Interval Entropy Of Two Kinds Of Intuitionistic Fuzzy Sets And Its Applications

Since the membership function of the fuzzy sets(FSs)has uncertainty,the entropy of the FSs is used to measure the degree of uncertainty of the FSs,the similarity measure is used to measure the degree of similarity between the FSs.The entropy and similarity measure of FSs are applied in multi-attribute decision making(MADM),pattern recognition and medical diagnosis.In this paper,the method of interval entropy of FSs is generalized for the defect of entropy of intuitionistic fuzzy sets(IFSs).The concept of interval entropy and interval similarity measure of IFSs and interval-valued intuitionistic fuzzy sets(IVIFSs)are proposed.The mutual transformation relationship between interval entropy and interval similarity measure and their application in fuzzy MADM are discussed.The main contents of this paper are as follows:(1)The definitions of interval entropy and interval similarity of IFSs are given.By analyzing the entropy formulas of existing IFSs,it is found that these entropy formulas sometimes have some disadvantages such as the inability to distinguish the uncertainty of IFSs.Based on the definition of entropy of IFSs and interval entropy of FSs,the definitions of interval entropy and interval similarity measure of IFSs are proposed.Several interval entropy and interval similarity formulas are mentioned.By constructing a new intuitionistic fuzzy set,it is proved that the interval entropy and the interval similarity measure can be transformed into each other.(2)The definitions of interval entropy and interval similarity measure of IVIFSs are given.By extending the interval entropy and interval similarity measure of IFSs,the definitions of interval entropy and interval similarity measure of IVIFSs are given.Several interval entropy formulas are proposed,the rationality of the interval entropy formula is illustrated by an example.Through the constructed interval-valued intuitionistic fuzzy set,the interval entropy can be transformed into interval similarity measure,and an interval similarity formula is obtained by the interval entropy formula.(3)The application of interval entropy of IFSs and IVIFSs is studied in MADM.Based on the principle of entropy weight method,the specific algorithm steps are showed.Using the interval entropy formulas from the first two chapters,the specific methods of intuitionistic fuzzy MADM and interval-valued intuitionistic fuzzy MADM with unknown attribute weights are given.The obtained results are compared with the attribute weight values calculated by the existing entropy formula and the ranking results of the program set,the effectiveness of interval entropy method is illustrated.