Fuzzy rank of a fuzzy matrix

Abstract By a fuzzy matrix we mean a rectangular array of fuzzy numbers. We introduce a fuzzy rank of a fuzzy matrix. This is a nonnegative fuzzy integer; that is a nondecreasing function from the set of nonnegative integers into the lattice [0, 1]. A fuzzy rank represents all information we posses on the possible values of the (usual) rank that can be assigned to a fuzzy matrix, at various levels of certainty. We show that the fuzzy rank of a product of two fuzzy matrices cannot exceed the fuzzy rank of either fuzzy matrix.