H.R. van Nauta Lemke

Similarity measures in fuzzy rule base simplification

In fuzzy rule-based models acquired from numerical data, redundancy may be present in the form of similar fuzzy sets that represent compatible concepts. This results in an unnecessarily complex and less transparent linguistic description of the system. By using a measure of similarity, a rule base simplification method is proposed that reduces the number of fuzzy sets in the model. Similar fuzzy sets are merged to create a common fuzzy set to replace them in the rule base. If the redundancy in the model is high, merging similar fuzzy sets might result in equal rules that also can be merged, thereby reducing the number of rules as well. The simplified rule base is computationally more efficient and linguistically more tractable. The approach has been successfully applied to fuzzy models of real world systems.

Rudder roll stabilization for ships

This paper describes the design of an autopilot for rudder roll stabilization for ships. This autopilot uses the rudder not only for course keeping but also for reduction of the roll. The system has a series of properties which make the controller design far from straightforward: the process has only one input (the rudder angle) and two outputs (the heading and the roll angle); the transfer from rudder to roll is non-minimum-phase; because large and high-frequency rudder motions are necessary, the non-linearities of the steering machine cannot be disregarded; the disturbances caused by the waves vary considerably in amplitude and frequency spectrum. In order to solve these problems a new approach to the LQG method has been developed. The control algorithms were tested by means of computer simulations, scale-model experiments and full-scale trials at sea. The results indicate that a rudder roll stabilization system is able to reduce the roll as well as a conventional fin stabilization system, while it requires less investments. Based on the results obtained in this project the Royal Netherlands Navy has decided to implement rudder roll stabilization on a series of ships under construction at this moment.

Fuzzy PID supervisor

A fuzzy supervisor for a conventional PID controller is described. In the design of the supervisor the knowledge of an expert in tuning the parameters of the PID controller is applied. Moreover, a performance index is formulated, which matches the requirements in real applications better than the integral criteria generally used. In a simulation set-up system performances of the PID controller with and without the fuzzy supervisor are compared for different values of the parameters of the process to be controlled.

A parametric generalized goal function for fuzzy decision making with unequally weighted objectives

In multiobjective fuzzy decision making, averaging operators are commonly used as goal functions. It is assumed that such a goal function attains the maximum value for the optimal alternative. A parametric generalized goal function is given that unifies many of the commonly used averaging operators for equally weighted objectives. The parameters can be interpreted as an indication of the decision makers optimism. Conditions are defined that a generalized weighted goal function should satisfy. A correct generalization of the goal function for unequally weighted objects is given.<<ETX>>

Rule base simplification with similarity measures

In fuzzy rule based models, redundancy may be present in the form of similar fuzzy sets, especially if the models are acquired from data by using techniques like fuzzy clustering or gradient learning. The result is an unnecessarily complex and a less effective linguistic description of the system. An automated method is proposed that reduces the number of fuzzy sets in the model using a similarity measure. A comprehensive linguistic description is obtained by linguistic approximation. A numerical example demonstrates the approach.

A Characteristic Optimism Factor in Fuzzy Decision-Making

Abstract In multi-objective attribute fuzzy decision making one wishes to select the best alternative. Such a selection is based on many different aspects of varying degrees of importance. To solve the problem of selection one has to find at least approximate values that represent the satisfaction of each alternative to all objectives and also values that represent the relative importance of each objective. Moreover, the operation necessary to combine the values corresponding to the objectives is not uniquely defined and has to be chosen. This paper presents a general formulation of different operators for the computation of these values and provides some insight into the effect of applying a particular operation. This can be considered as a subjective optimism index of the decision maker.

Fuzzy target selection in direct marketing

Discusses some essential requirements for the introduction of computational intelligence techniques in the field of financial services, and reports on an investigation carried out concerning the possibilities and expected success of using fuzzy systems in some business chapters of the Dutch ING group. Based on this investigation, the subject of direct marketing is chosen for a pilot study of the application of data-driven modeling techniques using fuzzy clustering and iterative gain-charts refinement. This is compared with the present practice using statistical tools.

Selecting an aggregation operator for fuzzy decision making

In decision making one is interested in the preference ordering of the alternatives, rather than the exact numerical values that are assigned to the alternatives. This means that an aggregation operator that is able to combine criteria in a similar way to human beings need not reproduce the same numerical values as long as it produces a similar preference ordering as that of the humans. In this paper, previously published empirical data are analyzed from the point of view of preference orderings. A number of aggregation operators are used to approximate the preference ordering done by human beings. None of the operators give very good results. Moreover, there is not a significant difference in the performance of the t-norms or the compensatory operators. The operators can achieve, however, a partially correct ordering of the alternatives.<<ETX>>

Fuzzy arithmetic-based interpolative reasoning for nonlinear dynamic fuzzy systems

Abstract FAIR (fuzzy arithmetic-based interpolative reasoning)—a fuzzy reasoning scheme based on fuzzy arithmetic, is presented here. Linguistic rules of the Mamdani type, with fuzzy numbers as consequents, are used in an inference mechanism similar to that of a Takagi–Sugeno model. The inference result is a weighted sum of fuzzy numbers, calculated by means of the extension principle. Both fuzzy and crisp inputs and outputs can be used, and the chaining of rule bases is supported without increasing the spread of the output fuzzy sets in each step. This provides a setting for modeling dynamic fuzzy systems using fuzzy recursion. The matching in the rule antecedents is done by means of a compatibility measure that can be selected to suit the application at hand. Different compatibility measures can be used for different antecedent variables, and reasoning with sparse rule bases is supported. The application of FAIR to the modeling of a nonlinear dynamic system based on a combination of knowledge-driven and data-driven approaches is presented as an example.

FUZZY CONTROL FOR MULTIVARIABLE SYSTEMS

Abstract In this paper a fuzzy control algorithm for regulator control of multivariable systems based on a state space model of the system is introduced. Its application to several linear systems is illustrated and compared with systems controlled by means of linear feedback laws as obtained via an INA-design or linear output feedback. The application of this algorithm for two inputs two outputs laboratory set up will be discussed to illustrate its robustness.