Abstract
In this paper we wish to construct solutions for x to the fuzzy matrix equation Ax = b when the elements in A and b are triangular fuzzy numbers. A is square and always non-singular. We argue that the previous method of solving for x , based on the extension principle and regular fuzzy arithmetic, should be abandoned since it too often fails to produce a solution. We present six new solutions of which we show that five are identical. We then adopt the common value X of these five new solutions as our solution to Ax = b . We show that X is a fuzzy vector which is the generalization to R n of real fuzzy numbers. We also show how these results pertain to, and extend, previous research on this problem within the area of interval analysis.
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