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The Paradoxical Success of Fuzzy Logic
 IEEE Expert
, 1993
"... Applications of fuzzy logic in heuristic control have been highly successful, but which aspects of fuzzy logic are essential to its practical usefulness? This paper shows that an apparently reasonable version of fuzzy logic collapses mathematically to twovalued logic. Moreover, there are few if any ..."
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Applications of fuzzy logic in heuristic control have been highly successful, but which aspects of fuzzy logic are essential to its practical usefulness? This paper shows that an apparently reasonable version of fuzzy logic collapses mathematically to twovalued logic. Moreover, there are few if any published reports of expert systems in realworld use that reason about uncertainty using fuzzy logic. It appears that the limitations of fuzzy logic have not been detrimental in control applications because current fuzzy controllers are far simpler than other knowledgebased systems. In the future, the technical limitations of fuzzy logic can be expected to become important in practice, and work on fuzzy controllers will also encounter several problems of scale already known for other knowledgebased systems. 1
Design of a largescale expert system using fuzzy logic for uncertaintyreasoning
, 1994
"... There exist in the literature today many contributions dealing with the incorporation of fuzzy logic in expert systems. But, unfortunately, much of what has been proposed can only be applied tosmallscale expert systems, that is when the number of rules is in the dozens as opposed to in the hundreds ..."
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There exist in the literature today many contributions dealing with the incorporation of fuzzy logic in expert systems. But, unfortunately, much of what has been proposed can only be applied tosmallscale expert systems, that is when the number of rules is in the dozens as opposed to in the hundreds. Rete networks have been used in the more traditional expert systems to ameliorate the computational burden that would be associated with matching all the rules with all the facts on each cycle of the inference engine. In this paper, we present a more general Rete network that is particularly suitable for reasoning with fuzzy logic. In our new class of Rete networks, before anyfactsbecome available, there are the fuzzy membership functions associated with the di erent terms in the ruleantecedents. Upon the assertion of a fact into the working memory, the pattern matcher \pushes &quot; the fact into the appropriate branches of the network and calculates via a supmin operation the degree of match between the fact and the rule term. This degreeofmatch number is then propagated down the rest of the network in keeping with the rules of the fuzzy logic employed. 1
Fuzzy Concepts and Formal Methods: A Fuzzy Logic Toolkit for Z
 In To Appear in Proceedings for ZB2000
, 2000
"... It has been recognised that formal methods are useful as a modelling tool in requirements engineering. Specification languages such as Z permit the precise and unambiguous modelling of system properties and behaviour. However some system problems, particularly those drawn from the IS problem domain, ..."
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It has been recognised that formal methods are useful as a modelling tool in requirements engineering. Specification languages such as Z permit the precise and unambiguous modelling of system properties and behaviour. However some system problems, particularly those drawn from the IS problem domain, may be difficult to model in crisp or precise terms. It may also be desirable that formal modelling should commence as early as possible, even when our understanding of parts of the problem domain is only approximate. This paper suggests fuzzy set theory as a possible representation scheme for this imprecision or approximation.
Fuzzy Concepts and Formal Methods: Some Illustrative Examples
 In Proceedings of the Seventh AsiaPacific Software Engineering Conference
, 1999
"... It has been recognised that formal methods are useful as a modelling tool in requirements engineering. Specification languages such as Z permit the precise and unambiguous modelling of system properties and behaviour. However some system problems, particularly those drawn from the IS problem domain, ..."
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It has been recognised that formal methods are useful as a modelling tool in requirements engineering. Specification languages such as Z permit the precise and unambiguous modelling of system properties and behaviour. However some system problems, particularly those drawn from the IS problem domain, may be difficult to model in crisp or precise terms.
Classification and Approximation with RuleBased Networks
, 1993
"... This thesis describes the architecture of learning systems which can explain their decisions through a rulebased knowledge representation. Two problems in learning are addressed: pattern classification and function approximation. In Part I, a pattern classifier for discretevalued problems is prese ..."
