Hans-Jürgen Zimmermann

RWTH Aachen University · Lehrstuhl für Operations Research

Since the following are personal observations, it might be appropriate to tell the reader some relevant facts of my background. They have shaped my views, which otherwise might seem strange to some colleagues in other disciplines: Due to several flights of approaching fronts during last world war and from eastern Germany I arrived in the West in 19...

When I met Da Ruan the first time in 1990, serving on his PhD committee, I was impressed by the quality and insight of his thesis and his argumentation. I did not expect, however, what a long and fruitful cooperation would follow. His PhD thesis focussed on a topic that was of basic importance to fuzzy inference and in which I was personally very i...

Fuzzy Set Theory has been developed during the last decades to a demanding mathematical theory. There exist more than 50,000 publications in this area by now. Unluckily the number of reports on applications of fuzzy technology has become very scarce. The reasons for that are manifold: Real applications are normally not single-method-applications bu...

Data analysis has been described as “the search for structure in data”, or as a means of reducing complexity. Most of the traditional methods for data analysis or data mining are dichotomous, i.e. they assume that patterns to be detected are two-valued. Whenever this is not the case the relationship between data or elements on one hand and classes...

Decision analysis and decision support is an area in which applications of fuzzy set theory, have been found since the early 1970s. Algorithmic as well as knowledge-based approaches have been suggested. The meaning of the term “decision” has also been defined differently in different areas, as has the meaning of “uncertainty”. This paper will first...

In spite of other uses of the term “mathematical programming” it shall be interpreted here as it is normally done in Operations Research, i.e. an algorithmic approach to solving models of the type $$\begin{array}{*{20}{l}} {{\text{maximize f(x)}}} \\ {{\text{such that }}{{\text{g}}_{\text{i}}}(x) = 0,{\text{i = 1,}} \ldots {\text{,m}}} \end{array}$...

Since its inception in 1965, the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of this theory can be found, for example, in artificial intelligence, computer science, medicine, control engineering, decision theory, expert systems, logic, management science, operations research, pattern recognition, and...

Unluckily, in the recent literature the number of papers on the application of intelligent systems, especially fuzzy sets, have been decreasing considerably The potential for those applications, however, has not diminished at all. On the contrary, the more complex applications become and the more decision support systems rely on human knowledge and...

Most data-mining algorithms assume static behavior of the incoming data. In the real world, the situation is different and most continuously collected data streams are generated by dynamic processes, which may change over time, in some cases even drastically. ...

The concept of fuzzy sets is presented as a new tool for the formulation and solution of systems and decision problems which contain fuzzy components or fuzzy relationships. After a brief description of the basic theory of fuzzy sets, implications to systems theory and decision making are indicated. Fuzzy set theory is then applied to fuzzy linear...

We are primarily concerned with the problem of representing imprecise statements and knowledge as well as drawing conclusions based on this type of knowledge. Our particular interest is to establish an efficient method, capable to represent and apply (i.e. reason with) imprecise knowledge within real problems. In the present paper we first introduc...

This chapter is on scope and problems of manufacturing management (MM), contexts and uncertainty in MM, intelligent approaches in project management, inventory management, and production logistics. The other subject included is intelligent production planning and control.

Information overload is becoming one of the problems that hinder the effectiveness of e-government services. Intelligent e-government services with personalized recommendation techniques can provide a solution for this problem. Existing recommendation ...

During the last two to three decades, many scientific as well business areas have moved from a situation of a lack of (electronically) readable information into a situation of abundant data. Data warehouses appeared, and the problem of extracting information from large masses of data became more and more important. Also knowledge became a very prec...

Es wurde schon mehrmals erwähnt, dass im OR nicht nur die Güte einer berechneten Lösung relevant ist, sondern auch der Aufwand der zu treiben ist, eine bestimmte Lösung zu bestimmen. Bei optimierenden Verfahren ist die Optimalität der Lösung garantiert, so dass früher die wesentlichen Merkmale für den Vergleich von Algorithmen der benötigte Speiche...

Lineares Programmieren ist der am besten entwickelte Teil der „Mathematischen Programmierung“. Entsprechend dem angelsächsischen Gebrauch des Begriffs „mathematical programming“ soll unter Mathematischer Programmierung das Gebiet des OR verstanden werden, das sich mit der Optimierung von Funktionen unter Nebenbedingungen befasst.

