Open AccessFinding Inverse of a Fuzzy Matrix using Eigen value Method
Author(s) -
Hamed Farahani,
M. J. Ebadi,
Hossein Jafari
Publication year - 2019
Publication title -
international journal of innovative technology and exploring engineering
Language(s) - English
Resource type - Journals
ISSN - 2278-3075
DOI - 10.35940/ijitee.b6295.129219
Subject(s) - mathematics , inverse , fuzzy logic , matrix (chemical analysis) , eigenvalues and eigenvectors , fuzzy number , polynomial , fuzzy associative matrix , matrix polynomial , polynomial matrix , mathematical optimization , algorithm , fuzzy set , computer science , mathematical analysis , artificial intelligence , geometry , materials science , physics , quantum mechanics , composite material
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.