The logical data independence and physical data independence are necessary for data mining particularly for BIG DATA. The data base defining inherency with fuzziness will reduce the time in Information retrieval. The Data Mining is very fast using the fuzzy log for BIG DATA. In this paper, fuzzy data mining is studied and fuzzy association dependency is defied. The fuzzy MapReducibg algorithm is studied for BIG DATA to reduce the retrieval time for BIG DATA. This algorithm wills qick reference to perticular information and actual information will be secured.