Fuzzy Probability Approximation Space and Its Information Measures
نویسندگان
چکیده
Rough set theory has attracted much attention in modeling with imprecise and incomplete information. A generalized approximation space, called fuzzy probability approximation space has been proposed by introducing probability into fuzzy approximation space. The novel definition combines three types of uncertainty into a model. Information or knowledge is considered as a partition of the universe in rough set framework. We introduce Yager’s entropy to measure knowledge quantity implied in fuzzy probability approximation space. It’s shown that the information measure for fuzzy probability approximation space is a rational extension of the Shannon’s one and it degrades to Shannon’s entropy in case where attributes are nominal and objects are equality-probable. Then a uniform information measure for Pawlak’s rough set model, fuzzy rough set model and fuzzy probability rough set model is formed based one Yager’s entropy.
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