Uncertainty Measures Of Type-2 Fuzzy Sets And Type-2 Intuitionistic Fuzzy Sets

Since entropy can reflect the confusion degree of information,and similarity measures can express the proximity of different information systems,they have become important research directions in the theories and application of type-2 fuzzy sets and type-2 intuitionistic fuzzy sets in recent years.At present,the construction and application of type-2fuzzy entropy of decision-making problems for selecting the optimal scheme continue to be worth studying.The existing similarity measure formulas of type-2 fuzzy sets exist some problems,such as large computation and weak ability to distinguish the different data,so it is necessary to continue to discuss the similarity measure of type-2 fuzzy sets.At the same time,type-2 intuitionistic fuzzy sets have stronger uncertainty,and their applications in decision-making problem,pattern recognition and other fields are worth further exploration.Firstly,based on the axiomatic criterion of type-2 fuzzy entropy,a new type-2 fuzzy entropy formula is introduced by cosine function,the hesitation and fuzziness of type-2fuzzy sets are taken into account.In the decision-making process,the risk attitude of decision-makers is considered and a risk appetite factor is induced.At the same time,considering the interplay of the primary membership degree and the sub-degree membership,we give a new scoring matrix,and build a nonlinear optimization model under the environment that the attribute weights are completely unknown to observe the impact of risk appetite on attribute weights based on the entropy.Secondly,based on the method of Riemann's closeness,a new similarity measure formula is proposed.The formula is proved to satisfy the similarity measure criterion of type-2 fuzzy sets,which is more widely applicable than the existing formula.And good clustering effect can be achieved by applying it to clustering algorithm.Finally,the axiomatic definition of similarity measures in type-2intuitionistic fuzzy sets is proposed.Furthermore,the similarity measure formula is given and applied to decision-making problems,which provide a new idea for decision-making under type-2 intuitionistic fuzzy environment.