An operational test for the existence of a consistent increasing quasi-concave value function

• Establishing necessary and sufficient conditions for the existence of an increasing quasi-concave value function consistent with preference information given by DM. Developing operational, tractable easy to use test checking a desirable function. Constructing linear non-linear functions. The is important issue in various fields including Economics, Multiple Criteria Decision Making, Applied Mathematics. A equivalent convex-to-the-origin indifference contours, very common assumption Economics. In this paper, we establish satisfying aforementioned properties. This leads such addition developing test, construct