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In this paper, we discuss two new computational techniques for solving a generalized fully fuzzy linear system (FFLS) with arbitrary triangular fuzzy numbers (m, ɑ, β). The methods eliminate the non-negative restriction on the fuzzy coefficient matrix that has been considered by almost every method in the literature and relies on the decomposition of the dual FFLS into a crisp linear system that can be further solved by a variety of classical methods. To illustrate the proposed methods, numerical examples are solved and the obtained results are discussed. The methods pose several advantages over the existing methods to solve a simple or dual FFLS. [ABSTRACT FROM AUTHOR]