Studying on solution of fuzzy relation equations

E. Sanchez (“Resolution of composite fuzzy relation equations”, Inform. and Control, vol. 30, pp. 38-48, 1976) provided a methodology for the solution of certain basic fuzzy relational equations. In this methodology, an algorithm named α-composite was reported to calculate the supremum of solution sets in the fuzzy relation equation A o R=B. Drawing inspiration from this methodology, this paper presents a method to obtain not only the supremum but also the interval of the solutions. Because each such interval is widest, it provides exactly all the widest solution sets which meet our expectations. Moreover, this new algorithm strives to cut down the number of computation rules and to accomplish the simplification of the calculation