Showing papers on "Fuzzy associative matrix published in 1997"

A fuzzy clustering-based rapid prototyping for fuzzy rule-based modeling

Abstract: This paper presents different approaches to the problem of fuzzy rules extraction by using fuzzy clustering as the main tool. Within these approaches we describe six methods that represent different alternatives in the fuzzy modeling process and how they can be integrated with a genetic algorithms. These approaches attempt to obtain a first approximation to the fuzzy rules without any assumption about the structure of the data. Because the main objective is to obtain an approximation, the methods we propose must be as simple as possible, but also, they must have a great approximative capacity and in that way we work directly with fuzzy sets induced in the variables input space. The methods are applied to four examples and the errors obtained are specified in the different cases.

Checking the coherence and redundancy of fuzzy knowledge bases

Abstract: Checking the coherence of a set of rules is an important step in knowledge base validation. Coherence is also needed in the field of fuzzy systems. Indeed, rules are often used regardless of their semantics, and it sometimes leads to sets of rules that make no sense. Avoiding redundancy is also of interest in real-time systems for which the inference engine is time consuming. A knowledge base is potentially inconsistent or incoherent if there exists a piece of input data that respects integrity constraints and that leads to logical inconsistency when added to the knowledge base. We more particularly consider knowledge bases composed of parallel fuzzy rules. Then, coherence means that the projection on the input variables of the conjunctive combination of the possibility distributions representing the fuzzy rules leaves these variables completely unrestricted (i.e., any value for these variables is possible) or, at least, not more restrictive than integrity constraints. Fuzzy rule representations can be implication-based or conjunction-based; we show that only implication-based models may lead to coherence problems. However, unlike conjunction-based models, they allow to design coherence checking processes. Some conditions that a set of parallel rules has to satisfy in order to avoid inconsistency problems are given for certainty or gradual rules. The problem of redundancy, which is also of interest for fuzzy knowledge bases validation, is addressed for these two kinds of rules.

Fuzzy regulators and fuzzy observers: a linear matrix inequality approach

Abstract: This paper presents LMI (linear matrix inequality) based designs of fuzzy control systems based on new relaxed stability conditions. LMI based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions. The design procedures realize effective and practical designs by utilizing other LMIs with respect to decay rate and constraints on control input and output. A design example for a nonlinear system demonstrates the utility of the LMI based design procedures.

A comparative design and tuning for conventional fuzzy control

Abstract: A new methodology is introduced for designing and tuning the scaling gains of the conventional fuzzy logic controller (FLC) based on its well-tuned linear counterpart. The conventional FLC with a linear rule base is very similar to its linear counterpart. The linear three-term controller has proportional, integral and/or derivative gains. Similarly, the conventional fuzzy three-term controller also has fuzzy proportional, integral and/or derivative gains. The new concept "fuzzy transfer function" is invented to connect these fuzzy gains with the corresponding scaling gains. The comparative gain design is presented by using the gains of the well-tuned linear counterpart as the initial fuzzy gains of the conventional FLC. Furthermore, the relationship between the scaling gains and the performance can be deduced to produce the comparative tuning algorithm, which can tune the scaling gains to their optimum by less trial and error. The performance comparison in the simulation demonstrates the viability of the new methodology.

An algorithm for fuzzy multi-criteria decision making

Abstract: The paper presents a new algorithm for solving the general fuzzy multi-criteria decision making (MCDM) problem involving fully data expressed by means of linguistic terms. A fuzzy performance matrix representing the overall assessment of alternatives with respect to each criterion is obtained by using interval arithmetic. To avoid the complex and unreliable ranking process of fuzzy numbers, the /spl alpha/-cut concept is used to transform the fuzzy performance matrix into an interval performance matrix. Incorporated with the decision maker's attitude towards risk, an overall preference index is obtained by applying the concept of the degree of similarity to the ideal solution using a vector matching function. The algorithm developed is simple and comprehensible with easy computation which facilitates its use in a decision support system for the general fuzzy MCDM problem. An example is presented to demonstrate its applicability.

An Efficient Method for Extracting Fuzzy Classification Rules from High Dimensional Data

Abstract: We present an efficient method for extracting fuzzy classification rules from high dimensional data. A cluster estimation method called subtractive clustering is used to efficiently extract rules from a high dimensional feature space. A complementary search method can quickly identify the important input features from the resultant high dimensional fuzzy classifier, and thus provides the ability to quickly generate a simpler, more robust fuzzy classifier that uses a minimal number of input features. These methods are illustrated through the benchmark iris data and through two aerospace applications.

Incremental neuro-fuzzy systems

Abstract: The poor scaling behavior of grid-partitioning fuzzy systems in case of increasing data dimensionality suggests using fuzzy systems with a scatter-partition of the input space. Jang has shown that zero-order Sugeno fuzzy systems are equivalent to radial basis function networks (RBFNs). Methods for finding scatter partitions for RBFNs are available, and it is possible to use them for creating scatter-partitioning fuzzy systems. A fundamental problem, however, is the structure identification problem, i.e., the determination of the number of fuzzy rules and their positions in the input space. The supervised growing neural gas method uses classification or regression error to guide insertions of new RBF units. This leads to a more effective positioning of RBF units (fuzzy rule IF-parts, resp.) than achievable with the commonly used unsupervised clustering methods. Example simulations of the new approach are shown demonstrating superior behavior compared with grid-partitioning fuzzy systems and the standard RBF approach of Moody and Darken.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Lithology determination from well logs with fuzzy associative memory neural network

Abstract: An artificial intelligence technique of fuzzy associative memory is used to determine rock types from well-log signatures. Fuzzy associative memory (FAM) is a hybrid of neural network and fuzzy expert system. This new approach combines the learning ability of neural network and the strengths of fuzzy linguistic modeling to adaptively infer lithologies from well-log signatures based on (1) the relationships between the lithology and log signature that the neural network have learned during the training and/or (2) geologist's knowledge about the rocks. The method is applied to a sequence of the Ordovician rock units in northern Kansas. This paper also compares the performances of two different methods, using the same data set for meaningful comparison. The advantages of FAM are: (1) expert knowledge acquired by geologists is fully utilized; (2) this knowledge is augmented by the neural network learning from the data, when available; and (3) FAM is "transparent" in that the knowledge is explicitly stated in the fuzzy rules.

Minimizing the fuzzy rule base and maximizing its performance by a multiobjective genetic algorithm

Abstract: In this paper, we explain how a GA-based multiobjective fuzzy rule selection method can be applied to high-dimensional pattern classification problems with many continuous attributes. Our rule selection method has two objectives to minimize the number of selected fuzzy if-then rules and to maximize the number of correctly classified patterns. Since the number of candidate fuzzy if-then rules in the rule selection method exponentially increases as the number of attributes increases, the rule selection method cannot handle all the fuzzy if-then rules as candidate rules when it is applied to high-dimensional pattern classification problems with many attributes. Thus we have to restrict the number of candidate rules. For this purpose, we generate only fuzzy if-then rules with a small number of antecedent conditions as candidate rules. The ability of our rule selection method is examined by computer simulations on a real-world pattern classification problem with many continuous attributes.