Sequential Adaptive Fuzzy Inference System for Function Approximation Problems

This paper introduces three hybrid methods for the generation and optimization of rules and membership functions of a fuzzy logic controller for nonlinear systems. The proposed methods overcome the deficiency of a systematic approach for optimal design of fuzzy controllers. An optimally designed fuzzy logic controller should have the least number of fuzzy variables and fuzzy rules and the best possible configuration of fuzzy rules in the rule table. The first strategy of this paper is a two-phase optimization problem: in the first phase, the number of fuzzy variables and their arrangement in the rule table are optimized by a genetic algorithm; in the second phase, the parameters of the membership functions are optimized via extended Kalman filtering. The second strategy tries to achieve the goals of the first method all in one phase by modifying the chromosome structure of the genetic algorithm. Then in the next step, a local search algorithm is utilized to improve the obtained results. The third strategy is similar to the second strategy in structure. However, along with optimizing the number of fuzzy variables and membership parameters, the number of fuzzy rules is also optimized. The first and second strategies are obliged to use every possible combination of fuzzy variables in the rule table; however, the third strategy is capable of distinguishing between useful and useless fuzzy rules in the rule table. The introduced strategies are applied to an automotive cruise control system. The results of the simulations show the effectiveness of the proposed methods and the superiority of the latter approaches over the former ones.

Simplification of ANFIS based on importance-confidence-similarity measures

Fuzzy neural networks have both the interpretability of fuzzy systems and the self-learning ability of neural networks, but they will face the challenge of “rule explosion” when dealing with high-dimensional data. Moreover, the structure and parameter identifications of models are generally performed in two stages, and this always attends to one thing and loses another in terms of interpretability and predictive performance. In this paper, a fuzzy neural network regression method (FNNR) that coordinates structure identification and parameter identification is proposed. To alleviate the problem of rule explosion, the structure identification and parameter identification are coordinated in the training process, and the numbers of fuzzy rules and fuzzy partitions are effectively limited, while the parameters of fuzzy rules are optimized. The symmetrical architecture of the FNNR is designed for automatic structure identification. An alternate training strategy is adopted by treating discrete and continuous parameters differently, and thus the convergence efficiency of the algorithm is improved. To enhance interpretability, regularized terms are designed from fuzzy rule level and fuzzy partition level to guide the model to learn fuzzy rules with simple structures and clear semantics. The experimental results show that the proposed method has both a compact structure and high precision.

Fuzzy systems based on fuzzy if-then rules have been applied to various problems. The main application area has been fuzzy control problems. In many cases, such fuzzy systems can handle only a few input variables. This is because the number of fuzzy if-then rules exponentially increases as the number of input variables increases. In this paper, we try to design fuzzy classification systems based on fuzzy if-then rules for multidimensional pattern classification problems with many attributes. For designing such fuzzy classification systems, we compare two frameworks in the area of genetics-based machine learning: the Michigan approach and the Pittsburgh approach. The performance of fuzzy rule-based classification systems is also compared with that of various pattern classification methods. In computer simulations, we use a wine classification problem with 13 attributes, a cancer diagnosis problem with 9 attributes, and a credit approval problem with 14 attributes. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(12): 10–19, 1997

In this chapter, we explain how multi-objective genetic algorithms can be applied to the design of fuzzy rule-based systems for pattern classification problems. For a multi-class pattern classification problem with many continuous attributes (e.g., wine classification with 13 continuous attributes [1]), a fuzzy rule-based classification system is designed by a multi-objective genetic algorithm [2, 3] with two objectives: to minimize the size of the fuzzy rule-based classification system and to maximize its performance [4, 5]. The size of the fuzzy rule-based classification system is expressed by the number of fuzzy if-then rules, and its performance is measured by the number of correctly classified training patterns. In our approach to the design of the fuzzy rule-based classification system, first a large number of fuzzy if-then rules are generated from training patterns as candidate rules for the rule selection. Then a small number of fuzzy if-then rules are selected from the candidate rules by the two-objective genetic algorithm. The two-objective genetic algorithm tries to find all the non-dominated solutions (i.e., non-dominated rule sets) of the rule selection problem with the above-mentioned objectives. One difficulty of the rule selection method for high-dimensional pattern classification problems with many continuous attributes is that the number of candidate fuzzy if-then rules becomes intractably large. For example, the number of candidate rules is 613 ≅ 1.3 × 1010 for the wine classification problem with 13 continuous attributes if we have six fuzzy sets (terms) on each axis of the 13-dimensional pattern space.

We examine the performance of compact fuzzy rule-based classification systems that consist of a small number of simple fuzzy rules with high comprehensibility. Those fuzzy systems are designed in a heuristic manner using rule selection criteria. We first describe fuzzy rule-based classification. Next we describe heuristic rule selection criteria using the terminology in data mining: confidence and support. A small number of fuzzy rules are extracted from numerical data based on each rule selection criterion. Then we examine the classification performance of extracted fuzzy rules through computational experiments on a number of benchmark data sets from the UCI ML Repository. Our results should be viewed as the lowest benchmark performance of fuzzy rule-based classification systems because fuzzy rules are extracted using a simple heuristic method with no optimization or tuning procedures. Nevertheless our results on some data sets are comparable to reported results by the C4.5 algorithm in the literature.

