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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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Cited by 69 (1 self)
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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
Toward a generalized theory of uncertainty (GTU)An outline
 Information Sciences
, 2005
"... It is a deepseated tradition in science to view uncertainty as a province of probability theory. The generalized theory of uncertainty (GTU) which is outlined in this paper breaks with this tradition and views uncertainty in a much broader perspective. Uncertainty is an attribute of information. A ..."
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Cited by 39 (1 self)
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It is a deepseated tradition in science to view uncertainty as a province of probability theory. The generalized theory of uncertainty (GTU) which is outlined in this paper breaks with this tradition and views uncertainty in a much broader perspective. Uncertainty is an attribute of information. A fundamental premise of GTU is that information, whatever its form, may be represented as what is called a generalized constraint. The concept of a generalized constraint is the centerpiece of GTU. In GTU, a probabilistic constraint is viewed as a special––albeit important––instance of a generalized constraint. A generalized constraint is a constraint of the form X isr R, where X is the constrained variable, R is a constraining relation, generally nonbivalent, and r is an indexing variable which identifies the modality of the constraint, that is, its semantics. The
What Are Fuzzy Rules and How to Use Them
 Fuzzy Sets and Systems
, 1996
"... Fuzzy rules have been advocated as a key tool for expressing pieces of knowledge in "fuzzy logic". However, there does not exist a unique kind of fuzzy rules, nor is there only one type of "fuzzy logic". This diversity has caused many a misunderstanding in the literature of fuzzy control. The paper ..."
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Cited by 31 (12 self)
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Fuzzy rules have been advocated as a key tool for expressing pieces of knowledge in "fuzzy logic". However, there does not exist a unique kind of fuzzy rules, nor is there only one type of "fuzzy logic". This diversity has caused many a misunderstanding in the literature of fuzzy control. The paper is a survey of different possible semantics for a fuzzy rule and shows how they can be captured in the framework of fuzzy set and possibility theory. It is pointed out that the interpretation of fuzzy rules dictates the way the fuzzy rules should be combined. The various kinds of fuzzy rules considered in the paper (gradual rules, certainty rules, possibility rules, and others) have different inference behaviors and correspond to various intended uses and applications. The representation of fuzzy unlessrules is briefly investigated on the basis of their intended meaning. The problem of defining and checking the coherence of a block of parallel fuzzy rules is also briefly addressed. This iss...
A systematic approach to the assessment of fuzzy association rules. Data Mining and Knowledge Discovery
, 2006
"... In order to allow for the analysis of data sets including numerical attributes, several generalizations of association rule mining based on fuzzy sets have been proposed in the literature. While the formal specification of fuzzy associations is more or less straightforward, the assessment of such ru ..."
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Cited by 30 (6 self)
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In order to allow for the analysis of data sets including numerical attributes, several generalizations of association rule mining based on fuzzy sets have been proposed in the literature. While the formal specification of fuzzy associations is more or less straightforward, the assessment of such rules by means of appropriate quality measures is less obvious. Particularly, it assumes an understanding of the semantic meaning of a fuzzy rule. This aspect has been ignored by most existing proposals, which must therefore be considered as adhoc to some extent. In this paper, we develop a systematic approach to the assessment of fuzzy association rules. To this end, we proceed from the idea of partitioning the data stored in a database into examples of a given rule, counterexamples, and irrelevant data. Evaluation measures are then derived from the cardinalities of the corresponding subsets. The problem of finding a proper partition has a rather obvious solution for standard association rules but becomes less trivial in the fuzzy case. Our results not only provide a sound justification for commonly used measures but also suggest a means for constructing meaningful alternatives. 1.
A Logical Approach To Interpolation Based On Similarity Relations
, 1996
"... One of the possible semantics of fuzzy sets is in terms of similarity, namely a grade of membership of an item in a fuzzy set can be viewed as the degree of resemblance between this item and prototypes of the fuzzy set. In such a framework, an interesting question is how to devise a logic of similar ..."
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Cited by 25 (11 self)
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One of the possible semantics of fuzzy sets is in terms of similarity, namely a grade of membership of an item in a fuzzy set can be viewed as the degree of resemblance between this item and prototypes of the fuzzy set. In such a framework, an interesting question is how to devise a logic of similarity, where inference rules can account for the proximity between interpretations. The aim is to capture the notion of interpolation inside a logical setting. In this paper, we investigate how a logic of similarity dedicated to interpolation can be defined, by considering different natural consequence relations induced by the presence of a similarity relation on the set of interpretations. These consequence relations are axiomatically characterized in a way that parallels the characterization of nonmonotonic consequence relationships. It is shown how to reconstruct the similarity relation underlying a given family of consequence relations that obey the axioms. Our approach strikingly differs ...
Fuzzy Rules in CaseBased Reasoning
 in Conf. AFIA99 Raisonnement à Partir de Cas
, 1999
"... Similaritybased fuzzy rules are proposed as a basic tool for modelling and formalizing parts of the casebased reasoning methodology within the framework of approximate reasoning. The use of different types of rules for encoding the heuristic reasoning principle underlying casebased problem s ..."
