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Symmetric Solution of Fuzzy Linear Systems Using Probability Density Function

Khabat Barzinji, Normah Maan, Nor’aini Aris


In this paper, the existing symmetric method for finding solutions of fuzzy linear system is extended. This extended method is proposed in order to solve a non singular (n n) matrix with real coefficients and the right hand side is trapezoidal fuzzy number with nonzero spread. In this method we use probability density function to solve the 1-cut system, where the three types of solutions with some constrains are obtained. The derivation of the maximal and minimal solutions of the system with some constrains is also shown. We also proved the normality and the convexity of the three solutions and concluded that the solutions are trapezoidal fuzzy vectors. The applicability of the proposed methods is illustrated with numerical examples.


Fuzzy Linear System, Symmetric Spread, Fuzzy Vector Solution, United Solution Set (USS), Tolerable Solution Set (TSS), Controllable Solution Set (CSS), Probability Density Function

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