Abstract. Abstract. The notion of a fuzzy linear system of equations as a set of five special interval systems of equations is introduced. The notions of weak and strong solvability (feasibility) of a fuzzy linear system of equations in five grades (crisp, quasi-crisp, semi-crisp, quasi-fuzzy, and fuzzy) are introduced. The criteria of weak solvability and feasibility of fuzzy linear systems of equations in the five grades are substantiated. Other properties of fuzzy systems and their weak solutions in all the five grades are proved.

Keywords: fuzzy system, system solvability and admissibility.