Hans Hellendoorn

Defuzzification in Fuzzy Controllers

An important subject in fuzzy control theory is tuning of a fuzzy controller. If one wants to tune a fuzzy controller, one can focus on the choice of rules, membership functions, number of input and output fuzzy sets and their degree of overlapping, implication, and connection operations, and defuzzification method. All these choices are closely related and in no way independent of each other. We describe six important defuzzification methods and their respective merits and shortcomings, dependent on the rules, domains, etc. Further, we give an alternative approach for the case in which the output fuzzy sets have different shapes or are asymmetrical. We illustrate this by several examples.

Design and development of fuzzy systems at Siemens R&D

In the 1980s several Siemens groups inside and outside Germany started activities within the area of fuzzy control and classification. Siemens Corporate Research and Development in Munich decided to start a central research group, to coordinate and support the activities within the groups. This research group had three main assignments, namely (1) to bring Siemens to the state-of-the-art fuzzy control and classification, (2) to develop software tools to support the implementation of fuzzy systems, and (3) to build up a methodology for the design and development of fuzzy systems. The author mainly deals with this third assignment. He shows several aspects of the design and development of fuzzy controllers and exemplifies this process by the defuzzification methodology.<<ETX>>

Stability of Fuzzy Control Systems

FKBC has been proven to be a powerful tool when applied to the control of processes which are not amenable to conventional, analytic design techniques. The design of most of the existing FKBC has relied mainly on the process operator’s or control engineer’s experience based heuristic knowledge. Hence, the controller’s performance is very much dependent on how good this expertise is. Thus, from the control engineering point of view, the major effort in fuzzy knowledge based control has been devoted to the development of particular FKBC for specific applications rather than to general analysis and design methodologies for coping with the dynamic behavior of control loops. The development of such methodologies is of primary interest for control theory and engineering. In particular, stability analysis is of extreme importance, and the lack of satisfactory formal techniques for studying the stability of process control systems involving FKBC has been considered a major drawback of FKBC.

Fuzzy control with fuzzy inputs: the need for new rule semantics

The standard computation taking place in a fuzzy logic controller proceeds from crisp inputs and via the consecutive steps of fuzzification, inference, and defuzzification computes a crisp control output. However, this computational practice simplifies to an extent the actual developments taking place in the closed loop. In reality, the knowledge about the current values of the controller input is very often available via sensory measurements. In this case, one has to take into account the negative side effects that come up with the use of sensors, in particular the presence of noisy measurements. In the paper the authors consider one particular way of dealing with noisy controller inputs, namely transforming the noise-distribution into a fuzzy set and then feeding back the so obtained fuzzy signal to the controller input. Adopting this approach requires that the shape of the input fuzzy signal should be reflected as much as possible in the output fuzzy signal so that important noise characteristics are preserved. In the paper the authors describe the requirements on the shape of the fuzzy output signal given a certain fuzzy input signal and show that the existing semantics for fuzzy IF-THEN rules do not satisfy these requirements. The authors propose new semantics for such rules which together with max-min composition produces the desired results.<<ETX>>

After the fuzzy wave reached Europe

Abstract We briefly describe the situation of the fuzzy community in Europe before the fuzzy wave. We show that there was a lot of expertise in almost all subareas of fuzzy logic. Then we describe some aspects of the fuzzy wave itself, in particular fuzzy control and first generation fuzzy systems that played a role during the time the fuzzy wave reached Europe. We also make some remarks about European companies and their activities during this time. Then we discuss the situation after the fuzzy wave, some aspects of second generation fuzzy systems, the combination of fuzzy logic with other theories and techniques, and some new application areas. Finally, we will discuss the chances of fuzzy systems in Europe in the future.

Fuzzy system technologies at Siemens R&D

Abstract Applications of fuzzy logic are usually identified with fuzzy control. But besides fuzzy control there are many other fuzzy theories that are used in applications, among them fuzzy classification and diagnosis. Fuzzy control has to do with closed loops, but besides the large amount of fuzzy control applications there are many other fuzzy theories being used in applications, among them fuzzy classification and diagnosis. We consider several recent results in fuzzy control and show their use in applications. Furthermore, we give some examples of applications in fuzzy classification and fuzzy diagnosis.

Fuzzy neural traffic control and forecasting

Fuzzy systems can be used to represent human knowledge. Traffic technology is a science where this property of fuzzy logic can be very well adapted because it is hard to make mathematical models due to human influences and complex connections between input parameters. One example of the use of fuzzy logic in traffic control is in highway speed control systems. The goal is to optimally use the highway. We first describe a fuzzy system for traffic flow control and incident recognition that has been in use for some time. Another example that we describe is fuzzy logic in forecasting whether a particular parking garage is full or not. We describe the input parameters and the structure of the fuzzy system. Furthermore, we show how neural networks can be used to improve the performance of the system.<<ETX>>

Fuzzy traffic management for modern telecommunications

We describe applications of fuzzy logic in the area of broadband telecommunication networks. Call Admission Control (CAC) and Usage Parameter Control (UPC) play an important role in the traffic man...

Fuzzy control in telecommunications

Fuzzy logic is an excellent heuristic method to aid in coming to grips with the complexity problem in communication and computer networks. Four examples show the use of fuzzy logic in routing. (1) We show the use of explicitly available information in the form of routing tables. (2) We show the use of implicitly available information in the form of experience and heuristic knowledge in distributed networks. Then we show the use of fuzzy logic in (3) call admission control and (4) usage parameter control programs for broadband ISDN networks.

The Mathematics of Fuzzy Control

One of the major developments of fuzzy set theory, fuzzy logic was primarily designed to represent and reason with some particular form of knowledge. It was assumed that the knowledge would be expressed in a linguistic or verbal form, and also that the whole exercise should not be a mere intellectual undertaking, but must also be operationally powerful so that computers can be used. However, when using a language-oriented approach for representing knowledge about a certain system of interest, one is bound to encounter a number of nontrivial problems. Suppose, for example [119], that you are asked how strongly you agree that a given number x ∈ [0, 20] is a large number. One way to answer this question is to say that if x ≥ d then you agree it is a large number and if x < d then you disagree. Thus, if you place a mark on an agree—disagree scale, it might be distributed uniformly over the right half of the scale whenever x ≥ d and uniformly over the left half if x < d. Such a person is called a threshold person.