Name
Abstract | ||
|---|---|---|
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 applied to reciprocal relations. We provide two compelling cases: the 4/6 theorem, expressing that the winning probability relation of a set of independent random variables is at least 66.66% product-transitive, and the 5/6 theorem, expressing that the mutual rank probability relation associated with a given poset is at least 83.33% product-transitive. Moreover, these lower bounds turn out be rather conservative, illustrating that, from a frequentist point of view, transitivity is abundant. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1016/j.fss.2015.06.020 | Fuzzy Sets and Systems |
Keywords | Field | DocType |
Cycle-transitivity,Quasi-copula,Mutual rank probability relation,Reciprocal relation,Winning probability relation,Transitivity | Discrete mathematics,Reciprocal,Random variable,Combinatorics,Frequentist inference,Commutative property,Euclidean relation,Upper and lower bounds,Partially ordered set,Mathematics,Transitive relation | Journal |
Volume | Issue | ISSN |
281 | C | 0165-0114 |
Citations | PageRank | References |
1 | 0.36 | 21 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bernard De Baets | 1 | 2994 | 300.39 |
| Karel De Loof | 2 | 34 | 4.77 |
| Hans De Meyer | 3 | 305 | 42.39 |