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.

Fuzzy association rules for handling continuous attributes

Abstract: Association rules are frequently used for describing association (i.e., co-occurrence) among attribute values in the field of data mining. When an attribute is continuous (i.e., real-valued) such as height, length and weight, its domain is usually discretized into several intervals. Fuzzy rules are recognized as a convenient tool for handling continuous attributes in a human understandable manner. When we use fuzzy rules, the domain of each continuous attribute is discretized into several fuzzy sets. A linguistic label is usually associated with each fuzzy set especially when linguistic interpretations of fuzzy rules are required. In this paper, we first fuzzify the concept of association rules. That is, we show fuzzy versions of two measures (i.e., confidence and support) that are used for evaluating each association rule in the field of data mining. Then we illustrate these two measures of fuzzy rules for function approximation and pattern classification problems. Finally we examine the relation between the classification performance of fuzzy rules and the definition of their certainty grades through computer simulations. Simulation results show that the direct use of confidence as a certainty grade is not always appropriate from the viewpoint of classification performance.

A general approach to criteria aggregation using fuzzy measures

Abstract: The central focus of this work is to provide a general formulation for the aggregation of multi-criteria. This formulation is based upon the use of fuzzy subsets to model the criteria and the use of fuzzy measures to capture the interrelationship between criteria. A form of the fuzzy integral is used to connect these two to obtain the overall decision function. We are particularly interested here in the formulations obtained under different assumptions about the nature of the underlying fuzzy measure. We show how a number of the classic aggregation methods fall out as special cases of this very general formulation.

Avoiding exponential parameter growth in fuzzy systems

Abstract: For standard fuzzy systems where the input membership functions are defined on a grid on the input space, and all possible combinations of rules are used, there is an exponential growth in the number of parameters of the fuzzy system as the number of input dimensions increases. This "curse of dimensionality" effect leads to problems with design of fuzzy controllers (e.g., how to tune all these parameters), training of fuzzy estimators (e.g., complexity of a gradient algorithm for training, and problems with "over parameterization" that lead to poor convergence properties), and with computational complexity in the implementation for practical problems. We introduce a fuzzy system whose number of parameters grows linearly depending upon the number of inputs, even though it is constructed by using all possible combinations of the membership functions in defining the rules. We prove that this fuzzy system is equivalent to the standard fuzzy system as long as its parameters are specified in a certain way. Then, we show that it still holds the universal approximator property by using the Stone-Welerstrass theorem. Finally, we illustrate the performance of the fuzzy system via an application.

A highly interpretable fuzzy rule base using ordinal structure for obstacle avoidance of mobile robot

Abstract: Conventional fuzzy logic controller is applicable when there are only two fuzzy inputs with usually one output. Complexity increases when there are more than one inputs and outputs making the system unrealizable. The ordinal structure model of fuzzy reasoning has an advantage of managing high-dimensional problem with multiple input and output variables ensuring the interpretability of the rule set. This is achieved by giving an associated weight to each rule in the defuzzification process. In this work, a methodology to design an ordinal fuzzy logic controller with application for obstacle avoidance of Khepera mobile robot is presented. The implementation will show that ordinal structure fuzzy is easier to design with highly interpretable rules compared to conventional fuzzy controller. In order to achieve high accuracy, a specially tailored Genetic Algorithm (GA) approach for reinforcement learning has been proposed to optimize the ordinal structure fuzzy controller. Simulation results demonstrated improved obstacle avoidance performance in comparison with conventional fuzzy controllers. Comparison of direct and incremental GA for optimization of the controller is also presented.