THE EFFECT OF DRAZIN INVERSE IN SOLVING SINGULAR DUAL FUZZY LINEAR SYSTEMS

Year 2013, Volume: 1 Issue: 2, 150 - 157, 01.12.2013

Muharram Nıkuıe

https://izlik.org/JA59YE48EK

Abstract

The dual fuzzy linear system A˜x = B ˜x + ˜y where A, B are bothcrisp matrices, ˜x and ˜y are fuzzy vectors is called a singular dual fuzzy linearsystem while the coefficients matrix of the extended linear system of it be acrisp singular matrix. In this paper, on the solving the singular dual fuzzylinear system using Drazin inverse is discussed

Keywords

Fuzzy number , Dual fuzzy system , Drazin inverse , Singular matrices

References

• Abbasbandy, S., Otadi, M., Mosleh, M., Minimal solution of general dual fuzzy linear sys- tems, Chaos, Solutions and Fractals, 37 (2008), 1113-1124.
• Allahviranloo, T., Hosseinzadeh Lotfi, F., Khorasani Kiasari, M., Khezerloo, M.,On the fuzzy solution of LR fuzzy linear systems , Applied Mathematical Modelling, 37 (2013), 1170-1176. [3] Allahviranloo, T., Ghanbari, M.,On the algebraic solution of fuzzy linear systems based on interval theory, J. Applied Mathematical Modelling, 36 (2012), 5360-5379.
• Asady, B., Mansouri, P., Numerical Solution of Fuzzy Linear Systems, International Journal Computer Mathematics , 86 (2009), 151-162.
• Ben, A., Greville, I., Generalized inverses : theory and applications, Springer-Verlag New York, Inc., 2003. [6] Campbell, S., Meyer, C., Generalized Inverses of Linear Transformations Pitman London, 1979.
• Ming, Ma., Friedman, M., Kandel, A., Duality in fuzzy linear systems, Fuzzy Sets and Sys- tems, 109 (2000), 55-58.
• Nikuie, M., Mirnia, M.K., Mahmoudi, Y., Some results about the index of matrix and Drazin inverse, Mathematical Sciences Quarterly Journal, 4 (2010), 283-294.
• Nuraei, R., Allahviranloo, T., Ghanbari, M., Finding an inner estimation of the solution set of a fuzzy linear system, Applied Mathematical Modelling, 37 (2013), 5148-5161.
• Wait, R.,The numerical solution of algebric equations, Wiley, 1979.
• Zengtal, G., Xiaobin, G., Inconsistent fuzzy matrix equations and its fuzzy least squares solutions, Applied Mathematics Modelling, 35 (2011), 1456-1469.
• Zheng, L., A characterization of the Drazin inverse, Linear Algebra and its Applications, 335 (2001), 183-188. Young Researchers and Elite Club, Islamic Azad University, Tabriz Branch, Tabriz, IRAN
• E-mail address: nikuie [e-mail]