The Study Of Intuitionistic Fuzzy Sets

This paper is mainly about intuitionistic fuzzy sets.In this paper a connection between intuitionistic fuzzy special sets (IFSS)and intuitionistic fuzzy sets (IFS)was built up.Firstly,by the use of the concept of IFSS,the concept of intuitionistic nested sets (INS) is presented and have proved that an IFS can be considered as an equivalent class of an INS.The conclusion make a theoretical base for IFS's study. Secondly,the concept of cut sets of IFS is introduced and the properties of cut sets of IFS are discussed. Thirdly,decomposition theorem, representation theorem and extension principle of IFS are obtained .Finally,two applications to representation theorem of IFS are discussed. One is about intuitionistic fuzzy relation,the concept of intuitionistic fuzzy relation is introduced and by the use of representation theorem the composition of intuitionistic fuzzy relation is ob-tained.The other is about ntuitionistic fuzzy group,the concept of G intuitionistic nested sets (GINS) is presented and by the use of representation theorem ntuitionistic fuzzy group is defined in another way.