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Abstract and Applied AnalysisVolume 2014 2014, Article ID 315290, 10 pages

Research ArticleDepartment of Information Management and Innovation Center for Big Data and Digital Convergence, Yuan Ze University, Taoyuan 32003, Taiwan

Received 2 January 2014; Accepted 22 April 2014; Published 11 May 2014

Academic Editor: Juan Carlos Cortés

Copyright © 2014 Jun-Lin Lin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A system of fuzzy relational equations with the max-Archimedeant-norm composition was considered. The relevant literatureindicated that this problem can be reduced to the problem offinding all the irredundant coverings of a binary matrix. Adivide-and-conquer approach is proposed to solve this problem and,subsequently, to solve the original problem. This approach wasused to analyze the binary matrix and then decompose the matrixinto several submatrices such that the irredundant coverings ofthe original matrix could be constructed using the irredundantcoverings of each of these submatrices. This step was performedrecursively for each of these submatrices to obtain theirredundant coverings. Finally, once all the irredundant coveringsof the original matrix were found, they were easily converted intothe minimal solutions of the fuzzy relational equations. Experiments on binary matrices, with the number of irredundantcoverings ranging from 24 to 9680, were also performed. Theresults indicated that, for test matrices that could initially bepartitioned into more than one submatrix, this approach reducedthe execution time by more than three orders of magnitude. For theother test matrices, this approach was still useful becausecertain submatrices could be partitioned into more than onesubmatrix.

Autor: Jun-Lin Lin, Hung-Chjh Chuan, and Laksamee Khomnotai

Fuente: https://www.hindawi.com/


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