Abstract
Sylvester matrix equation is one of the most popular equations used in control theory. In applying the uncertainty, vague, ambiguity and incomplete real problem, this equation can be employed with the fuzzy theory. In this study, we present a preliminary study on how the Sylvester matrix equation is solved when its parameters are fuzzy or known as fully fuzzy Sylvester matrix equation (FFSME). This study shows that the FFSME can be transferred to linear system, as in the case of crisp linear Sylvester matrix equation. We also show that the transformation of FFSME to linear system passes on fully fuzzy linear system (FFLS), subsequently the solution of FFLS is obtained by its associated linear system, which equivalent to fuzzy solution of FFSME. A numerical example is given to illustrate this transformation. Finally, we draw some conclusions concerning the related future directions towards this study.
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