In Abschnitt 2.4 wurde im Zusammenhang mit dem Begriff der „beschränkten Rationalität“ darauf hingewiesen, dass Menschen, wenn sie sich von der Komplexität eines zu lösenden Problems überfordert fühlen, dazu neigen, u. a. komplexe Probleme in kleinere Teilprobleme zu zerlegen. Hierfür gibt es wohl primär zwei Gründe: 1. Die für die adäquate Charakt...

Der Begriff des Graphen sowie graphentheoretische Verfahren finden im Bereich des Operations Research verbreitet Anwendung. Spezielle Formen von Graphen — Bäume — haben wir schon bei den Entscheidungsbaumverfahren kennengelernt, ohne dass dafür Kenntnisse in der Graphentheorie notwendig waren. Nützlich sind solche Kenntnisse allerdings auf anderen...

Der Ursprung des Begriffes „Operational Research“ ist zweifellos in den Jahren 1937 bis 1939 in England zu suchen. Er entstand 1937 zur Bezeichnung einer Gruppe von Wissenschaftlern in der englischen Armee, die den Auftrag hatte, „Forschung bezüglich der operationalen Nutzung des Radars durchzuführen“ (Tomlinson, 1971, S. XI). Waddington (Waddingto...

Die Nichtlineare Programmierung beschäftigt sich mit der Bestimmung optimaler Lösungen zu dem Grundmodell der mathematischen Programmierung maximiere f(x) so dass \( {g_i}\left( x \right)\left\{ {\begin{array}{*{20}{c}} \leqslant \\ = \\ \geqslant \end{array}} \right\}{b_i},i = 1, \ldots ,m, \), wobei allerdings im Gegensatz zur Linearen Programmie...

In Abschnitt 3.6 war bereits darauf hingewiesen worden, dass die Forderung der Ganzzahligkeit der optimalen Lösung einige der Annahmen verletzt, die die Anwendung des Simplex-Verfahrens erlaubt. Für allgemeine gemischt-ganzzahlige Modelle wurde in Abschnitt 3.6 auch schon das „klassische“ Gomory Verfahren beschrieben. Dies ist zwar in der letzten Z...

Es wurde schon in der Einführung darauf hingewiesen, dass zum Operations Research nicht nur die mathematischen Methoden zur Lösung von Real- oder Rechenmodellen gehören, sondern auch das Modellieren von Problemen. Während sich die folgenden Kapitel 3 bis 7 primär mit den Lösungsmethoden beschäftigen, soll in diesem Kapitel das Gebiet des OR betrach...

In diesem Buch finden Sie die Brücke zwischen klassischem Operations Research und den modernen Gebieten der Heuristik und der Theorie unscharfer Mengen. Klassische und moderne Verfahren und Modelle der Unternehmensforschung sind didaktisch geschickt dargestellt. Das Buch ist entscheidungs- und EDV-orientiert. Mit besonderen Kapiteln über Heuristike...

Even though the first publication in the area of fuzzy set theory (FST)—one of the ingredients of computational intelligence (CI)—appeared in 1965, the development of this theory for almost 20 years remained in the academic realm. Almost all basic concepts, theories, and methods were, however, developed during this period. Fuzzy control opened the...

We interpretfu#pr linear programming (FLP) problems with fu#hM coe #cients andfu#M5 inequ#5ND y relations as mu#N59N6 fu#59 reasoning schemes (MFR), where the antecedents of the scheme correspond to the constraints of the FLP problem and the fact of the scheme is the objective of the FLP problem. Then thesolu#146 process consists of two steps: firs...

Advances in Computational Intelligence and Learning: Methods and Applications presents new developments and applications in the area of Computational Intelligence, which essentially describes methods and approaches that mimic biologically intelligent behavior in order to solve problems that have been difficult to solve by classical mathematics. Gen...

Fuzzy technology has already been used considerably in different areas of logistics primarily for evaluation of traffic flows, for data mining in traffic management, for data fusion in traffic supervision and for fuzzifying existing control devices. It is now being used to considerably reduce the complexity of online decision making in container ha...

We interpretfupr linear programming (FLP) problems with fuhM coe #cients andfuM5 inequ5ND y relations as muN59N6 fu59 reasoning schemes (MFR), where the antecedents of the scheme correspond to the constraints of the FLP problem and the fact of the scheme is the objective of the FLP problem. Then thesolu146 process consists of two steps: first, for...

We interpretfupr linear programming (FLP) problems (where some or all coe#- cients can befu]5 sets and theinequZC+ y relations betweenfuvZ sets can be given by a certainfuta relation) as mu265+Z fu65 reasoning schemes (MFR), where the antecedents of the scheme correspond to the constraints of the FLP problem and the fact of the scheme is the object...

