Topic
Fuzzy associative matrix
About: Fuzzy associative matrix is a research topic. Over the lifetime, 8027 publications have been published within this topic receiving 194790 citations.
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TL;DR: A sufficient condition to guarantee the stability of the proposed fuzzy control system is proposed in terms of Lyapunov's method and can be applied to the design of a Fuzzy-PID control system.
223 citations
TL;DR: A new rule-refinement scheme is proposed that is based on the maximization of fuzzy entropy on the training set, which is expected to have the advantages of improving the generalization capability of initial fuzzy IF-THEN rules and simultaneously overcoming the overfitting of refinement.
Abstract: When fuzzy IF-THEN rules initially extracted from data have not a satisfying performance, we consider that the rules require refinement. Distinct from most existing rule-refinement approaches that are based on the further reduction of training error, this paper proposes a new rule-refinement scheme that is based on the maximization of fuzzy entropy on the training set. The new scheme, which is realized by solving a quadratic programming problem, is expected to have the advantages of improving the generalization capability of initial fuzzy IF-THEN rules and simultaneously overcoming the overfitting of refinement. Experimental results on a number of selected databases demonstrate the expected improvement of generalization capability and the prevention of overfitting by a comparison of both training and testing accuracy before and after the refinement.
222 citations
TL;DR: A rule-base self-extraction and simplification method is proposed to establish interpretable fuzzy models from numerical data and some approximate similarity measures are presented and a parameter fine-tuning mechanism is introduced to improve the accuracy of the simplified model.
222 citations
TL;DR: A zero-sum two-person game with imprecise values in its matrix of payoffs is considered and a method for its solution based on the establishment of a Fuzzy Linear Programming problem for each player is proposed.
220 citations
TL;DR: The Wang-Mendel method for generating fuzzy rules from data is enhanced to make it a comprehensive and flexible fuzzy system approach to data description and prediction, and an algorithm to optimize the fuzzy predictive models is proposed.
Abstract: In this paper, the so-called Wang-Mendel (WM) method for generating fuzzy rules from data is enhanced to make it a comprehensive and flexible fuzzy system approach to data description and prediction. In the description part, the core ideas of the WM method are used to develop three methods to extract fuzzy IF-THEN rules from data. The first method shows how to extract rules for the user-specified cases, the second method generates all the rules that can be generated directly from the data, and the third method extrapolates the rules generated by the second method over the entire domain of interest. In the prediction part, two fuzzy predictive models are constructed based on the fuzzy IF-THEN rules extracted by the methods of the description part. The first model gives a continuous output and is suitable for predicting continuous variables, and the second model gives a piecewise constant output and is suitable for predicting categorical variables. We show that by comparing the prediction accuracy of the fuzzy predictive models with different numbers of fuzzy sets covering the input variables, we can rank the importance of the input variables. We also propose an algorithm to optimize the fuzzy predictive models, and show how to use the models to solve pattern recognition problems. Throughout this paper, we use a set of real data from a steel rolling plant to demonstrate the ideas and test the models.
220 citations