A learning process for fuzzy control rules using genetic algorithms

The purpose of this paper is to present a genetic learning process for learning fuzzy control rules from examples. It is developed in three stages: the first one is a fuzzy rule genetic generating process based on a rule learning iterative approach, the second one combines two kinds of rules, experts rules if there are and the previously generated fuzzy control rules, removing the redundant fuzzy rules, and the thrid one is a tuning process for adjusting the membership functions of the fuzzy rules. The three components of the learning process are developed formulating suitable genetic algorithms.     

Intelligent data analysis and model interpretation with spectral analysis fuzzy symbolic modeling

This paper proposes fuzzy symbolic modeling as a framework for intelligent data analysis and model interpretation in classification and regression problems. The fuzzy symbolic modeling approach is based on the eigenstructure analysis of the data similarity matrix to define the number of fuzzy rules in the model. Each fuzzy rule is associated with a symbol and is defined by a Gaussian membership function. The prototypes for the rules are computed by a clustering algorithm, and the model output parameters are computed as the solutions of a bounded quadratic optimization problem. In classification problems, the rules’ parameters are interpreted as the rules’ confidence. In regression problems, the rules’ parameters are used to derive rules’ confidences for classes that represent ranges of output variable values. The resulting model is evaluated based on a set of benchmark datasets for classification and regression problems. Nonparametric statistical tests were performed on the benchmark results, showing that the proposed approach produces compact fuzzy models with accuracy comparable to models produced by the standard modeling approaches. The resulting model is also exploited from the interpretability point of view, showing how the rule weights provide additional information to help in data and model understanding, such that it can be used as a decision support tool for the prediction of new data.     

Extracting compact fuzzy rules for nonlinear system modeling using subtractive clustering,GA and unscented filter

This paper presents a two stage procedure for building optimal fuzzy model from data for nonlinear dynamical systems. Both stages are embedded into Genetic Algorithm (GA) and in the first stage emphasis is placed on structural optimization by assigning a suitable fitness to each individual member of population in a canonical GA. These individuals represent coded information about the structure of the model (number of antecedents and rules). This information is consequently utilized by subtractive clustering to partition the input space and construct a compact fuzzy rule base. In the second stage, Unscented Filter (UF) is employed for optimization of model parameters, that is, parameters of the input–output Membership Functions (MFs).     

Almost compactness in fuzzy topological spaces

We introduce and study almost compactness for fuzzy topological spaces. We show that the almost continuous image of an almost compact fuzzy topological space is almost compact. Moreover, we show that generally almost compactness for fuzzy topological spaces is not product-invariant, but if X and Y are almost fuzzy topological spaces and X is product related to Y, then their fuzzy topological product is almost compact.     

Rule generation for hierarchical collaborative fuzzy system

A new method of rule generation for the hierarchical collaborative fuzzy system, HCFS, is proposed. This HCFS is structured like various parallel fuzzy subsystems and it overcomes the dimensionality problem and the lack of interpretability of most of the traditional fuzzy systems, when dealing with complex real-world problems. An association process of different fuzzy systems is presented in this work, through the use of a relevance concept of a fuzzy system. The result of this aggregation is a collaborative structure where all sub-models have the ability to gradually improve the overall accuracy of approximation by adding their own contributions. For this structure we propose a new algorithm to be used in the procedures of the three learning phases: the structure building, the parametric identification and the division of the learning data among the various levels of the hierarchical structure. This new fuzzy modelling technique automatically generates and tunes the sets of fuzzy rules in the hierarchical collaborative structure (HCS). The effectiveness of the proposed HCFS model in handling high-dimensional and complex problems is demonstrated through various numerical simulations.     

An interpretability improvement for fuzzy rule bases obtained by the iterative rule learning approach

Interpretability is one of the key concepts in many of the applications using the fuzzy rule-based approach. It is well known that there are many different criteria around this concept, the complexity being one of them. In this paper, we focus our efforts in reducing the complexity of the fuzzy rule sets. One of the most interesting approaches for learning fuzzy rules is the iterative rule learning approach. It is mainly characterized by obtaining rules covering few examples in final stages, being in most cases useless to represent the knowledge. This behavior is due to the specificity of the extracted rules, which eventually creates more complex set of rules. Thus, we propose a modified version of the iterative rule learning algorithm in order to extract simple rules relaxing this natural trend. The main idea is to change the rule extraction process to be able to obtain more general rules, using pruned searching spaces together with a knowledge simplification scheme able to replace learned rules. The experimental results prove that this purpose is achieved. The new proposal reduces the complexity at both, the rule and rule base levels, maintaining the accuracy regarding to previous versions of the algorithm.     

基于结构元理论及信息熵的模糊多属性决策方法

主要目的是讨论当权重完全未知时的模糊多属性决策方法,其中运用了结构元理论和信息熵方法.首先,简单地介绍了这两种方法的基本原理.然后,提出了基于这两种方法的决策模型,给出了模糊权重函数的求解公式.最后,把该方法应用于考核、评估干部的问题.     

The fuzzy intersection rule in variational analysis with applications

The fuzzy intersection rule for Fréchet normal cones in Asplund spaces was established by Mordukhovich and the author using the extremal principle, which appears more convenient to apply in some applications. In this paper, we present a complete discussion of this rule in various aspects. We show that the fuzzy intersection rule is another characterization of the Asplund property of the space. Various applications are considered as well. In particular, a complete set of fuzzy calculus rules for general lower semicontinuous functions are established.     

Redundant fuzzy rules exclusion by genetic algorithms

A genetic-algorithm-based method for exclusion of the potential redundant if-then fuzzy rules that have been extracted from numerical input-output data is proposed. The main idea is the input-space separation into activation rectangles, corresponding to certain output intervals. The generation of fuzzy rules and the membership functions are based on these activation rectangles and appropriate fuzzy rules inference mechanism is proposed. As the method usually produces too many rules, it is necessary to exclude the potential redundant if-then rules. The concept for varying the family of sensitivity parameters, defining the overlapping of the fuzzy regions is proposed. The genetic algorithms are used to resolve the following combinatorial optimization problem: the generation of families of sensitivity parameters. In this way the potential redundant if-then fuzzy rules are excluded.

The method formalizes the synthesis of the fuzzy system and could be used for function approximation, classification and control purposes. An illustrative example for implementation of the method for traffic fuzzy control is given.