Multi-attribute Decision-making And Clustering Of Several Types Of Fuzzy Information Based On Archimedes Norm

Fuzzy set provides an effective way to deal with complex uncertain problems.The various extended forms of fuzzy set describe the uncertain information more comprehensively.Among the more typical forms are intuitionistic fuzzy set,neutrosophic set,hesitant fuzzy set and so on.As the main forms of complex fuzzy information expression,intuitionistic fuzzy set,neutrosophic set and hesitant fuzzy set have been widely used in decision analysis,cluster analysis,medical diagnosis,artificial intelligence and other fields.Multiple attribute decision making and clustering are important directions in the research of complex fuzzy information,which have attracted more and more scholars at home and abroad.Multiple attribute decision making of complex fuzzy information is an important part of modern decision science.Information fusion is an effective way to solve this complex fuzzy information multiple attribute decision problem.In fuzzy clustering,the establishment of fuzzy similar matrix is a foundation of fuzzy clustering.It is also an important research direction to synthesize fuzzy similar matrix into fuzzy equivalent matrix for clustering.Both the aggregation operator in information fusion and the matrix synthesis in clustering are related to the operation problem.But the operation of aggregation operator is mainly based on the Algebraic t-norm and t-conorm,and the matrix synthesis is based on the max-min t-norm and t-conorm.Algebraic t-norm and t-conorm as well as the max-min t-norm and t-conorm are special cases of Archimedean norms.Archimedean norms provide general rules for the operation of aggregation operator and matrix synthesis.Based on intuitionistic fuzzy set,neutrosophic set and hesitant fuzzy set,scholars have extended branches,such as single-valued neutrosophic set,normal neutrosophic set,neutrosophic soft set,intuitionistic hesitant fuzzy set and dual hesitant fuzzy set.Therefore,this paper focuses on the multiple attribute decision making problems of normal neutrosophic set and dual hesitant fuzzy set and the clustering problem of single-valued neutrosophic set.In this paper,the main contents are as follows:(1)Frist,the concepts of score function,accuracy function and partial operational laws are defined under the nonnegative normal neutrosophic environment.Considering the correlation between any aggregation arguments,the dual generalized nonnegative normal neutrosophic weighted Bonferroni mean operator and dual generalized nonnegative normal neutrosophic weighted geometric Bonferroni mean operator are investigated,and their properties are presented.Here,these two operators are applied to deal with a multiple attribute decision making of nonnegative normal neutrosophic number.(2)Geometric Heornian mean have advantages when considering the interrelationship of aggregation arguments.And Archimedean norms provides generalized operational rules for dual hesitant fuzzy set.Thus,it is necessary to extend the geometric Heornian mean operator to the dual hesitant fuzzy environment based on Archimedean norms.The dual hesitant fuzzy geometric Heronian mean operator and dual hesitant fuzzy geometric weighted Heronian mean operator based on Archimedean norms are developed.Their properties and special case are investigated.Moreover,a multiple attribute decision making method is proposed.(3)The concept of composite matrix based on Archimedean norms is defined under singlevalued neutrosophic environment.Then,a synthesis method of single-valued neutrosophic equivalent matrix based on Archimedean norms is given.A ?-cutting matrix of single-valued neutrosophic number matrix is also introduced.Moreover,their related properties are studied.Furthermore,a clustering algorithm based on the single-valued neutrosophic equivalent matrix is developed.On the basis of the above theoretical research,the relevant examples for each decision making and clustering method are given.The feasibility of the proposed methods are demonstrated.The influence of parameters on the decision making results in multiple attribute decision making is analyzed.At the same time,the comparative analysis with other existing methods are given,and the advantages of the proposed methods are verified from the results.