The goal of this research is to develop a group technology (GT) cell formation methodology, with the inclusion of fuzziness usually found in industry. Three studies are conducted. The first study establishes a procedure through which a nonbinary machine-component matrix is constructed. This matrix forms the basis of the following two studies. The second study applies the nonbinary matrix concept to the single linkage clustering algorithm. The third study focuses on a modified rank order clustering algorithm that involves fuzzy set theory. The modified single linkage and modified rank order clustering algorithm are compared and the strengths and weaknesses are discussed. The flexibility provided by the fuzzy set-based method is presented.