SOLVING SYSTEMS OF LINEAR FUZZY EQUATIONS

In this paper we wish to construct solutions for xBAR to the fuzzy matrix equation AxBAR = bBAR when the elements in ABAR and bBAR are triangular fuzzy numbers. ABAR is square and always non-singular. We argue that the previous method of solving for xBAR, 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 XBAR of these five new solutions as our solution to AxBAR = bBAR. We show that XBAR 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.