Finding Inverse of a Fuzzy Matrix using Eigen value Method
Hamed Farahani1, M. J. Ebadi2, Hossein Jafari3
1Hamed Farahani, Department of Mathematics, Chabahar Maritime University, Chabahar, Iran.
2M. J. Ebadi*, Department of Mathematics, Chabahar Maritime University, Chabahar, Iran.
3Hossein Jafari, Department of Mathematics, Chabahar Maritime University, Chabahar, Iran.
Manuscript received on November 15, 2019. | Revised Manuscript received on 24 November, 2019. | Manuscript published on December 10, 2019. | PP: 3030-3037 | Volume-9 Issue-2, December 2019. | Retrieval Number: B6295129219/2019©BEIESP | DOI: 10.35940/ijitee.B6295.129219
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: The present paper extends a concept of the inverse of a matrix that its elements are fuzzy numbers, which may be implemented to model imprecise and uncertain features of the problems in the real world. The problem of inverse calculation of a fuzzy matrix is converted to solving a fuzzy polynomial equations (FPEs) system. In this approach, the fuzzy system is transformed to an equivalent system of crisp polynomial equations. The solutions of the crisp polynomial equations system is computed using eigenvalue method. Also, using Gröbner basis properties a criteria for invertibility of the fuzzy matrix is introduced. Furthermore, a novel algorithm is proposed to find a fuzzy inverse matrix. Achieving all entries of a fuzzy inverse matrix at a time is a big advantage comparing the existence methods. In the end, some illustrative examples are presented to demonstrate the algorithm and concepts.
Keywords: Eigenvalue, Fuzzy Numbers, Fuzzy Matrix, Fuzzy Identity Matrix, Fuzzy Linear Equation System.
Scope of the Article: Fuzzy Logics