Hans-Jürgen Zimmermann

Bio: Hans-Jürgen Zimmermann is an academic researcher from RWTH Aachen University. The author has contributed to research in topics: Fuzzy logic & Fuzzy set. The author has an hindex of 37, co-authored 147 publications receiving 11234 citations.

Fuzzy sets theory and applications

Abstract: 1: Some theoretical Aspects.- 1.1 Mathematics and fuzziness.- 1.2 Radon-Nikodym Theorem for fuzzy set-valued measures.- 1.3 Construction of a probability distribution from a fuzzy information.- 1.4 Convolution of fuzzyness and probability.- 1.5 Fuzzy sets and subobjects.- 2: From theory to applications.- 2.1 Outline of a theory of usuality based on fuzzy logic.- 2.2 Fuzzy sets theory and mathematical programming.- 2.3 Decisions with usual values.- 2.4 Support logic programming.- 2.5 Hybrid data - various associations between fuzzy subsets and random variables.- 2.6 Fuzzy relation equations : methodology and applications.- 3: Various particular applications.- 3.1 Multi criteria decision making in crisp and fuzzy environments.- 3.2 Fuzzy subsets applications in O.R. and management.- 3.3 Character recognition by means of fuzzy set reasoning.- 3.4 Computerized electrocardiography and fuzzy sets.- 3.5 Medical applications with fuzzy sets.- 3.6 Fuzzy subsets in didactic processes.

Fuzzy set theory

Abstract: Seit Beginn der neunziger Jahre wird unter dem Schlagwort źFuzzy Logic" von einer Vielzahl von Anwendungen der Theorie unscharfer Mengen vor allem in Japan berichtet. Dies hat in Europa und hier insbesondere in Deutschland zu einem Umdenken bei Wissenschaftlern und Praktikern gefuhrt, die lange Zeit die Potentiale der neuen Technologie verkannten. Nun ist schlagartig eine sehr groβe Nachfrage nach Informationen zu diesem Thema entstanden. Dieser Artikel gibt einen Uberblick uber die wesentlichen Grundlagen der Theorie unscharfer Mengen und zeigt potentielle Anwendungen auf. Since the beginning nineties, entitled with the catchword "Fuzzy Logic" reports have been given on numerous, predominantly Japanese applications of fuzzy set theory. This had brought about a change in thinking for scientists and practitioners in Europe and, in particular, in Germany. Had the potentials of this new technology for a long time been underestimated, there now suddenly springs up a very high demand for information on this topic. This article gives a survey of the fundamentals of fuzzy set theory and describes potential applications.

Fuzzy global optimization of complex system reliability

Abstract: 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 weight; and optimal reliability allocation in a multistage mixed system with constraints on cost, weight, and volume have been solved. Four numerical examples have been solved to demonstrate the effectiveness of the present methodology. The influence of various kinds of aggregators is also studied. The inefficiency of the noncompensatory min operator has been demonstrated. One of the well-known global optimization meta-heuristics, the threshold accepting, has been invoked to take care of the optimization part of the model. A software has been developed to implement the above model. The results obtained are encouraging.

Fuzzy Set Theory - and Its Applications

Abstract: 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 book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.

Fuzzy Sets and Fuzzy Logic: Theory and Applications

Abstract: Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets, Uncertainty, and Information—an earlier work of Professor Klir and Tina Folger—Fuzzy Sets and Fuzzy Logic addresses practically every significant topic in the broad expanse of the union of fuzzy set theory and fuzzy logic. To me Fuzzy Sets and Fuzzy Logic is a remarkable achievement; it covers its vast territory with impeccable authority, deep insight and a meticulous attention to detail. To view Fuzzy Sets and Fuzzy Logic in a proper perspective, it is necessary to clarify a point of semantics which relates to the meanings of fuzzy sets and fuzzy logic. A frequent source of misunderstanding fias to do with the interpretation of fuzzy logic. The problem is that the term fuzzy logic has two different meanings. More specifically, in a narrow sense, fuzzy logic, FLn, is a logical system which may be viewed as an extension and generalization of classical multivalued logics. But in a wider sense, fuzzy logic, FL^ is almost synonymous with the theory of fuzzy sets. In this context, what is important to recognize is that: (a) FLW is much broader than FLn and subsumes FLn as one of its branches; (b) the agenda of FLn is very different from the agendas of classical multivalued logics; and (c) at this juncture, the term fuzzy logic is usually used in its wide rather than narrow sense, effectively equating fuzzy logic with FLW In Fuzzy Sets and Fuzzy Logic, fuzzy logic is interpreted in a sense that is close to FLW. However, to avoid misunderstanding, the title refers to both fuzzy sets and fuzzy logic. Underlying the organization of Fuzzy Sets and Fuzzy Logic is a fundamental fact, namely, that any field X and any theory Y can be fuzzified by replacing the concept of a crisp set in X and Y by that of a fuzzy set. In application to basic fields such as arithmetic, topology, graph theory, probability theory and logic, fuzzification leads to fuzzy arithmetic, fuzzy topology, fuzzy graph theory, fuzzy probability theory and FLn. Similarly, hi application to applied fields such as neural network theory, stability theory, pattern recognition and mathematical programming, fuzzification leads to fuzzy neural network theory, fuzzy stability theory, fuzzy pattern recognition and fuzzy mathematical programming. What is gained through fuzzification is greater generality, higher expressive power, an enhanced ability to model real-world problems and, most importantly, a methodology for exploiting the tolerance for imprecision—a methodology which serves to achieve tractability,

Fuzzy logic in control systems: fuzzy logic controller. II

Abstract: For pt.I see ibid., vol.20, no.2, p.404-18, 1990. The basic aspects of the FLC (fuzzy logic controller) decision-making logic are examined. Several issues, including the definitions of a fuzzy implication, compositional operators, the interpretations of the sentence connectives 'and' and 'also', and fuzzy inference mechanisms, are investigated. Defuzzification strategies, are discussed. Some of the representative applications of the FLC, from laboratory level to industrial process control, are briefly reported. Some unsolved problems are described, and further challenges in this field are discussed. >

Fuzzy logic in control systems : fuzzy logic controller. Part II

Abstract: During the past several years, fuzzy control has emerged as one of the most active and fruitful areas for research in the applications of fuzzy set theory. Fuzzy control is based on fuzzy logic. The fuzzy logic controller (FLC) based on fuzzy logic provides a means of converting a linguistic control strategy based on expert knowledge into an automatic control strategy. A survey of the FLC is presented; a general methodology for constructing an FLC and assessing its performance is described; and problems that need further research are pointed out