Lodwick, Weldon A. and Dubois, Didier Interval linear systems as a necessary step in fuzzy linear systems. (2015) Fuzzy Sets and Systems, 281. 227-251. ISSN 0165-0114
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(Document in English)
PDF (Author's version) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 943kB |
Official URL: http://dx.doi.org/10.1016/j.fss.2015.03.018
Abstract
This article clarifies what it means to solve a system of fuzzy linear equations, relying on the fact that they are a direct extension of interval linear systems of equations, already studied in a specific interval mathematics literature. We highlight four distinct definitions of a systems of linear equations where coefficients are replaced by intervals, each of which based on a generalization of scalar equality to intervals. Each of the four extensions of interval linear systems has a corresponding solution set whose calculation can be carried out by a general unified method based on a relatively new concept of constraint intervals. We also consider the smallest multidimensional intervals containing the solution sets. We propose several extensions of the interval setting to systems of linear equations where coefficients are fuzzy intervals. This unified setting clarifies many of the anomalous or inconsistent published results in various fuzzy interval linear systems studies.
Item Type: | Article |
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Additional Information: | Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at Fuzzy Sets and Systems website : http://www.sciencedirect.com/science/article/pii/S0165011415001670 |
HAL Id: | hal-01285665 |
Audience (journal): | International peer-reviewed journal |
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Institution: | French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE) Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE) Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE) Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE) Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE) Other partners > University of Colorado Denver (USA) |
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Deposited On: | 09 Mar 2016 14:20 |
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