Alternative theorems such as Farkas' lemma and Gordan's theorem usually play important roles in considering optimization problems and because of that, many kinds of valuable extensions have been established; Jeyakumar \cite{Jeya} produces a generalized Gordan's theorem for a vector-valued function in 1986. Li \cite{Li} in 1999 and Yang et al.\cite{Yang} in 2000, extend it to the case of set-valued maps. However, these theorems rely on some assumptions related to convexity to make systems in a bilinear form. In this talk, I would like to introduce alternative theorems from a set-valued analytic point of view, using the set-relations proposed by Kuroiwa, Tanaka, and Ha \cite{Kuroiwa} in 1997. They can be considered in a topological vector space with the set-relations induced by a convex ordering cone. A similar approach with scalarizing functions for vectors had been done by Nishizawa, Onodsuka, and Tanaka \cite{Nishizawa} in 2005. They prove some alternative theorems with no convex assumption by nonlinear scalarizations, not bilinear forms. We reviewed these results and found a way of generalizations. I show 12 types of alternative theorems given by scalarizing functions for sets. Comparing with previous studies, our results achieve the subdivision of the case and the simplification of the forms of them simultaneously. Also, important properties are still conserved. Reducing some conditions, we recognize that some of 12 types imply several Gordan-type theorems. This fact may allow our theorems to have a suitability of extensions of previous results. %