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265
A fusion approach for managing multigranularity linguistic term sets in decision making
, 2000
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Measures of similarity among fuzzy concepts: A comparative analysis
 Int. J. Approx. Reason
, 1987
"... Many measures of similarity among fuzzy sets have been proposed in the literature, and some have been incorporated into linguistic approximation procedures. The motivations behind these measures are both geometric and settheoretic. We briefly review 19 such measures and compare their performance i ..."
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Cited by 60 (1 self)
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Many measures of similarity among fuzzy sets have been proposed in the literature, and some have been incorporated into linguistic approximation procedures. The motivations behind these measures are both geometric and settheoretic. We briefly review 19 such measures and compare their performance in a behavioral experiment. For crudely categorizing pairs of fuzzy concepts as either "'similar " or "'dissimilar, ""all measures performed well. For distinguishing between degrees of similarity or dissimilarity, certain measures were clearly superior and others were clearly inferior; for a few subjects, however, none of the distance measures adequately modeled their similarity judgments. Measures that account for ordering on the base variable proved to be more highly correlated with subjects " actual similarity judgments. And, surprisingly, the best measures were ones that focus on only one "'slice " of the membership function. Such measures are easiest to compute and may provide insight into the way humans judge similarity among fuzzy concepts.
Qualitative and Quantitative Simulation: Bridging the Gap
 Artificial Intelligence
, 1997
"... Shortcomings of qualitative simulation and of quantitative simulation motivate combining them to do simulations exhibiting strengths of both. The resulting class of techniques is called semiquantitative simulation. One approach to semiquantitative simulation is to use numeric intervals to represe ..."
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Cited by 52 (1 self)
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Shortcomings of qualitative simulation and of quantitative simulation motivate combining them to do simulations exhibiting strengths of both. The resulting class of techniques is called semiquantitative simulation. One approach to semiquantitative simulation is to use numeric intervals to represent incomplete quantitative information. In this research we demonstrate semiquantitative simulation using intervals in an implemented semiquantitative simulator called Q3. Q3 progressively refines a qualitative simulation, providing increasingly specific quantitative predictions which can converge to a numerical simulation in the limit while retaining important correctness guarantees from qualitative and interval simulation techniques. Q3's simulations are based on a technique we call step size refinement. While a pure qualitative simulation has a very coarse step size, representing the state of a system trajectory at relatively few qualitatively distinct states, Q3 interpolates newly expl...
A fuzzy sets based linguistic approach: Theory and applications, Approximate Reasoning in Decision Analysis eds
, 1982
"... F~zzy sets theory and fuzzy logic constitute the basis for the l inguist ic approach. Under this approach, variables can assume l inguist ic values. Each l inguis t ic value is characterized by a label and a meaning. The label is a sentence of a language. The meaning is a fuzzy subset of a universe ..."
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Cited by 39 (1 self)
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F~zzy sets theory and fuzzy logic constitute the basis for the l inguist ic approach. Under this approach, variables can assume l inguist ic values. Each l inguis t ic value is characterized by a label and a meaning. The label is a sentence of a language. The meaning is a fuzzy subset of a universe of discourse. Models, based on this approach, can be constructed to simulate approximate reasoning. The implementation of these models presents two major problems, namely how to associate a label to an unlabelled fuzzy set on the basis of semantic s imi lar i ty ( l inguist ic approximation) and how to perform arithmetic operations with fuzzy numbers. For each problem a solution is proposed. Two i l lus t ra t ive applications are discussed. There are situations where i t is more natural to handle uncertainty by fuzzy set theory (Zadeh 1965) than by probability theory. * Such is the case when dealing with the inherent imprecision of concepts involved in human reasoning and natural language. (Lakoff 1973, Zadeh 1975b,~1975c, Hersch 1975, Gaines 1976, Gupta 1977).
A Fuzzy Logic Based Bidding Strategy for Autonomous Agents in Continuous Double Auctions
 IEEE Transactions on Knowledge and Data Engineering
, 2002
"... Increasingly many systems are being conceptualised, designed and implemented as marketplaces in which autonomous software entities (agents) trade services. These services can be commodities in ecommerce applications or data and knowledge services in information economies. In many of these cases, th ..."
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Cited by 34 (9 self)
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Increasingly many systems are being conceptualised, designed and implemented as marketplaces in which autonomous software entities (agents) trade services. These services can be commodities in ecommerce applications or data and knowledge services in information economies. In many of these cases, there are both multiple agents that are looking to procure services and multiple agents that are looking to sell services at any one time. Such marketplaces are termed continuous double auctions (CDAs). Against this background, this paper develops new algorithms that buyer and seller agents can use to participate in CDAs. These algorithms employ heuristic fuzzy rules and fuzzy reasoning mechanisms in order to determine the best bid to make given the state of the marketplace. Moreover, we show how an agent can dynamically adjust its bidding behaviour to respond e ectively to changes in the supply and demand in the marketplace. We then show, by empirical evaluations, how our agents outperform four of the most prominent algorithms previously developed for CDAs (several of which have been shown to outperform human bidders in experimental studies).
