Search

Showing total 3 results
Start Over Search Limiters Full Text Topic algebra Topic mathematical optimization Journal international journal of approximate reasoning
3 results

1. Design of nearest neighbor classifiers: multi-objective approach

Author

Chen, Jian-Hung, Chen, Hung-Ming, and Ho, Shinn-Ying

Subjects
*MATHEMATICAL optimization, *ALGORITHMS, *APPROXIMATION theory, *ALGEBRA
Abstract

Abstract: The goal of designing optimal nearest neighbor classifiers is to maximize classification accuracy while minimizing the sizes of both reference and feature sets. A usual way is to adaptively weight the three objectives as an objective function and then use a single-objective optimization method for achieving this goal. This paper proposes a multi-objective approach to cope with the weight tuning problem for practitioners. A novel intelligent multi-objective evolutionary algorithm IMOEA is utilized to simultaneously edit compact reference and feature sets for nearest neighbor classification. Three comparison studies are designed to evaluate performance of the proposed approach. It is shown empirically that the IMOEA-designed classifiers have high classification accuracy and small sizes of reference and feature sets. Moreover, IMOEA can provide a set of good solutions for practitioners to choose from in a single run. The simulation results indicate that the IMOEA-based approach is an expedient method to design nearest neighbor classifiers, compared with an existing single-objective approach. [Copyright &y& Elsevier]

Published
2005
Full Text
View/download PDF

2. Making Discrete Sugeno Integrals More Discriminant

Author

Hélène Fargier, Didier Dubois, Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), and Université Fédérale Toulouse Midi-Pyrénées

Subjects
Mathematical optimization, Qualitative decision theory, Sugeno integral, 02 engineering and technology, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Theoretical Computer Science, Qualitative analysis, Artificial Intelligence, 0502 economics and business, 0202 electrical engineering, electronic engineering, information engineering, dec-models, 050205 econometrics, Mathematics, Applied Mathematics, 05 social sciences, Lexicographical order, Weighting, Algebra, Choquet integral, Discriminant, Lexicographic ordering, 020201 artificial intelligence & image processing, Software, Coding (social sciences)
Abstract

DFarg007; International audience; This paper deals with qualitative evaluation processes when the worth of items is computed by means of Sugeno integral. One limitation of this approach is the coarse ranking of items it produces. In order to refine this ranking, generalizations of leximin and leximax to Sugeno integrals are studied. Numerical encodings of such generalized lexicographic methods are described by means of mappings from the qualitative value scale to the reals. In some of these transformations Sugeno integral is changed into a Choquet integral. The issue of refining the capacity at work in Sugeno integral also receives a preliminary examination. This work relies on a previous similar attempt at refining prioritized minimum and maximum aggregations (in the setting of decision under uncertainty) into a so-called bigstepped weighted average, encoding a very refined qualitative lexicographic ordering of items.

Published
2009

3. Approximation by Shepard type pseudo-linear operators and applications to Image Processing

Author

Imre J. Rudas, Hajime Nobuhara, Barnabás Bede, and Emil Daniel Schwab

Subjects
Constant coefficients, Mathematical optimization, Shepard operators, Image Processing, Applied Mathematics, Fuzzy set, Pseudo-analysis, Image processing, Spectral theorem, Operator theory, Fourier integral operator, Theoretical Computer Science, Algebra, Artificial Intelligence, Product (mathematics), Pseudo-linear approximation, Approximation, Software, Mathematics, Generator (mathematics)
Abstract

Recently, it has been shown that sum and product are not the only operations that can be used in order to define concrete approximation operators. Several other operations provided by fuzzy sets theory can be used. In the present paper, pseudo-linear approximation operators are investigated from the practical point of view in Image Processing. We study max–min, max–product Shepard type approximation operators together with Shepard operators based on pseudo-operations generated by an increasing continuous generator. It is shown that in several cases these outperform classical approximation operators based on sum and product operations.

Published
2009
Full Text
View/download PDF