This paper addresses the application of a modified threshold accepting algorithm (MTA) for minimizing the number of rules in a fuzzy rule-based classification system, while guaranteeing high classification power. In terms of computational time required, the MTA outperforms the GA approaches, which are applied to this multi-objective combinatorial o...

 This paper presents a novel hybrid of the two complimentary technologies of soft computing viz. neural networks and fuzzy logic to design a fuzzy rule based pattern classifier for problems with higher dimensional feature spaces. The neural network component of the hybrid, which acts as a pre-processor, is designed to take care of the all-important...

Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The...

In order to prevent confusion about fuzzy measures and measures of fuzziness, we shall first briefly describe the meaning and features of fuzzy measures. In the late 1970s, Sugeno defined a fuzzy measure as follows: Sugeno [1977]: B is a Borel field of the arbitrary set (universe) X.

In chapter 2, the basic definition of a fuzzy set was given and the original set-theoretic operations were discussed. The membership space was assumed to be the space of real numbers, membership functions were crisp functions, and the operations corresponded essentially to the operations of dual logic or Boolean algebra.

Data bases are one form of modeling parts of the real world. They may contain descriptions of technical systems, of enterprises, of scientific activities, of landscapes (geographical information systems), or other domains. The world of data bases is the world of digital computers, one of the most typical dichotomous systems. It is, therefore, not s...

A fuzzy function is a generalization of the concept of a classical function. A classical function f is a mapping (correspondence) from the domain D of definition of the function into a space S; f(D) ⊆ S is called the range of f. Different features of the classical concept of a function can be considered to be fuzzy rather than crisp. Therefore diff...

The scope of applications of fuzzy sets—increasingly together with neural nets— is very large and still growing continuously. The closer the problem is to human evaluation, intuition, perception, and decision making, the less dichotomous is the problem structure and the more relevant and promising is the application of fuzzy technology.

In the first nine chapters of this book, we covered the basic foundations of the theory of fuzzy sets as they can be considered today in an undisputed fashion. Many more concepts and theories could not be discussed, either because of space limitations, because they cannot yet be considered ready for a textbook, or they are too specific and advanced...

The terms model, theory, and law have been used with a variety of meanings, for a number of purposes, and in many different areas of our lives. It is therefore necessary to define more accurately what we mean by models, theories, and laws in order to describe their interrelationships and to indicate their use before we can specify the requirements...

Most of our traditional tools for formal modeling, reasoning, and computing are crisp, deterministic, and precise in character. By crisp we mean dichotomous, that is, yes-or-no-type rather than more-or-less type. In conventional dual logic, for instance, a statement can be true or false—and nothing in between. In set theory, an element can either b...

As already mentioned in section 1.1, the type of uncertainty modeling chosen is entirely up to the modeler if and when a formal model is under consideration which does not pretend to model reality correctly.

The objective of fuzzy logic control (FLC) systems is to control complex processes by means of human experience. Thus fuzzy control systems and expert systems both stem from the same origins. However, their important differences should not be neglected. Whereas expert systems try to exploit uncertain knowledge acquired from an expert to support use...

The definitions of “expert systems” vary considerably. Rather than specifying here which of the numerous definitions we accept, or introducing an additional definition, we shall just mention a number of features of expert systems, which might be accepted by most designers and users of expert systems and which seem to be of relevance with respect to...

Die Fuzzy Set Theorie (FST) wurde erstmals in der Veröffentlichung von Zadeh [Zadeh 1965] als rem formale Theorie vorgestellt. Sie kann als eine Verallgemeinerung entweder der klassischen Mengenlehre oder der dualen Logik angesehen werden. Zu Beginn wurde sie primär als eine Modellierungssprache für nicht stochastische Unsicherheit angesehen, was z...

For the first time, the principal component analysis has been used to reduce the feature space dimension in fuzzy rule based pattern classifiers. A modified threshold accepting algorithm (MTA) proposed elsewhere by V. Ravi and H.-J. Zimmermann [European Journal of Operational Research 123 (1) (2000) 16–28] has been used to minimize the number of ru...

One goal of scenario analysis is to investigate possible future developments. In order to cover almost all alternatives it is desirable to analyze as many different scenarios as possible. On the other hand the complexity of the analysis grows as the number of scenarios increases. This often limits the number of scenarios considered. At this point d...

This contribution is dedicated to two issues, which are important to engineering applications and, in particular, to nuclear engineering. Dynamic fuzzy data analysis concentrates on the monitoring of dynamic systems . It considers trajectories rather than states and sometimes allows the detection of malfunctions earlier and better than with a compa...

