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This paper considers an optimization problem with a linear objective function under the constraints expressed by a system of fuzzy relation equations using max-as (Algebraic Sum) composition. First, some properties of minimal solutions of the system with fuzzy relation equations and max-as composition are shown. Then, a new algorithm for solving the optimization problem is derived. The numerical examples have been provided to illustrate the theoretical results. OPSOMMING Hierdie artikel bestudeer ‘n optimiseringsprobleem met ‘n lineere doelwitfunksie en wasige randvoorwaardes met ‘n algebraiese somsamestelling. Aanvanklik word sommige eienskappe van die minimale oplossings van die wasige vergelykings en die algebraiese samestelling getoon. Daarna word ‘n nuwe algoritme vir die oplossing van die optimiseringsprobleem afgelei. Numeriese voorbeelde word voorsien om die teoretiese resultate te ondersteun.

A NEW ALGORITHM FOR OPTIMIZATION OF THE FUZZY RELATION EQUATION WITH MAXALGEBRAIC SUM COMPOSITION