Consistent models of transitivity for reciprocal preferences on a finite ordinal scale

In this paper we consider a decision maker who shows his/her preferences for different alternatives through a finite set of ordinal values. We analyze the problem of consistency taking into account some transitivity properties within this framework. These properties are based on the very general class of conjunctors on the set of ordinal values. Each reciprocal preference relation on a finite ordinal scale has both a crisp preference and a crisp indifference relation associated to it in a natural way. Taking this into account, we have started by analyzing the problem of propagating transitivity from the preference relation on a finite ordinal scale to the crisp preference and indifference relations. After that, we carried out the analysis in the opposite direction. We provide some necessary and sufficient conditions for that propagation, and therefore, we characterize the consistent class of conjunctors in each direction.