Gasilov, Nizami; Amrahov, Şahin Emrah; Fatullayev, Afet Golayoğlu; Karakaş, Halil İbrahim; Akın, Ömer A geometric approach to solve fuzzy linear systems. (English) Zbl 1356.65094 CMES, Comput. Model. Eng. Sci. 75, No. 3, 189-203 (2011). Summary: 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. Cited in 2 Documents MSC: 65F05 Direct numerical methods for linear systems and matrix inversion 26E50 Fuzzy real analysis PDFBibTeX XMLCite \textit{N. Gasilov} et al., CMES, Comput. Model. Eng. Sci. 75, No. 3, 189--203 (2011; Zbl 1356.65094)