University Of Tehran Press Journal of Algorithms and Computation 2476-2776 Articles in Press 2022 01 14 A comparison between the resolution and linear optimization of FREs defined by product t-norm and geometric mean operator 1 12 85485 10.22059/jac.2022.85485 EN Journal Article 2022 01 14 In this paper, a type of fuzzy system is firstly investigated whereby the feasible region is defined by the fuzzy relational equalities and the geometric mean as fuzzy composition. Some related basic and theoretical properties are derived and the feasible region is completely determined. Moreover, a comparison is made between this region and FRE defined by product t-norm. Finally, an example is described to illustrate the differences of these two FRE systems. https://jac.ut.ac.ir/article_85485_4fd9f3903e06b1470c32424950e5e0f2.pdf