Author

# Hans-Jürgen Zimmermann

Bio: Hans-Jürgen Zimmermann is an academic researcher from RWTH Aachen University. The author has contributed to research in topic(s): Fuzzy logic & Fuzzy set. The author has an hindex of 37, co-authored 147 publication(s) receiving 11234 citation(s).

##### Papers

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TL;DR: It is shown that solutions obtained by fuzzy linear programming are always efficient solutions and the consequences of using different ways of combining individual objective functions in order to determine an “optimal” compromise solution are shown.

Abstract: In the recent past numerous models and methods have been suggested to solve the vectormaximum problem. Most of these approaches center their attention on linear programming problems with several objective functions. Apart from these approaches the theory of fuzzy sets has been employed to formulate and solve fuzzy linear programming problems. This paper presents the application of fuzzy linear programming approaches to the linear vectormaximum problem. It shows that solutions obtained by fuzzy linear programming are always efficient solutions. It also shows the consequences of using different ways of combining individual objective functions in order to determine an “optimal” compromise solution.

3,117 citations

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01 Jan 1987-

TL;DR: This book discusses the Logic of Decisions, Behavioral Decision Theory, and Decision Technology, as well as an Interactive Decision Support System for Fuzzy and Semi-fuzzy Multi-Objective Problems.

Abstract: 1 Introduction.- The Logic of Decisions, Behavioral Decision Theory, and Decision Technology.- Optimization, Outranking, Evaluation.- Basics of Fuzzy Set Theory.- 2 Individual Decision Making in Fuzzy Environments.- Symmetrical Models.- Nonsymmetrical Models.- Fuzzy Utilities.- 3 Multi-Person Decision Making in Fuzzy Environments.- Basic Models.- Fuzzy Games.- Fuzzy Team Theory.- Fuzzy Group Decision Making.- 4 Fuzzy Mathematical Programming.- Fuzzy Linear and Nonlinear Programming.- Fuzzy Multi-Stage Programming.- 5 Multi-Criteria Decision Making in Ill-Structured Situations.- Fuzzy Multi-Criteria Programming.- Multi-Attribute Decision Making (MADM).- Fuzzy Outranking.- 6 Operators and Membership Functions in Decision Models.- Axiomatic, Pragmatic, and Empirical Justification.- The Measurement of Membership Functions.- Selecting Appropriate Operators in Decision Models.- 7 Decision Support Systems.- Knowledge-Based vs. Data-Based Systems.- Linguistic Variables, Fuzzy Logic, Approximate Reasoning.- An Interactive Decision Support System for Fuzzy and Semi-fuzzy Multi-Objective Problems.- Expert Systems and Fuzzy Sets.

1,190 citations

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TL;DR: The results of the experiments support the hypothesis that people often use compensatory procedures and suggest a new class of operators which varies with respect to a parameter of compensation.

Abstract: The interpretation of a decision as the intersection of fuzzy sets, computed by applying either the minimum or the product operator to the membership functions of the fuzzy sets concerned implies that there is no compensation between low and high degrees of membership. If, on the other hand, a decision is defined to be the union of fuzzy sets, represented by the maximum or algebraic sum of the degrees of membership, full compensation is assumed. Managerial decisions hardly even represent any of these extremes. The aggregation of subjective categories in the framework of human decisions or evaluations almost always shows some degree of compensation. This indicates that human beings partially are using non-verbal aggregation procedures which do not correspond to the verbal and logical connectives ‘and’ and ‘or’. The results of our experiments support the hypothesis that people often use compensatory procedures. Several well-known operators are tested. However, they do not predict our data very well. Therefore a new class of operators is suggested which varies with respect to a parameter of compensation. Our data do confirm this concept.

886 citations

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TL;DR: Fuzzy linear programming belongs to goal programming in the sense that implicitly or explicitly aspiration levels have to be defined at which the membership functions of the fuzzy sets reach their maximum or minimum.

Abstract: This chapter introduces a type of mathematical programming, in which not all constraints have to be crisp, i.e. in which certain violations of the constraints are tolerable. Also the goals do not have to be maximized or minimized as in classical mathematical programming, they are substituted by aspiration levels, that have to be met as well as possible. Sensitivity analysis and parametric programming are involved in two ways. Since different kinds of constraints exist in fuzzy linear programming sensitivity analysis becomes more complicated and can lead to additional insights. Parametric programming can be used to arrive at a fuzzy set “decision”, starting from a crisp maximizing decision.

551 citations

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TL;DR: This paper deals with the properties of their methods in the case of 'generalized modus tollens', and investigates the other new fuzzy reasoning methods obtained by introducing the implication rules of many valued logic systems.

Abstract: L.A. Zadeh, E.H. Mamdani, and M. Mizumoto et al. have proposed methods for fuzzy reasoning in which the antecedent involves a fuzzy conditional proposition 'If x is A then y is B', with A and B being fuzzy concepts. Mizumoto et al. have investigated the properties of their methods in the case of 'generalized modus ponens'. This paper deals with the properties of their methods in the case of 'generalized modus tollens', and investigates the other new fuzzy reasoning methods obtained by introducing the implication rules of many valued logic systems. Finally, the properties of syllogism and contrapositive are investigated under each fuzzy reasoning method.

484 citations

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31 Jul 1985-

TL;DR: The book updates the research agenda 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.

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.

7,661 citations

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01 Jan 1995-

TL;DR: Fuzzy Sets and Fuzzy Logic is a true magnum opus; it addresses practically every significant topic in the broad expanse of the union of fuzzy set theory and fuzzy logic.

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,

7,039 citations

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01 Apr 1990-

TL;DR: The basic aspects of the FLC (fuzzy logic controller) decision-making logic are examined and 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.

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. >

5,371 citations

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TL;DR: 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.

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

4,823 citations

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TL;DR: It is shown that solutions obtained by fuzzy linear programming are always efficient solutions and the consequences of using different ways of combining individual objective functions in order to determine an “optimal” compromise solution are shown.

Abstract: In the recent past numerous models and methods have been suggested to solve the vectormaximum problem. Most of these approaches center their attention on linear programming problems with several objective functions. Apart from these approaches the theory of fuzzy sets has been employed to formulate and solve fuzzy linear programming problems. This paper presents the application of fuzzy linear programming approaches to the linear vectormaximum problem. It shows that solutions obtained by fuzzy linear programming are always efficient solutions. It also shows the consequences of using different ways of combining individual objective functions in order to determine an “optimal” compromise solution.

3,117 citations