OATAO - Open Archive Toulouse Archive Ouverte Open Access Week

Interval linear systems as a necessary step in fuzzy linear systems

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

[img]
Preview
(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
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
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (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)
Laboratory name:
Statistics:download
Deposited By: IRIT IRIT
Deposited On:09 Mar 2016 14:20

Repository Staff Only: item control page