General consistency conditions for fuzzy interval-valued preference relations

We define four types of general consistency conditions for fuzzy interval-valued additively reciprocal preference relations. These are far-reaching generalizations, on one hand, of the Krejčí's conditions, Krejčí (2017) [5] and, on the other hand, of the FG-transitivities defined by Świtalski (2003) [11]. We use the concept of the so-called consistency set, which gives possibility of considering more general conditions than the traditional additive consistency of Tanino. We prove theorems characterizing all the conditions by easily verifiable inequalities. Our characterization results for weak consistency and consistency generalize the results of Krejčí. We define consistency indexes related to considered consistency sets and show that in some situations these indexes can give more subtle characterization of consistency status of a given relation than the conditions presented by Krejčí.