Max-Min averaging operator: fuzzy inequality systems and resolution

 Minimum and maximum operators are two well-known t-norm and s-norm used frequently in fuzzy systems. In this paper, two different types of fuzzy inequalities are simultaneously studied where the convex combination of minimum and maximum operators is applied as the fuzzy relational composition. Some basic properties and theoretical aspects of the problem are derived and four necessary and sufficient conditions are presented. Moreover, an algorithm is proposed to solve the problem and an example is described to illustrate the algorithm.