Affiliations: [a]
Department of Basic Science, Chabahar Maritime University, Chabahar, Iran
| [b]
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
| [c]
Department of Mathematics, Hamedan University of Technology, Hamedan, Iran
Correspondence:
[*]
Corresponding author. Mahmoud Paripour, Department of Mathematics, Hamedan University of Technology, Hamedan 65155-579, Iran. Tel.: +98 81 38411538; Fax: +98 81 38380520; E-mails: [email protected]; [email protected].
Abstract: The occurrence of imprecision in the real world is inevitable due to some unexpected situations. The imprecision is often involved in any engineering design process. The imprecision and uncertainty are often interpreted as fuzziness. Fuzzy systems have an essential role in the uncertainty modeling, which can formulate the uncertainty in the actual environment. In this paper, a new method based on linear algebra for resolution of a fuzzy complex system of linear equations is presented. Moreover, a new algorithm is designed to find all the solutions of the system based on the eigenvalue method. Thanks to our approach, we can find all the solutions of the system at a time. Also, we are able to determine when the solution sets of the system are nonempty sets.To illustrate the easy application of the proposed method, numerical examples are given and the obtained results are discussed.
Keywords: Triangular fuzzy number, fuzzy complex number, fuzzy complex system of linear equations, Gröbner bases, eigenvalues
