The Operations of Fuzzy Cardinalities

Due to the difficulties involved in defining the cardinalities of fuzzy sets, the research on this subject has been advancing very slowly. In an earlier paper, we gave a much more appropriate definition. Thus, we not only obtained most of the results with respect to the cardinalities in Cantor′s set theory, but also succeeded in obtaining many new properties of the cardinalities of fuzzy sets. In this paper, the operations of the cardinalities of fuzzy sets, including the sum, the product, and the power, are discussed in detail.