A study on the transitivity of probabilistic and fuzzy relations

作者：Martinetti D; Montes I; Diaz S^*; Montes S

来源：Fuzzy Sets and Systems, 2011, 184(1): 156-170.

DOI：10.1016/j.fss.2011.06.017

• Probabilistic relation
• Fuzzy relation
• T-transitivity
• Cycle-transitivity
• Stochastic order

Given a set of alternatives we consider a fuzzy relation and a probabilistic relation defined on such a set. We investigate the relation between the T-transitivity of the fuzzy relation and the cycle-transitivity of the associated probabilistic relation. We provide a general result, valid for any t-norm and we later provide explicit expressions for important particular cases. We also apply the results obtained to explore the transitivity satisfied by the probabilistic relation defined on a set of random variables. We focus on uniform continuous random variables.

• 出版日期2011-12-1