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https://hdl.handle.net/20.500.11851/6085
Title: | A Geometric Approach to Solve Fuzzy Linear Systems | Authors: | Gasilov, Nizami Amrahov, Şahin Emrah Fatullayev, Afet Golayoğlu Karakas, Halil İbrahim Akın, Ömer |
Keywords: | Fuzzy linear system triangular fuzzy number generalized permutation matrix |
Issue Date: | 2011 | Publisher: | Tech Science Press | Abstract: | In this paper, linear systems with a crisp real coefficient matrix and with a vector of fuzzy triangular numbers on the right-hand side are studied. A new method, which is based on the geometric representations of linear transformations, is proposed to find solutions. The method uses the fact that a vector of fuzzy triangular numbers forms a rectangular prism in n-dimensional space and that the image of a parallelepiped is also a parallelepiped under a linear transformation. The suggested method clarifies why in general case different approaches do not generate solutions as fuzzy numbers. It is geometrically proved that if the coefficient matrix is a generalized permutation matrix, then the solution of a fuzzy linear system (FLS) is a vector of fuzzy numbers irrespective of the vector on the right-hand side. The most important difference between this and previous papers on FLS is that the solution is sought as a fuzzy set of vectors (with real components) rather than a vector of fuzzy numbers. Each vector in the solution set solves the given FLS with a certain possibility. The suggested method can also be applied in the case when the right-hand side is a vector of fuzzy numbers in parametric form. However, in this case, alpha-cuts of the solution cannot be determined by geometric similarity and additional computations are needed. | URI: | https://hdl.handle.net/20.500.11851/6085 | ISSN: | 1526-1492 1526-1506 |
Appears in Collections: | Matematik Bölümü / Department of Mathematics Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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