Research On Multi-attribute Decision Making Method Based On Complex Cubic Fuzzy Sets

Since Zadeh proposed the concept of fuzzy set in 1965,it has attracted the attention of many scholars.The multi-attribute decision-making method of fuzzy sets has been applied in various fields of real life,such as engineering,economics,management and so on.However,with the development of economy and society,the existing fuzzy multi-attribute decision-making methods have been difficult to solve complex multi-attribute decision-making problems.Therefore,many scholars have successively proposed various extended models of fuzzy sets,and they have achieved fruitful results.Among them,cubic set and complex fuzzy set are two very classic models,but complex fuzzy set only has membership function and lacks the description of non-membership function.A cubic set has no additional phase term and cannot represent changes in phase.In order to make up for these deficiencies and further improve the accuracy of the multi-attribute decision-making method,a new hybrid model,called complex cubic fuzzy set,is obtained by combining cubic sets and complex fuzzy sets.The main research work is as follows:(1)By combining two models of complex fuzzy set and cubic set,a hybrid model called complex cubic fuzzy set is proposed,some of its algebraic operation rules are defined,and the basic properties of these operations are studied.Based on the defined algebraic operation rules,complex cubic fuzzy weighted average operator and complex cubic fuzzy weighted geometric operator are constructed.By studying their basic properties,some complex cubic fuzzy multi-attribute decision-making methods are further proposed to solve complex multi-attribute decision-making question.(2)A series of complex cubic fuzzy Hamacher operators are constructed.Under the complex cubic fuzzy environment,the complex cubic fuzzy Hamacher average operator and the complex cubic fuzzy Hamacher geometric operator are constructed,and some special cases of these operators are studied in detail.Based on the constructed complex cubic fuzzy Hamacher operator,a complex cubic fuzzy multi-attribute decision-making method is further proposed.By adjusting the value of parameter λ,the influence of parameter λ change on the decision-making result is analyzed.(3)Based on the distance measure formula of the traditional fuzzy set model,the distance measure formula of the complex cubic fuzzy set model is studied in detail,including the complex cubic fuzzy weighted Hamming distance measure,the complex cubic fuzzy normalized Hamming distance measure,Complex cubic fuzzy weighted Euclidean distance measure,complex cubic fuzzy normalized Euclidean distance measure and complex cubic fuzzy normalized distance measure based on Hausdorff measure.According to the defined complex cubic fuzzy distance measure,combined with Hierarchical K-means clustering algorithm,a complex cubic fuzzy Hierarchical K-means clustering algorithm is constructed and applied to solve the clustering problem in complex cubic fuzzy environment.