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

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.