Hybrid Probabilistic Models of Fuzzy and Rough Events
Rolly Intan*,**, Masao Mukaidono*, and Hung T. Nguyen***
*Department of Computer Science, Meiji University, Kawasaki-shi, Kanagawa-ken, Japan
**Petra Christian University, Siwalankerto 121-131, Surabaya, Indonesia 60236
***New Mexico State University, Las Cruces, NM 88003-8001, USA
This paper discusses the relationship between probability and fuzziness based on the process of perception. As a generalization of the crisp set, the fuzzy set is used to model fuzzy events as proposed by Zadeh. Similarly, we may consider the rough set to represent a rough event in terms of probability measures. Special attention will be given to conditional probability of fuzzy events as well as the conditional probability of rough events. Several combinations of formulation and properties are examined. In the relation to evidence theory, the probability of a rough event may be considered as a connecting bridge between belief-plausibility measures and the probability measures. Moreover, a generalized fuzzy-rough event is introduced to generalize both fuzzy and rough events.