Fuzzy Sets and Systems
Solving fuzzy equations: a new solution concept
Fuzzy Sets and Systems
Solving linear and quadratic fuzzy equations
Fuzzy Sets and Systems
Solving systems of linear fuzzy equations
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Duality in fuzzy linear systems
Fuzzy Sets and Systems
Iteration algorithms for solving a system of fuzzy linear equations
Fuzzy Sets and Systems
Fuzzy Sets and Systems: Theory and Applications
Fuzzy Sets and Systems: Theory and Applications
Fuzzy linear systems of the form A1x+b1=A2x+b2
Fuzzy Sets and Systems
Maximal- and minimal symmetric solutions of fully fuzzy linear systems
Journal of Computational and Applied Mathematics
Fuzzy symmetric solutions of fuzzy matrix equations
Advances in Fuzzy Systems
Approximate solution of dual fuzzy matrix equations
Information Sciences: an International Journal
Approximating solutions of fully fuzzy linear systems: A financial case study
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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In this paper, we propose a simple and practical method to solve a fuzzy linear system AX@?=b@?, where X@? and b@? are fuzzy triangular vectors with non-zero spreads and matrix A is nonsingular with real coefficients. The aim of this paper is twofold. First, we obtain the crisp solution of a fuzzy linear system. To this end, we solve the 1-cut of a fuzzy linear system. Second, we allocate some unknown symmetric spreads to any rows of fuzzy linear system in 1-cut position. Thus, a fuzzy linear system in 1-cut will be transformed to a system of interval equations. The symmetric spreads of each element of a fuzzy vector solution are derived by solving such an interval system. Moreover, based on the obtained symmetric spreads we derive three types of solutions. However, one of the mentioned spreads has pessimistic/optimistic attitude that is determined with a decision maker. It seems that such a solution is a connection solution between Tolerable Solution Set (TSS) and Controllable Solution Set (CSS). Also, we derive the maximal solution and the minimal solution of an original fuzzy linear system which are placed in TSS and CSS, respectively. Finally, some numerical examples are given to illustrate the efficiency and ability of the proposed method.