Build Complicated Granules with Generalized Operations of Fuzzy Sets

Granular computing is a new paradigm in intelligent computing after L.A. Zadeh proposed the information granulation. In the procedure of processing granules, we often meet with fuzzy sets, also being granules, built on different universes, especially complicated composed universes. This paper gives the generalized definitions of the union and the intersection of two fuzzy sets defined on different universes which are in the forms of Cartesian product. The existing definitions of union and intersection of fuzzy sets separately given by L.A. Zadeh, P.Zh. Wang&H.X. Li, and K. Chakrabarty etc. may be treated as the particular cases of this new definition. Some properties of fuzzy sets are investigated under the new definition. The result allows us to deal with the operations of fuzzy sets over different universes, and thus is useful in the process of knowledge acquisition, knowledge representation, and granular computing.