Jorge Recasens Ferrés

Generation and Characterization of Fuzzy T-preorders

This article studies T-preorders that can be generated in a natural way by a single fuzzy subset. These T-preorders are called one-dimensional and are of great importance, because every T-preorder can be generated by combining one-dimensional T-preorders. In this article, 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 the Analytical Hierarchical Process. Finally, strong complete T-preorders, important in decision-making problems, are also characterized.This article studies T-preorders that can be generated in a natural way by a single fuzzy subset. These T-preorders are called one-dimensional and are of great importance, because every T-preorder can be generated by combining one-dimensional T-preorders.; In this article, 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 the Analytical Hierarchical Process. Finally, strong complete T-preorders, important in decision-making problems, are also characterized.

One-dimensional T-preorders

This paper studies T-preorders by using their Representation Theorem that states that every T-preorder on a set X can be generated in a natural way by a family of fuzzy subsets of X. Especial emphasis is made on the study of one-dimensional T-preorders (i.e.: T-preorders that can be generated by only one fuzzy subset). Strong complete T-preorders are characterized.This paper studies T -preorders by using their Representation Theorem that states that every T -preorder on a set X can be generated in a natural way by a family of fuzzy subsets of X . Especial emphasis is made on the study of onedimensional T -preorders (i.e.: T -preorders that can be generated by only one fuzzy subset). Strong complete T -preorders are characterized.