Error Estimations For Indirect Measurements: Randomized Vs. Deterministic Algorithms For "BlackBox" Programs
 HANDBOOK ON RANDOMIZED COMPUTING, KLUWER, 2001
, 2000
"... In many reallife situations, it is very difficult or even impossible to directly measure the quantity y in which we are interested: e.g., we cannot directly measure a distance to a distant galaxy or the amount of oil in a given well. Since we cannot measure such quantities directly, we can measure ..."
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Cited by 32 (15 self)
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In many reallife situations, it is very difficult or even impossible to directly measure the quantity y in which we are interested: e.g., we cannot directly measure a distance to a distant galaxy or the amount of oil in a given well. Since we cannot measure such quantities directly, we can measure them indirectly: by first measuring some relating quantities x1 ; : : : ; xn , and then by using the known relation between x i and y to reconstruct the value of the desired quantity y. In practice, it is often very important to estimate the error of the resulting indirect measurement. In this paper, we describe and compare different deterministic and randomized algorithms for solving this problem in the situation when a program for transforming the estimates e x1 ; : : : ; e xn for x i into an estimate for y is only available as a black box (with no source code at hand). We consider this problem in two settings: statistical, when measurements errors \Deltax i = e x i \Gamma x i are inde...
Support Vector Learning for Fuzzy RuleBased Classification Systems
, 2003
"... To design a fuzzy rulebased classi cation system (fuzzy classi er) with good generalization abilityina high dimensional feature space has been an active research topic for a long time. As a powerful machine learning approach for pattern recognition problems, support vector machine (SVM) is known to ..."
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Cited by 29 (1 self)
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To design a fuzzy rulebased classi cation system (fuzzy classi er) with good generalization abilityina high dimensional feature space has been an active research topic for a long time. As a powerful machine learning approach for pattern recognition problems, support vector machine (SVM) is known to have good generalization ability. More importantly, an SVM can work very well on a high (or even in nite) dimensional feature space. This paper investigates the connection between fuzzy classi ers and kernel machines, establishes a link between fuzzy rules and kernels, and proposes a learning algorithm for fuzzy classi ers. We rst show that a fuzzy classi er implicitly de nes a translation invariant kernel under the assumption that all membership functions associated with the same input variable are generated from location transformation of a reference function. Fuzzy inference on the IFpart of a fuzzy rule can be viewed as evaluating the kernel function. The kernel function is then proven to be a Mercer kernel if the reference functions meet certain spectral requirement. The corresponding fuzzy classi er is named positive de  nite fuzzy classi er (PDFC). A PDFC can be built from the given training samples based on a support vector learning approach with the IFpart fuzzy rules given by the support vectors. Since the learning process minimizes an upper bound on the expected risk (expected prediction error) instead of the empirical risk (training error), the resulting PDFC usually has good generalization. Moreover, because of the sparsity properties of the SVMs, the number of fuzzy rules is irrelevant to the dimension of input space. In this sense, we avoid the "curse of dimensionality." Finally, PDFCs with dierent reference functions are constructed using the su...
www.elsevier.com/locate/fss Operations on type2 fuzzy sets
, 2000
"... In this paper, we discuss set operations on type2 fuzzy sets (including join and meet under minimum=product tnorm), algebraic operations, properties ofmembership grades oftype2 sets, and type2 relations and their compositions. All this is needed to implement a type2 fuzzy logic system (FLS). c ..."
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Cited by 22 (2 self)
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In this paper, we discuss set operations on type2 fuzzy sets (including join and meet under minimum=product tnorm), algebraic operations, properties ofmembership grades oftype2 sets, and type2 relations and their compositions. All this is needed to implement a type2 fuzzy logic system (FLS). c ○ 2001 Elsevier Science B.V. All rights reserved.
Preference modelling
 State of the Art in Multiple Criteria Decision Analysis
, 2005
"... This paper provides the reader with a presentation of preference modelling fundamental notions as well as some recent results in this field. Preference modelling is an inevitable step in a variety of fields: economy, sociology, psychology, mathematical programming, even medicine, archaeology, and ob ..."
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Cited by 19 (1 self)
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This paper provides the reader with a presentation of preference modelling fundamental notions as well as some recent results in this field. Preference modelling is an inevitable step in a variety of fields: economy, sociology, psychology, mathematical programming, even medicine, archaeology, and obviously decision analysis. Our notation and some basic definitions, such as those of binary relation, properties and ordered sets, are presented at the beginning of the paper. We start by discussing different reasons for constructing a model or preference. We then go through a number of issues that influence the construction of preference models. Different formalisations besides classical logic such as fuzzy sets and nonclassical logics become necessary. We then present different types of preference structures reflecting the behavior of a decisionmaker: classical, extended and valued ones. It is relevant to have a numerical representation of preferences: functional representations, value functions. The concepts of thresholds and minimal representation are also introduced in this section. In section 7, we briefly explore the concept of deontic logic (logic of preference) and other formalisms associated with &quot;compact representation of preferences &quot; introduced for special purposes. We end the paper with some concluding remarks.
The Set of Fuzzy Rational Numbers and Flexible Querying
 Journal of Fuzzy Sets and Systems
, 2005
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