FUZZY INCLUSION LINEAR SYSTEMS

Document Type : Research Paper

Author

Department of Mathematics, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran

Abstract

In this manuscript, we introduce  a new class of fuzzy problems, namely ``fuzzy inclusion linear systems" and   propose a fuzzy solution set for it. Then, we present a theoretical discussion about the relationship between  the fuzzy solution set of a  fuzzy inclusion linear system and the algebraic solution of a fuzzy linear system. New necessary and sufficient conditions are derived for obtaining the unique algebraic solution for a fuzzy linear system. Also, all new concepts are illustrated by numerical examples.

Keywords


[1] T. Allahviranloo, Numerical methods for fuzzy system of linear equations, Applied Mathematics
and Computation, 155 (2004), 493–502.
[2] T. Allahviranloo and M. Ghanbari, On the algebraic solution of fuzzy linear systems based
on interval theory, Applied Mathematical Modelling, 36 (2012), 5360–5379.
[3] T. Allahviranloo and M. Ghanbari, Solving Fuzzy Linear Systems by Homotopy Perturbation
Method, International Journal of Computational Cognition, 8(2) (2010), 24–30.
[4] T.Allahviranloo, M. Ghanbari, A.A. Hosseinzadeh, E. Haghi and R. Nuraei, A note on “Fuzzy
linear systems”, Fuzzy Sets and Systems, 177 (2011), 87–92.
[5] T. Allahviranloo and M. Ghanbari, A new approach to obtain algebraic solution of interval
linear systems, Soft Computing, 16 (2012), 121–133.
[6] T. Allahviranloo, E. Haghi and M. Ghanbari, The nearest symmetric fuzzy solution for a
symmetric fuzzy linear system, An. St. Univ. Ovidius Constanta, 20(1) (2012), 151–172.
[7] T. Allahviranloo and S. Salahshour, Fuzzy symmetric solution of fuzzy linear systems, Journal
of Computational and Applied Mathematics, 235(16) (2011), 4545–4553.
[8] T. Allahviranloo, R. Nuraei, M. Ghanbari, E. Haghi and A. A. Hosseinzadeh, A new metric
for L-R fuzzy numbers and its application in fuzzy linear systems, Soft Computing, 16 (2012),
1743-1754.
[9] B. Bede and S. G. Gal, Generalizations of the differentiability of fuzzy-number-valued functions
with applications to fuzzy differential equations, Fuzzy Sets and Systems, 151 (2005),
581–599.
[10] R. Ezzati, Solving fuzzy linear systems, Soft Computing, 15(2010), 193-197.
[11] M. Friedman, M. Ming and A. Kandel, Fuzzy linear systems, Fuzzy Sets and Systems,
96(1998), 201–209.
[12] M. Ghanbari, T. Allahviranloo and E. Haghi, Estimation of algebraic solution by limiting the
solution set of an interval linear system, Soft Computing, 16(12) (2012), 2135–2142.
[13] M. Ghanbari and R. Nuraei, Convergence of a semi-analytical method on the fuzzy linear
systems, Iranian Journal of Fuzzy Systems, 11(4) (2014), 45–60.
[14] M. Ghanbari and R. Nuraei, Note on new solutions of LR fuzzy linear systems using ranking
functions and ABS algorithms, Fuzzy Inf. Eng., 5(3) (2013), 317–326.
[15] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984),
215–229.
[16] R. Nuraei, T. Allahviranloo and M. Ghanbari, Finding an inner estimation of the solution
set of a fuzzy linear system, Applied Mathematical Modelling, 37 (2013), 5148–5161.
[17] C. Wu and M. Ming, On embedding problem of fuzzy number space: Part 1, Fuzzy Sets and
Systems, 44 (1991), 33–38.