Transfer-stable aggregation functions : applications, challenges, and emerging trends

The original transfer-stable aggregation functions generalized the arithmetic means to finite chains. The idea of applying these functions was later demonstrated by purchasing several products depending on the quality and price of the products. This paper aims to continue this idea and show other possible applications of transfer-stable aggregation functions. We identify several concerns in various applications and present possible remedies to address these concerns. We show different types of lattices could be used to compile the assignment of a given application problem. Based on this finding, we can very effectively divide the products into so-called qualitative classes. We conclude that distance-stable lattices are most effective in these applications. Moreover, we also show that the classes better reflect reality using these lattices.