A method for deriving order compatible fuzzy relations from convex fuzzy partitions

We address a special kind of fuzzy relations capable of modeling that two elements in the universe of discourse are similar to the extent that they are close to each other with respect to a given total order. These order compatible fuzzy relations are reflexive and symmetric but not necessarily T-transitive. We address the requirements to construct such relations from a large class of fuzzy partitions that obey some requirements from the fuzzy sets in the partition, such as convexity, that are useful but not severely constraining. We also propose a new method to obtain those fuzzy relations from these partitions.