One goal of scenario analysis is to investigate possible future developments. In order to cover almost all alternatives it is desirable to analyze as many different scenarios as possible. On the other hand the complexity of the analy-sis grows as the number of scenarios increases. This often limits the number of scenarios considered. At this point...

In this paper, several kinds of possibility distributions of fuzzy variables are studied in possibilistic linear programming problems to reflect the inherent fuzziness in fuzzy decision problems. Interval and triangular possibility distributions are used to express the non-interactive cases between the fuzzy decision variables, and exponential poss...

The problem of optimizing the reliability of complex systems has been modeled as a fuzzy multi-objective optimization problem. Three different kinds of optimization problems: reliability optimization of a complex system with constraints on cost and weight; optimal redundancy allocation in a multistage mixed system with constraints on cost and weigh...

This paper highlights the need to reduce the dimension of the feature space in classification problems of high dimensions without sacrificing the classification power considerably. We propose a methodology for classification tasks which comprises three phases: (i) feature selection, (ii) automatic generation of fuzzy if–then rules and (iii) reducti...

Uncertainty is involved in many real phenomena. Whether one considers uncertainty explicitly when modeling such a phenomenon is one of the modeling decisions, the result of which will depend on the context. If, however, the modeler decides to consider uncertainty, he or she will have to select the method for modeling it. Some scientists claim that...

In this paper, a kind of decision problem in upper-level decision-making systems is formalized by a set of fuzzy satisfaction levels offered by decision-makers. These fuzzy satisfaction levels leave some feasible region for decision variables. The exponential possibility distributions of decision variables are studied to obtain an approximate regio...

The field of "intelligent interfaces and systems" has seen a fast growth last decade. An impressive number of papers, conference tutorials, and volumes were devoted to the topic. Ten years ago, intelligent systems constituted a rather exotic topic and many were skeptic that such systems amount to more than a nice name. Nowadays, intelligent systems...

This paper focusses on the investigation of a pattern recognition method based on the fuzzy integral. Until now this method has used a general fuzzy measure, which is characterized by exponential complexity. Naturally this led to some difficulties in practical applications of this pattern recognition method. In this paper, a heuristic algorithm for...

Even though the first publication in the area of fuzzy set theory (FST) appeared already in 1965, the development of this theory for almost 20 years remained in the academic realm. Almost all basic concepts, theories and methods were, however, developed during this period. Fuzzy control opened the gate to real applications for FST. Particularly in...

In data analysis, objects are usually represented by feature vectors, each describing a state of an object at a point of time. Most methods for data analysis use only these feature vectors and do not take into account changes over time. They can therefore be called static. But often a “dynamic” approach, which utilizes the feature changes over time...

The main objective of machine diagnosis is the early recognition of mechanical defects in a machine, which is often referred to as preventive maintenance. This may result in the reduction of faults and higher machine availability. Preventive maintenance can be performed periodically in fixed time intervals, by demand due to machine faults, or conti...

Data Analysis can be considered either as “the search for structure in data (J.C. Bezdek and Pal, 1992)or as a way to reduce the complexity of large masses of data. We shall focus in this paper on the second point of view. In order to clarify the terminology of data analysis used throughout this paper a brief description of its general process is g...

Dieser Aufsatz beschäftigt sich ausschließlich mit Anwendungen bzw. der Modellierung von Anwendungen.

Die Fuzzy Set Theorie (FST) wurde erstmals in der Veröffentlichung von Zadeh [29] als rein formale Theorie vorgestellt. Sie kann als eine Verallgemeinerung entweder der klassischen Mengenlehre oder der dualen Logik angesehen werden. Zu Beginn wurde sie primär als eine Modellierungssprache für nichtstochastische Unsicherheit angesehen, was zu einem...

Fuzzy Algorithms for Control gives an overview of the research results of a number of European research groups that are active and play a leading role in the field of fuzzy modeling and control. It contains 12 chapters divided into three parts. Chapters in the first part address the position of fuzzy systems in control engineering and in the AI com...

Since the late 1980s, a large number of very user-friendly tools for fuzzy control, fuzzy expert systems, and fuzzy data analysis have emerged. This has changed the character of this area and started the area of `fuzzy technology'. The next large step in the development occurred in 1992 when almost independently in Europe, Japan and the USA, the th...

An abstract is not available.

Much has been written about the decline of Operational Research. In the 1960s it had already been proclaimed dead and the decreasing number of OR departments in industrial enterprises seems to support this thesis. The question seems to be: ‘Why is OR apparently disappearing at a time when the major obstacles to OR applications in the past, namely l...

