Solving a linear programming problem with the convex combination of the max-min and the max-average fuzzy relation equations

In this paper, we introduce a fuzzy operator constructed by the convex combination of two known operators, max-min and max-average compositions [H.J. Zimmermann, Fuzzy set theory and it's application, Kluwer Academic Publishers, Boston, Dordrecht, London, 1999]. This operator contains some properties of the two known compositions when it generates the feasible region for linear optimization problems. We investigate linear optimization problems whose feasible region is the fuzzy sets defined with this operator. Thus, firstly, the structure of these fuzzy regions is considered and then a method to solve the linear optimization problems with fuzzy equation constraints regarding this operator is presented.