A generalization of stochastic and fuzzy transitivity for reciprocal fuzzy relations

b) moderate stochastic transitivity: For a reciprocal fuzzy relation Q : x2 + [O, 11 on a finite set of alternatives X , we introduce the concept of U-transitivity which is based upon the ordering of the matrix elements qij, qjk and qki of Q for all triples of indices i, j and k. We show that U-transitivity generalizes both stochastic and fuzzy transitivity. The U-transitivity of the secalled utility model is investigated. Furthermore, we describe a new dice game model of preferences given by rational numbers in the unit interval and establish the corresponding U-transitivity.