We interpret fuzzy linear programming (FLP) problems with fuzzy coe #cients and fuzzy inequality relations as multiple fuzzy reasoning schemes (MFR), where the antecedents of the scheme correspond to the constraints of the FLP problem and the fact of the scheme is the objective of the FLP problem. Then the solution process consists of two steps: fi...

It is argued that very often when talking about the uncertainty of a system people confuse the phenomena with the glasses (theories) which they use to observe or model the uncertain phenomenon. Some experts also claim, that there is only one valid theory or tool (f. i. probability theory) to model all kinds of uncertainty. In this paper it is sugge...

The process of patient care performed by an anaesthesiologist during high invasive surgery requires fundamental knowledge of the physiologic processes and a long standing experience in patient management to cope with the inter-individual variability of the patients. Biomedical engineering research improves the patient monitoring task by providing t...

The main objective of Concurrent Engineering is the reduction of development lead time. This shorter time-to-market is achieved by paralleling development and production activities. With the deliberate use of incomplete and uncertain information an enormous reduction of development lead time can be achieved in comparison to parallel activities whic...

During the last decade, fuzzy logic was successfully used to solve real world problems, in particular in engineering, management, medicine, traffic, etc. Technologies such as fuzzy control, fuzzy data analysis, and fuzzy multi-criteria decision analysis have been developed and used to solve many important applications. However, there is only a smal...

Decision analysis and decision support are an area in which applications of fuzzy set theory have been found since the early 1970s. Still, there are areas, such as fuzzy control, that have gained much wider acceptance in practice than fuzzy decision analysis. This paper describes where fuzzy decision support stands now, and what would have to be do...

The basic idea of Simultaneous Engineering is to parallelize activities in order to reduce the development lead time and thus the time to market. The processing of incomplete and uncertain information can achieve an enormous advantage in comparison to parallelization of activities based on exact information alone. Thus many activities can be starte...

Since L. Zadeh proposed the concept of a fuzzy set in 1965, the relationships between probability theory and fuzzy set theory have been further discussed. Both theories seem to be similar in the sense that both are concerned with some type of uncertainty and both use the [0, 1] interval for their measures as the range of their respective functions...

The complexity of the environment, in which strategic decisions are made, seems to be the main reason why intelligent decision support systems (IDSS, also called active DSS - ADSS) are needed. There are several reasons for the complexity: the information and knowledge for the decisions is incomplete, uncertain or imprecise or even inconsistent, the...

During the last few years intelligent machines appeared in nearly all technical areas, such as consumer electronics, robotics, and industrial control systems. There are for example washing machines that work very effectively, need comparably less power than in the past, and have short execution times because they adjust their washing cycles to each...

Die Theorie unscharfer Mengen (Fuzzy Set Theorie) hat sich nach einer “akademischen Periode” von ungefähr 20 Jahren, in der sie überwiegend bei Wissenschaftlern Interesse weckte, innerhalb der letzten fünf Jahre rasant zu einer Technologie entwickelt, die auch in der Wirtschaft großes Interesse geweckt hat. Der Übergang von der Theorie zur Technolo...

Die Fuzzy Set Theorie erlebte in der letzten Dekade einen wahren Applikationsboom in der Verfahrens- und Produktionstechnik. Diese Anwendungen wurden unter dem Namen Fuzzy Control bekannt [8–1]. Darüber hinaus hat die Kombination von Fuzzy Logik und Neuronalen Netzen ein hohes Interesse gefunden.

The first article on fuzzy set theory appeared in 1965 [8]. Since then, the number of publications in this area has grown to over 15 000. Many of these contributions are in mathematical areas (topology, analysis, graph theory, logic). To an increasing degree, however, this theory has been applied to various areas and has resulted in methods, tools,...

Im Mittelpunkt der Betrachtungen dieses Bandes steht die Frage, ob es einen Gegensatz zwischen Ökonomie und Ökologie gibt und ob hierzu Aussagen der Wirtschafts- und Umweltethik vorliegen. Die Antwort auf diese Fragen hängt sicherlich sehr davon ab, wie Wirtschaftsethik definiert wird und was man unter ›Ökonomie‹ versteht. Die Literatur auf dem Geb...

Behandelt Grundlagen, Perspektiven und Werkzeuge neuronaler Netze und ihre Anwendungen in Zusammenhang mit Fuzzy-Technologien in der Automatisierungstechnik und für die Datenanalyse.