The single-input-rule-modules (SIRMs) connected fuzzy reasoning method is an efficient way to reduce the number of fuzzy rules in the rule-based fuzzy controllers. However, there still exist fuzzy rule generation problems in the design process of the SIRMs connected fuzzy logic controllers (SIRMFLCs). To tackle this problem, this paper presents a prior information driven method for constructing the SIRMFLCs, including both type-2 and type-1 cases. Here, prior information means the requirements that the controllers must meet, e.g. continuity, symmetry and monotonicity of the controllers. To encode such prior information into the SIRMFLCs, the parameter conditions or constraints are provided. To show the effectiveness of the proposed method, applications to the stabilization control of the overhead crane system is given. Through utilizing the prior information to constrain the structures and parameters of fuzzy rules, the proposed strategy can reduce the blindness in the initialization of fuzzy rules and can generate the single input rule modules systematically.

Genetic Reinforcement Learning Algorithms for On-line Fuzzy Inference System Tuning Application to Mobile Robotic"

This paper proposes an adaptive self-learning fuzzy autopilot design for uncertain bank-to-turn (BTT) missiles due to external disturbances and system errors from the variations of the aerodynamic coefficients and control surface loss. The self-learning fuzzy systems called extended sequential adaptive fuzzy inference systems (ESAFISs) are utilized to compensate for these uncertainties in an adaptive backstepping architecture. ESAFIS is a real‐time self-learning fuzzy system with simultaneous structure identification and parameter learning. The fuzzy rules of the ESAFIS can be added or deleted based on the input data. Based on the Lyapunov stability theory, adaptation laws are derived to update the consequent parameters of fuzzy rules, which guarantees both tracking performance and stability. The robust control terms with the adaptive bound-estimation schemes are also designed to compensate for modeling errors of the ESAFISs by augmenting the self-learning fuzzy autopilot control laws. The proposed autopilot is validated under the control surface loss, aerodynamic parameter perturbations, and external disturbances. Simulation study is also compared with a conventional backstepping autopilot and a neural autopilot in terms of the tracking ability. The results illustrate that the designed fuzzy autopilot can obtain better steady‐state and transient performance with the dynamically self-learning ability.

This paper presents a new fuzzy inference system for modeling of nonlinear dynamic systems based on input and output data with measurement noise. The proposed fuzzy system has a number of fuzzy rules and parameter values of membership functions which are automatically generated using the extended relevance vector machine (RVM). The RVM has a probabilistic Bayesian learning framework and has good generalization capability. The RVM consists of the sum of product of weight and kernel function which projects input space into high dimensional feature space. The structure of proposed fuzzy system is same as that of the Takagi-Sugeno fuzzy model. However, in the proposed method, the number of fuzzy rules can be reduced under the process of optimizing a marginal likelihood by adjusting parameter values of kernel functions using the gradient ascent method. After a fuzzy system is determined, coefficients in consequent part are found by the least square method. Examples illustrate effectiveness of the proposed new fuzzy inference system.

Hierarchical genetic optimization of a fuzzy logic system for energy flows management in microgrids

In this paper, a methodology of adaptive pattern recognition based on adaptive hierarchical fuzzy rules is used to reconstruct the trace map of a printed circuit board. In order to implement this concept, hierarchical structures are discussed. Based on this, a frame-work of adaptive hierarchical fuzzy rule based pattern recognition is presented, where the different features of a pattern are delineated and sorted by different subsets of fuzzy rules, and subsets are arranged into different levels in the hierarchy. In the lower levels of the hierarchy, the fuzzy rules are formulated to delineate and sort the local features of a pattern, and in the higher levels of the hierarchy, the subsets of fuzzy rules are formulated to delineate and sort the global features of a pattern. The fuzzy rules in the lower level are fired first, to locate the sets of pixels hosting the local features, and then, these pixels are evaluated to see whether they exhibit global features. The parameters of fuzzy rules are adaptively changed in order to be more precise in delineating and sorting the features as more quantitative characteristics are being recovered from raw data. The hierarchy greatly reduces the number of the rules necessary for describing a pattern and also facilitates adding rules for new features or removing rules for faulty features of a pattern. As an example, the proposed approach is applied to extract the trace map from the X-ray image of a populated printed circuit board.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper proposes a cost-based fuzzy classification system for pattern classification problems with misclassification costs. The task is to minimize the total misclassification cost incurred by a fuzzy classification system consisting of a number of fuzzy if-then rules where the number of generated fuzzy if-then rules depends on the specification of fuzzy partitions for each axis. In the proposed fuzzy classification system the consequent class of a fuzzy if-then rule is determined so that the misclassification cost is minimal over the covered training patterns by the antecedent part of the rule. On the other hand, conventional fuzzy classification systems are compatibility-based. That is, the consequent class of a fuzzy if-then rule is determined from the compatibility of training patterns covered by the antecedent part of the rule. The grade of certainty of the fuzzy if-then rules in both classification systems is calculated by using the compatibility of training patterns from each class. In a series of computational experiments, we compare the performance of the proposed cost-based fuzzy classification systems with that of the conventional compatibility-based systems. The performance of both classifiers is measured for three real-world pattern classification problems.

40 - Techniques and Applications of Genetic Algorithm-Based Methods for Designing Compact Fuzzy Classification Systems

Fuzzy control rules and their natural control laws