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| Content Provider | Tech Science Press |
|---|---|
| Author | Gasilov, Nizami Amrahov, Şahin Emrah Karakaş, Halil İbrahim Akın, Ömer Fatullayev, Afet Golayoğlu Amrahov, Şahin Fatullayev, Afet Karakaş, Halil |
| 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. |
| Related Links | https://www.techscience.com/CMES/v75n3&4/26808 |
| Starting Page | 189 |
| Ending Page | 204 |
| ISSN | 15261492 |
| DOI | 10.3970/cmes.2011.075.189 |
| Issue Number | 3&4 |
| Journal | Computer Modeling in Engineering & Sciences (CMES) |
| Volume Number | 75 |
| e-ISSN | 15261506 |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | triangular fuzzy number generalized permutation matrix. Fuzzy linear system |
| Content Type | Text |
| Resource Type | Article |
| Subject | Computer Science Applications |
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