On transitivity of fuzzy preferences generated by utility functions with a random threshold

Interval orderings were introduced in neoclassical economics for exploring effects related to nontransitive preference relations. Interval orderings can be generated by utility functions with a threshold. We consider utility functions with a random threshold. In contrast to the crisp case fuzzy preference relations generated by such functions may be transitive. Conditions under which it occurs are presented in this paper. We specify membership functions and t-norms which provide transitive preferences. Addition of fuzzy numbers with respect to the specified t-norms does not increase the uncertainty.