Generation and Characterization of Fuzzy T-preorders

This paper studies T -preorders than can be generated in a natural way by a single fuzzy subset. These T -preorders are called one-dimensional and are of great importance, since every T -preorder can be generated by combining onedimensional ones. In the paper, the relation between fuzzy subsets generating the same T -preorder is given and one-dimensional T -preorders are characterized in two different ways: They generate linear crisp orderings on X and they satisfy a Sincov like functional equation. This last characterization is used to approximate a given T -preorder by a one-dimensional one by relating the issue to Saaty matrices used in Analytical Hierarchical Process. Finally, strong complete T -preorders, important in Decision Making problems, are also characterized.