of functions with natural hierarchical structure and can then be approximated by hierarchical Takagi-Sugeno fuzzy systems to achieve the universal approximation property.

The “curse of dimensionality” and “sparse rule base” are two common and important problems in conventional fuzzy systems. Using hierarchical fuzzy systems is an effective way to deal with the “curse of dimensionality” problem, whilst fuzzy rule interpolation offers a useful means for enhancing the robustness of fuzzy models, making inference possible in systems containing only a sparse rule base. In particular, backward fuzzy interpolation can be employed to allow interpolation to be carried out when certain antecedents of observation variables are absent, whereas conventional methods do not work. In order to deal with both “curse of dimensionality” and “sparse rule base” simultaneously, an initial idea of hierarchical bidirectional fuzzy interpolation is presented in this paper, combining hierarchical fuzzy systems and forwardlbackward fuzzy rule interpolation. Hierarchical bidirectional fuzzy interpolation is applicable to situations where a multiple multi-antecedent rules system needs to be reconstructed to a multi-layer fuzzy system and any sub-layer rule base is sparse. The implementation of this approach is based on fuzzy rule interpolative reasoning that utilities scale and move transformation. An illustrative example and application scenario are provided to demonstrate the efficacy of this proposed approach.

When applying gradient descent learning methods to hierarchical fuzzy systems, there is great difficulty in handling the intermediate variables introduced by the hierarchical structures, as the intermediate variables may go outside their definition domain that makes gradient descent learning invalid. To overcome this difficulty, this paper proposes a learning scheme that integrates a normalization process for intermediate variables into gradient descent learning. This ensures that gradient descent methods are applicable to, and correctly used for, learning general hierarchical fuzzy systems. Benchmark datasets are used to demonstrate the validity and advantages of the proposed learning scheme over other existing methods in terms of better accuracy, better transparency, and fewer fuzzy rules and parameters.

In this brief, a sensitivity analysis of hierarchical fuzzy system (HFS) is conducted, allowing a sensitivity order of controller inputs to be established and used in a hierarchical fuzzy system inputs placement process. The frequency response analysis method is used to analyze the sensitivity of the controller output with respect to perturbation. This sensitivity knowledge thus constitutes a platform on which three different designs of HFS are investigated. An automotive active suspension system is chosen as an application for the HFS models for performance verification purposes. The simulation results are provided and discussed in this brief.

Prediction of optimum sampling rates of air quality monitoring stations using hierarchical fuzzy logic control system

The application of hierarchical fuzzy logic system using genetic fuzzy rule generator architecture to robot navigation in presence of moving obstacles is considered. A hierarchical fuzzy logic system is proposed for collision avoidance and guidance of a robot systems. Simulation results and analysis are presented to show the effectiveness of the proposed method.

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

Fuzzy logic controllers suffer from rule explosion problem as the number of rules increases exponentially with the number of input variables. Although several methods have been proposed for eliminating the combinatorial rule explosion problem, none of them is fully satisfactory. In this paper, we describe a new adaptive method for the design of cascaded layer based hierarchical fuzzy system with high input dimensions. This new adaptive hierarchical architecture could be applied to dimensionality reduction in fuzzy modeling. An evolutionary algorithm based off-line leaning algorithm is employed to generate the fuzzy rules and their corresponding membership functions. The evolutionary learning paradigm is a powerful tool to tune the fuzzy logic controllers since it requires no prior knowledge about the system's behavior in order to formulate a set of functional control rules through adaptive learning. The resulting hierarchical fuzzy system has not only an equivalent approximation capability, but less number of fuzzy rules compared with the conventional fuzzy logic system. Simulation studies exhibit competing results with high accuracy that illustrating the effectiveness of the approach.

The present study presents the applications of a hierarchical fuzzy system in the traffic light system control process. In this paper a hierarchical fuzzy system was designed. This system is based on the fuzzy system for traffic lights control FS-TLC. The main advantage of the solution presented herein is a significant reduction of the number of defined rules. Additionally, owing to the use of hierarchical fuzzy systems, it is possible to greatly reduce the time required for computations and to reduce the use of memory in the systems designed. Also that systems can be significantly more effective in operation, and they allow a creation of faster controllers that may be implemented in the hardware architecture.

Hierarchical fuzzy inference based on Bandler-Kohout subproduct

Fuzzy logic systems have been extensively applied for solving many real world application problems because they are found to be universal approximators and many methods, particularly, gradient descent (GD) methods have been widely adopted for the optimization of fuzzy membership functions. Despite its popularity, GD still suffers some drawbacks in terms of its slow learning and convergence. In this study, the use of decoupled extended Kalman filter (DEKF) to optimize the parameters of an interval type-2 intuitionistic fuzzy logic system of Tagagi-Sugeno-Kang (IT2IFLS-TSK) fuzzy inference is proposed and results compared with IT2IFLS gradient descent learning. The resulting systems are evaluated on a real world dataset from Australia's electricity market. The IT2IFLS-DEKF is also compared with its type-1 variant and interval type-2 fuzzy logic system (IT2FLS). Analysis of results reveal performance superiority of IT2IFLS trained with DEKF (IT2IFLS-DEKF) over IT2IFLS trained with gradient descent (IT2IFLS-GD). The proposed IT2IFLS-DEKF also outperforms its type-1 variant and IT2FLS on the same learning platform.