University Of Tehran Press Journal of Algorithms and Computation 2476-2776 Articles in Press 2022 01 15 On the resolution of LP-FRE defined by the convex combination operator 1 12 85500 10.22059/jac.2022.85500 EN Journal Article 2022 01 15 In this paper, a linear programming problem is investigated in which the feasible region is formed as a special type of fuzzy relational equalities (FRE). In this type of FRE, fuzzy composition is considered as the convex combination operator. It is proved that the feasible region of the problem can be written by one maximum solution and a finite number of minimal solutions. Some theoretical properties of the feasible region are derived and some necessary and sufficient conditions are also presented to determine the feasibility of the problem. Based on some structural properties of the problem, an algorithm is presented to find the optimal solutions and finally, an example is described to illustrate the algorithm. https://jac.ut.ac.ir/article_85500_9aac5176bd34dae432d6c128dd0c8d2b.pdf