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Technical Report: UTEP-CS-17-11a


In the usual [0,1]-based fuzzy logic, the actual numerical value of a fuzzy degree can be different depending on a scale, what is important -- and scale-independent -- is the order between different values. To make a description of fuzziness more adequate, it is reasonable to consider interval-valued degrees instead of numerical ones. Here also, what is most important is the order between the degrees. If we have only order between the intervals, can we, based on this order, reconstruct the original numerical values -- i.e., the degenerate intervals? In this paper, we show that such a reconstruction is indeed possible, moreover, that it is possible under three different definitions of order between numerical values.

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