Generation and Characterization of Fuzzy T-preorders

8 years 7 months ago

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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. Keywords. T-preorder, Representation Theorem, generator, dimension, strong complete T-preorder

Dionís Boixader, Jordi Recasens

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