The logarithmic operational laws of intuitionistic fuzzy sets and intuitionistic fuzzy numbers

Intuitionistic fuzzy set (IFS) is an extension of fuzzy set. The basic element of an IFS is the ordered pair called intuitionistic fuzzy number (IFN). So far, some basic operational laws of IFNs are defined, but not including the logarithmic operation. In this paper, a logarithmic operational law a bout IFNs is defined, in which the base λ is a real number in (0, 1). Then some properties of the operational law are investigated, and four intuitionistic fuzzy information aggregation methods are proposed. Finally, the influences of logarithmic operation for IFNs and the selection of the logarithmic base λ in practice are discussed, and an example is illustrated to show the applications of the operational law and the aggregation methods.