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We establish a connection between two transitivity frameworks: the transitivity of fuzzy relations based on a commutative quasi-copula and the cycle-transitivity of reciprocal relations w.r.t. the dual quasi-copula as an upper bound function. Loosely speaking, it turns out that the latter can be characterized by imposing a lower bound on the relative frequency with which the former is fulfilled, when...
In this paper, the transitivity properties of reciprocal relations, also called probabilistic relations, are investigated within the framework of cycle-transitivity, which generalizes the concepts of T-transitivity, stemming from fuzzy set theory, and of stochastic transitivity, common to many mathematical models in psychology, social choice and welfare, financial mathematics, etc. It is emphasized...
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