Fuzzy Tensor And Its Application In Intuitionistic Fuzzy Information Aggregation Theory

With the rapid development of social economy and the improvement of sci-ence and technology,human beings are faced with an increasingly complicated actual decision making environment.Because of the fuzziness of decision makers’cognition and the uncertainty of decision making factors,it is difficult for decision makers to obtain certain decision information.Moreover,in an actual decision making process,more and more information affects the decision making process of decision makers,and the resulting dimension and magnitude of decision-making data become larger and larger;These difficulties make it difficult for decision mak-ers to make effective and rational decisions.As an important part of modern decision making theory and practice,the intuitionistic fuzzy multiple attribute decision making can effectively simulate complex decision making environment.However,the original decision making method based on matrix theory is diffi-cult to effectively solve practical complex decision making problems.Therefore,this paper will propose fuzzy tensor technique for the first time,and apply the fuzzy tensor technique in modeling,computation and synthetic integration studies of complex decision systems,and it is proved that this technique has important theoretical and applied value.The specific research contents are as follows:(1)In this paper,we define fuzzy tensor and its operation rules,and prove that the product of fuzzy tensor and fuzzy vector is a fuzzy linear transformation,and establish a generalized fuzzy comprehensive evaluation model based on fuzzy tensor for the first time,and propose an algorithm for the positive and negative problems of generalized fuzzy comprehensive evaluation.The feasibility and effectiveness of this model and algorithm are verified by two examples.It provides a new theory and method for solving the complex decision system represented by fuzzy multiple attribute group decision making.Compared with the previous methods,the model and method proposed in this paper has the characteristics of simple modeling,strong data processing capability and wide applicability.(2)For the intuitionistic fuzzy multiple attribute decision making problem with high-dimensional data features,we define the intuitionistic fuzzy tensor and its operation rules for the first time,and establish the generalized intuitionistic fuzzy weighted average operator and the generalized intuitionistic fuzzy weighted geometrical algorithm based on the intuitionistic fuzzy tensor in this paper.The two types of operators are idempotent,boundedness and monotonic.The nov-el method for solving intuitionistic fuzzy multiple attribute decision making and dynamic intuitionistic fuzzy multiple attribute decision making is proposed.The effectiveness and general applicability of the proposed method are verified by two typical examples.(3)For the interval-valued intuitionistic fuzzy multi-attribute group decision making and dynamic interval-valued intuitionistic fuzzy multiple attribute group decision making problem,we define interval-valued intuitionistic fuzzy tensor and its operation rules for the first time,and give the generalized interval-valued in-tuitionistic fuzzy weighted average operator and generalized interval-valued intu-itionistic fuzzy weighted geometric operator with the interval-valued intuitionistic fuzzy tensor as the core in this paper.By studying the properties of two kinds of operators,a new algorithm for solving multiple attribute group decision problems in interval-valued intuitionistic fuzzy environment is proposed.The effectiveness and practicality of the algorithm are verified by two practical examples.(4)For the problem of linguistic fuzzy multiple attribute group decision mak-ing,we define the triangular intuitionistic fuzzy tensor for the first time,and pro-pose a generalized triangular intuitionistic fuzzy aggregation operator based on triangular intuitionistic fuzzy tensor in this paper.The multiple attribute group decision making method based on generalized triangular intuitionistic fuzzy aggre-gation operator is established.The effectiveness and practicality of the method is verified by the numerical examples.