In this paper, a fully fuzzy linear system (FFLS) is considered. By defuzzifying, the (n × n) FFLS can be replaced by three (n × n) crisp linear systems, and consequently its homomorphic solution in canonical trapezoidal form based on three (n × n) crisp linear solutions associated with three parameters, value, ambiguity, and fuzziness, is calculated.

The main aim of this paper is to discuss Fuzzy Linear Matrix Equations (shown as FLME) of the form AXB = C for finding its fuzzy solutions. In this paper, the parametric form of the fuzzy linear system is used. Necessary and sufficient conditions for the existence of the set of fuzzy solutions are derived, and a numerical procedure for calculating the solutions is designed.