Transitivity of fuzzy strict preference relations in absence of incomparability.

The aim of this work is to study an essential property in the framework of fuzzy preference structures, which is the transitivity. In particular, we discuss the relationship between the transitivity of a fuzzy large preference relation R and the transitivity of the fuzzy strict preference relation P obtained from R when every pair of elements can be compared. We consider some of the most important types of transitivity for the fuzzy large preference relation R and identify the strongest type of transitivity of the corresponding fuzzy strict preference relation P.