Abstract: By introducing dynamic characteristics to finite ordinary set X, the ordinary set Xwas improved and P-sets(packet sets) was proposed. P-sets is a pair of sets composed of internal P-set XF(internal packet set XF) and outer P-set XF (outer packet set XF ) , or, (XF , XF ) is P-sets. P-sets has dynamic characteristics, that is, internal P-set has internal dynamic characteristics and outer P-set has outer dynamic characteristics. P-sets(XF，XF ) was introduced to fuzzy set A of L.A. Zadeh, the fuzzy set A of I.A. Zadeh was improved, P-fuzzy sets(packet fuzzy sets) was given. P-fuzzy sets is a pair of fuzzy sets composed of internal P-fuzzy set AI' (internal packet fuzzy set AI') and outer P-fuzzy set AF(outer packet fuzzy set AF ) , or, (AF ,AF ) is P-fuzzy sets. P-fuzzy sets has dynamic characteristics, some properties and applications of P-fuzzy sets were given. Under certain conditions,P-fuzzy sets (AF ,AF )can come back to the original of ordinary fuzzy set A of L. A. Zadeh. P-fuzzy sets has more extensive applications than fuzzy set of L. A. Zadeh. P-fuzzy sets is a new direction of fuzzy set theory and applied research.

Key words: P-fuzzy set, Internal P-set, Outer P-set, Cardinal theorem, Application