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Edge detection on interval-valued images

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Advances in Intelligent and Soft Computing 2011年 107卷 325-337页

作者： Lopez-Molina, C. De Baets, B. Barrenechea, E. Bustince, H. Dpto. Automatica y Computacion Universidad Publica de Navarra Spain Department of Applied Mathematics Biometrics and Process Control Ghent University Belgium

ISBN: (纸本)9783642240003

A digital image is an approximation of some real situation, and carries some uncertainty. In this work we model the ambiguity related to the brightness by associating an interval with each pixel, instead of a scalar brightness value. Then we adapt the Sobel method for edge detection to the new conditions of the image, leading to a representation of the edges in the shape of an interval-valued fuzzy set. To conclude, we illustrate the performance of the method and perform a qualitative comparison with the classical Sobel method on grayscale images. © 2011 Springer-Verlag Berlin Heidelberg.

关键词： Edge detection

Transitivity and negative transitivity in the fuzzy setting

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Advances in Intelligent and Soft Computing 2011年 107卷 91-100页

作者： Díaz, Susana De Baets, Bernard Montes, Susana Dept. Statistics and O. R. University of Oviedo Spain Dept. Appl. Math. Biometrics and Process Control Ghent University Belgium

ISBN: (纸本)9783642240003

A (crisp) binary relation is transitive if and only if its dual relation is negatively transitive. In preference modelling, if a weak preference relation is complete, the associated strict preference relation is its dual relation. It follows from here this well-known result: given a complete weak preference relation, it is transitive if and only if its strict preference relation is negatively transitive. In the context of fuzzy relations, transitivity is traditionally defined by a t-norm and negative transitivity, by a t-conorm. In this setting, it is also well known that a (valued) binary relation is T-transitive if and only if its dual relation is negatively S-transitive where S stands for the dual t-conorm of the t-norm T. However, in this context there are several proposals to get the strict preference relation from the weak preference relation. Also, there are different definitions of completeness. In this contribution we depart from a reflexive fuzzy relation. We assume that this relation is transitive with respect to a conjunctor (a generalization of t-norms). We consider almost all the possible generators and therefore all the possible strict preference relations obtained from the reflexive relation and we provide a general expression for the negative transitivity that those relations satisfy. © 2011 Springer-Verlag Berlin Heidelberg.

关键词： Fuzzy logic

On the role of acyclicity in the study of rationality of fuzzy choice functions

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On the role of acyclicity in the study of rationality of fuz...

International Conference on Intelligent Systems Design and Applications (ISDA)

作者： Davide Martinetti Bernard De Baets Susana Díaz Susana Montes Department Statistics and O. R University of Oviedo Oviedo Spain Department Appl.Mathematics Biometrics and Process Control University of Ghent Ghent Belgium

Fuzzy choice functions obtained from preference relations have been recently used to develop automated negotiation systems. This contribution contains a theoretical study of coherence conditions in the process of creating a fuzzy choice function from a preference relation. In particular, the role of the acyclicity property of fuzzy preference relations is studied in the framework of rationality of fuzzy choice functions. Two different definitions of fuzzy acyclicity are compared. The two classical ways of constructing a fuzzy choice function from a given fuzzy preference relation are considered and properties such as acyclicity and completeness are proved to be sufficient conditions to ensure that the constructed function is a rational choice function. Special attention has been paid to the choice of the t-norm too. The results obtained are also compared to the classical results on rationality in the theory of crisp choice functions.

关键词： Fuzzy sets Educational institutions Context Economics Intelligent systems Presses Software agents

Learning valued relations from data

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Advances in Intelligent and Soft Computing 2011年 107卷 257-268页

作者： Waegeman, Willem Pahikkala, Tapio Airola, Antti Salakoski, Tapio De Baets, Bernard KERMIT Department of Applied Mathematics Biometrics and Process Control Ghent University Coupure links 653 B-9000 Ghent Belgium Department of Information Technology Turku Centre for Computer Science University of Turku Joukahaisenkatu 3-5 B 20520 Turku Finland

ISBN: (纸本)9783642240003

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches typically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are in many real-world applications often expressed in a graded manner. A general kernel-based framework for learning relations from data is introduced here. It extends existing approaches because both crisp and valued relations are considered, and it unifies existing approaches because different types of valued relations can be modeled, including symmetric and reciprocal relations. This framework establishes in this way important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated on a case study in document retrieval. © 2011 Springer-Verlag Berlin Heidelberg.

关键词： Fuzzy set theory

A new method for computing continuous functions with fuzzy variable

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Journal of Applied Sciences 2011年第7期11卷 1143-1149页

作者： Ahmad, M.Z. Hasan, M.K. de Baets, B. Institute for Engineering Mathematics Universiti Malaysia Perlis 02000 Kuala Perlis Perlis Malaysia School of Information Technology Universiti Kebangsaan Malaysia 43600 UKM Bangi Selangor Malaysia Department of Applied Mathematics Biometrics and Process Control Ghent University Coupure Links 653 9000 Gent Belgium

This study proposes a new method for computing f(U) where f is a real continuous function and U is a fuzzy interval. The computation of f(U) is performed by incorporating optimisation technique into Zadeh's extension principle. By discretising α up to n finite numbers, a set of n closed and bounded intervals is obtained. Here, the computation of f on closed and bounded intervals is the same idea of solving unconstrained optimisation problems. For every finite numbers of α, if the function to be optimised is unimodal, the authors apply Brent's method. One of the main advantages of using this method is that it does not require the calculation of derivative. In case where f is reduced to monotone or to a straight line, the optimal solutions are obtained at the endpoints of intervals. This new strategy gives better results and requires only few function evaluations. An example is provided to illustrate the effectiveness of the proposed method. © 2011 Asian Network for Scientific Information.

