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Preliminary aspects on the development of a choice method for determining a best fitting case dependent fuzzy transitivity definition

E. E. Haven. Consortium McGill University


The choice of a fuzzy transitivity definition is in many instances case dependent. We propose in this paper a method which may help us reveal which choice of fuzzy transitivity definition may be preferred over another, in the event there exists a crisp linear ranking. If we have criteria varying in (inverse) proportion with a given limit we can find sufficient conditions which will ensure that a change in that limit will not induce a change in the fuzzy preferences over the alternatives. Using this finding we then argue for so called template induced rankings. The comparison of those induced rankings with the quasi-order rankings at a same a-cut, will provide us with a better understanding as to whether the particular choice of a fuzzy transitivity definition has been appropriate.

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