A new metric for L–R fuzzy numbers and its application in fuzzy linear systems

In this paper, a metric based on modified Euclidean metric on interval numbers, for L–R fuzzy numbers with fixed $$L(\cdot)$$ and $$R(\cdot)$$ is introduced. Then, it is applied for solving L–R fuzzy linear system (L–R-FLS) with fuzzy right-hand side, so that L–R-FLS is transformed to the minimization problem. The solution of the mentioned non-linear programming problem is our favorite fuzzy number vector solution. Two constructive Algorithms are proposed in detail and the method is illustrated by solving several numerical examples.

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