Information Systems on Hesitant Fuzzy Sets

Knowledge extraction from information systems is one of the most significant problems in artificial intelligence. This paper attempts to study information systems in the hesitant fuzzy domain. It studies information systems which has a set of possible membership values. Illustration of a case is provided where the hesitant membership values are arrived at from attribute values whose membership values are a family of sets. The membership value here would turn out to be a subset of the power set of membership values from the usual information system. Although it does not mean that it is arrived at from usual information systems. Reduct, core, relative reduct, relative core and the corresponding indiscernibility matrices are also studied. Apart from these, paper also discusses the homomorphisms between hesitant information systems. For two homomorphic information systems the reduct and core of one information system are the corresponding images of the reduct and core of the other information system under this homomorphism.