Solution of Fuzzy Relation Equations Using Composite Operators

Abstract

An analytic method for solving fuzzy relaion equation has been presented by Sanchez. He has dealt with Max•min composite equation A_??_R=B. The main feature of his method is to define composite operator, i.e., α -composite operator, to derive the maximum values of the solution. Actually, true solution is given by interval values. He has also considered Min•max composite equation AΔR=B for which e -composite operator is defined. The operator can derive the minimum values of interval solution. The characteristic feature of this paper is to exploit such composite operators which can derive whole solutions for Max•min and Min•max composite eqations. The advantage of using these operators is to be able to derive answers elegantly. As the result, _??_ and _??_ composite operators are presented to derive whole interval solutions for Max•min and Min•max composite eqations, respectively. The elegancy appears in the formulation of calculating answer set, evading traditional laborious algorithms for obtaining whole interval solutions.