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Cited by 4 (0 self)
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Similaritybased fuzzy rules are proposed as a basic tool for modelling and formalizing parts of the casebased reasoning methodology within the framework of approximate reasoning. The use of different types of rules for encoding the heuristic reasoning principle underlying casebased problem solving is discussed, which leads to different approaches to casebased inference. A model which combines a constraintbased and an exampleoriented approach is advocated more particularly. Besides, the use of modifiers in fuzzy rules is proposed for adapting the proposed formal model to the respective applications, and the problem of determining appropriate modifiers is considered in the context of casebased learning. 1 Introduction The guiding principle underlying most casebased reasoning (Cbr) systems is the "Cbr hypothesis" which, loosely spoken, assumes that "similar problems have similar solutions." More precisely, the idea of Cbr is to exploit the experience from similar ...
Rule model simplification
 Proc. Workshop on Computer Graphics
, 2006
"... Due to its high performance and comprehensibility, fuzzy modelling is becoming more and more popular in dealing with nonlinear, uncertain and complex systems for tasks such as signal processing, medical diagnosis and financial investment. However, there are no principal routine methods to obtain the ..."
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Cited by 3 (1 self)
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Due to its high performance and comprehensibility, fuzzy modelling is becoming more and more popular in dealing with nonlinear, uncertain and complex systems for tasks such as signal processing, medical diagnosis and financial investment. However, there are no principal routine methods to obtain the optimum fuzzy rule base which is not only compact but also retains high prediction (or classification) performance. In order to achieve this, two major problems need to be addressed. First, as the number of input variables increases, the number of possible rules grows exponentially (termed curse of dimensionality). It inevitably deteriorates the transparency of the rule model and can lead to overfitting, with the model obtaining high performance on the training data but failing to predict the unknown data successfully. Second, gaps may occur in the rule base if the problem is too compact (termed sparse rule base). As a result, it cannot be handled by conventional fuzzy inference such as Mamdani. This Ph.D. work proposes a rule base simplification method and a family of fuzzy interpolation methods to solve the aforementioned two problems. The proposed sim
Mining Gradual Dependencies Based on Fuzzy Rank Correlation. In Combining Soft Computing and Statistical Methods in Data Analysis
 Eds.) Advances in Intelligent and Soft Computing
, 2010
"... Abstract We propose a novel framework and an algorithm for mining gradual dependencies between attributes in a data set. Our approach is based on the use of fuzzy rank correlation for measuring the strength of a dependency. It can be seen as a unification of previous approaches to evaluating gradual ..."
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Cited by 3 (1 self)
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Abstract We propose a novel framework and an algorithm for mining gradual dependencies between attributes in a data set. Our approach is based on the use of fuzzy rank correlation for measuring the strength of a dependency. It can be seen as a unification of previous approaches to evaluating gradual dependencies and captures both, qualitative and quantitative measures of association as special cases. 1
A Fuzzy Set Approach to CaseBased Decision
"... : This paper is an attempt at providing a fuzzy setbased approach to casebased decision. Casebased decision consists in selecting an action to be applied to a current problem on the basis of a set of cases storing the results of various actions applied to similar, previously encountered, problems ..."
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Cited by 3 (2 self)
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: This paper is an attempt at providing a fuzzy setbased approach to casebased decision. Casebased decision consists in selecting an action to be applied to a current problem on the basis of a set of cases storing the results of various actions applied to similar, previously encountered, problems. Recently, Gilboa and Schmeidler have presented an axiomatic justification of a counterpart of the expected utility used in decision under uncertainty, where similarity degrees play a role somewhat analogous to probability, and have proposed to apply it to casebased decision. This proposal resembles Sugeno's approach to fuzzy control. The relation between the two approaches is investigated. Besides, another approach, based on possibility and necessity measures, is presented and discussed. The idea is to favor actions which have never given bad results in problems similar to the current problem. A much more permissive view considers all the actions which have given good results (at least on...
DominanceBased Rough Set Approach to CaseBased Reasoning
"... Abstract. Casebased reasoning is a paradigm in machine learning whose idea is that a new problem can be solved by noticing its similarity to a set of problems previously solved. We propose a new approach to casebased reasoning. It is based on rough set theory that is a mathematical theory for reas ..."
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Cited by 2 (2 self)
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Abstract. Casebased reasoning is a paradigm in machine learning whose idea is that a new problem can be solved by noticing its similarity to a set of problems previously solved. We propose a new approach to casebased reasoning. It is based on rough set theory that is a mathematical theory for reasoning about data. More precisely, we adopt Dominancebased Rough Set Approach (DRSA) that is particularly appropriate in this context for its ability of handling monotonicity relationship between ordinal properties of data related to monotonic relationships between attribute values in the considered data set. In general terms, monotonicity concerns relationship between different aspects of a phenomenon described by data: for example, “the larger the house, the higher its price ” or “the closer the house to the city centre, the higher its price”. In the perspective of casebased reasoning, we propose to consider monotonicity of the type “the more similar is y to x, the more credible is that y belongs to the same set as x”. We show that rough approximations and decision rules induced from these approximations can be redefined in this context and that they satisfy the same fundamental properties of classical rough set theory. 1