The aim of this paper is to analyse the solution of a fuzzy system when the classical solution based on standard fuzzy mathematics fails to exist. In particular we analyse the solution of the system Ax=b with A squared matrix with positive fuzzy coefficients and y crisp vector of positive elements. This system is particularly important for financial applications. We propose two different solution methods that are based respectively on the work of Buckley et al. (2002) and Friedman, Ming and Kandel (1998). An application to an important financial problem, the derivation of the artificial probabilities in a lattice framework, is provided.
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