关键词： Functions

On a generalization of the notion of a survival copula

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Advances in Intelligent and Soft Computing 2011年 107卷 147-156页

作者： De Baets, B. De Meyer, H. Mesiar, R. Dept of Applied Mathematics Biometrics and Process Control Ghent University Coupure links 653 B-9000 Gent Belgium Dept of Applied Mathematics and Computer Science Ghent University Krijgslaan 281 S9 B-9000 Gent Belgium Dept of Mathematics and Descriptive Geometry Slovak University of Technology Radlinského 11 813 68 Bratislava Slovakia

ISBN: (纸本)9783642240003

We introduce a transformation that acts on binary aggregation functions and that generalizes the transformation that maps copulas, a well-studied class of binary aggregation functions with a profound probabilistic interpretation, to their associated survival copulas. The new transformation, called double flipping, is the composition of two elementary flipping transformations introduced earlier, each operating on one of the arguments of the aggregation function. We lay bare the relationships between these elementary flipping operations and double flipping. We characterize different subclasses of flippable aggregation functions, in particular aggregation functions that have an absorbing element or that have a neutral element. In this investigation, the key role played by quasi-copulas and their dual operations is highlighted. These findings support the introduction of the term survival aggregation function. © 2011 Springer-Verlag Berlin Heidelberg.

关键词： Knowledge based systems

Benchmarking triple stores with biological data

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Benchmarking triple stores with biological data

Workshop on Semantic Web Applications and Tools for Life Sciences 2010, SWAT4LS 2010

作者： Mironov, Vladimir Seethappan, Nirmala Blondé, Ward Antezana, Erick Lindi, Bjørn Kuiper, Martin Trondheim Norway Trondheim Norway Dept. Applied Mathematics Biometrics and Process Control Ghent University Ghent Belgium

We have compared the performance of five non-commercial triple stores, Virtuoso-open source, Jena SDB, Jena TDB, SWIFT-OWLIM and 4Store. We examined three performance aspects: the query execution time, scalability and run-to-run reproducibility. The queries we chose addressed different ontological or biological topics, and we obtained evidence that individual store performance was quite query specific. We identified three groups of queries displaying similar behavior across the different stores: 1) relatively short response time, 2) moderate response time and 3) relatively long response time. OWLIM proved to be a winner in the first group, 4Store in the second and Virtuoso in the third. Our benchmarking showed Virtuoso to be a very balanced performer - its response time was better than average for all the 24 queries;it showed a very good scalability and a reasonable run-to-run reproducibility.

关键词： Benchmarking

Development of a fuzzy calculator for continuous functions of non-interactive fuzzy variables

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Development of a fuzzy calculator for continuous functions o...

作者： Scheerlinck, Karlien Vernieuwe, Hilde De Baets, Bernard Department of Applied Mathematics Biometrics and Process Control Ghent University Coupure links 653 Ghent Belgium

ISBN: (纸本)9789898425324

The goal of this paper is to develop a Fuzzy Calculator, making it possible to calculate functions of fuzzy intervals, as prescribed by the extension principle of Zadeh. The extension principle can be reversed, resulting in fixed α-levels for which the minimum and the maximum of the function has to be determined. This optimization problem can be tackled by different algorithms: Gradient Descent, SIMPSA, Particle Swarm Optimization and Particle Swarm optimization in combination with Gradient Descent. Two approaches are used to determine the number of α-levels: it is either fixed to a predetermined value, or it is initially chosen very small and subsequently expanded according to a suitable criterion. Both a non-parallel and a parallel implementation of the Fuzzy Calculator are designed. In the parallel version, communication is used to optimize the internal workings of PSO. The Fuzzy Calculator is applied to a number of test functions. The different combinations of optimization algorithms are evaluated, both by the final result and by the number of required model evaluations. The results indicate that the parallel implementation of the Fuzzy Calculator starting with a small number of α-levels and using PSO with Gradient Descent leads to the most accurate membership function.

关键词： Membership functions

An algorithm for generating consistent and transitive approximations of reciprocal preference relations

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An algorithm for generating consistent and transitive approx...

13th International Conference on Information processing and Management of Uncertainty, IPMU 2010

作者： Freson, Steven De Meyer, Hans De Baets, Bernard Gent B-9000 Belgium Department of Applied Mathematics Biometrics and Process Control Ghent University Coupure links 653 Gent B-9000 Belgium

ISBN: (纸本)3642140483

We establish an iterative algorithm to generate for any given reciprocal relation and any given type of transitivity fitting into the framework of cycle-transitivity, a unique reciprocal relation that approximates the given reciprocal relation and possesses the given transitivity property. In the context of decision making, the algorithm can be used to generate a consistent approximation of a non-consistent reciprocal preference relation. © 2010 Springer-Verlag Berlin Heidelberg.

关键词： Decision making