Optimal Scale Selection in Random Multi-scale Ordered Decision Systems

Aiming at the knowledge acquisition problem of multi-scale ordered information system obtained from random experiments,concepts of random multi-scale ordered information systems and dominance-equivalence-relations-based random multi-scale ordered decision systems are first introduced.Information granules in random multi-scale ordered information systems as well as lower and upper approximations of sets with respect to dominance relations induced by conditional attribute set under different scales are then described.Their relationships are also clarified.Finally,concepts of several types of optimal scales in random multi-scale ordered information systems and dominance-equivalence-relations-based random multi-scale ordered decision systems are defined.It is proved that belief and plausibility functions in the Dempster-Shafer theory of evidence can be used to characterize some optimal scales in random multi-scale ordered information systems and dominance-equivalence-relations-based random multi-scale ordered dec