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This thesis describes the architecture of learning systems which can explain their decisions through a rulebased knowledge representation. Two problems in learning are addressed: pattern classification and function approximation. In Part I, a pattern classifier for discretevalued problems is presented. The system utilizes an informationtheoretic algorithm for constructing informative rules from example data. These rules are then used to construct a computational network to perform parallel inference and posterior probability estimation. The network can be extended incrementally; that is, new data can be incorporated without repeating the training on previous data. It is shown that this technique performs comparably with other techniques including the backpropagation network while having unique advantages in incremental learning capability, training efficiency, and knowledge representation. Examples are shown of rulebased classification and explanation. In Part II, we present a metho...
AND CONCEPCION
"... VARIOUSMATHEMATICAL TOOLS AND THEORIES have found application in Library and Information Science (LIS).One of these is Fuzzy Set Theory (FST).FST is a generalization of classical Set Theory, designed to better model situations where membership of a set is not discrete but is “fuzzy.” The theory date ..."
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VARIOUSMATHEMATICAL TOOLS AND THEORIES have found application in Library and Information Science (LIS).One of these is Fuzzy Set Theory (FST).FST is a generalization of classical Set Theory, designed to better model situations where membership of a set is not discrete but is “fuzzy.” The theory dates from 1965,when Lotfi Zadeh published his seminal paper on the topic. As well as mathematical developments and extensions of the theory itself, there have been many applications of FST to such diverse areas as medical diagnoses and washing machines. The theory has also found application in a number of aspects of LIS. Information Retrieval (IR) is one area where FST can prove useful; this paper reviews IR applications of FST. Another major area of Information Science in which FST has found application is Informetrics; these studies are also reviewed. A few examples of the use of this theory in nonLIS domains are also examined. BACKGROUND When an information professional is confronted with a problem, there may be many different ways to tackle it. In the armoury of the profession, there are a number of tools and techniques that can be drawn upon to address the situation. A good problem solver needs to be aware of a wide range of tools that can be used in that particular situation. Tools developed for one specific situation may be applicable to others, though they be quite different. One class of tools that can be applied to library problems are mathematical tools. Mathematical tools are indispensable for solving a
Fuzzy Concepts and Formal Methods: Sample Specification for a Fuzzy Expert System
"... A fuzzy logic toolkit has been developed for the formal specification language Z. It permits the incorporation of fuzzy concepts into the language while retaining the precision of any Z specification. The toolkit provides the necessary operators, measures and modifiers for the definition and manipul ..."
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A fuzzy logic toolkit has been developed for the formal specification language Z. It permits the incorporation of fuzzy concepts into the language while retaining the precision of any Z specification. The toolkit provides the necessary operators, measures and modifiers for the definition and manipulation of fuzzy sets and relations. This paper illustrates how the toolkit can be used to specify a simple fuzzy expert system. The focus is on the specification of the rule base and the operations necessary for fuzzy inferencing. In particular the example illustrates the use of the fuzzy cartesian product and fuzzy set truncation operators and offers a generic definition for a centroid defuzzification function.
Fuzzy Concepts and Formal Methods
, 2002
"... It has been recognised that formal methods are useful as a modelling tool in requirements engineering. Specification languages such as Z permit the precise and unambiguous modelling of system properties and behaviour. However some system problems, particularly those drawn from the IS problem domain, ..."
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It has been recognised that formal methods are useful as a modelling tool in requirements engineering. Specification languages such as Z permit the precise and unambiguous modelling of system properties and behaviour. However some system problems, particularly those drawn from the IS problem domain, maybe difficult to model in crisp or precise terms. It mayalsobe desirable that formal modelling should commence as early as possible, even when our understanding of parts of the problem domain is only approximate. This chapter identifies the problem types of interest and argues that they are characterised by uncertainty and imprecision. It suggests fuzzy set theory as a useful formalism for modelling aspects of this imprecision. The chapter provides a summary of a toolkit for Z that defines the operators, measures and modifiers necessary for the manipulation of fuzzy sets and relations. It also illustrates, through a series of examples, howthe toolkit could be applied. The chapter concludes with a reflection on some more general issues that arose during the formulation of the illustrative examples.