@Article{cmes.2011.075.189,
AUTHOR = {Nizami Gasilov, Şahin Emrah Amrahov, Afet Golayoğlu Fatullayev, Halil İbrahim Karakaş, Ömer Akın},
TITLE = {A Geometric Approach to Solve Fuzzy Linear Systems},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {75},
YEAR = {2011},
NUMBER = {3&4},
PAGES = {189--204},
URL = {http://www.techscience.com/CMES/v75n3&4/26808},
ISSN = {1526-1506},
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.},
DOI = {10.3970/cmes.2011.075.189}
}