直觉模糊交叉影响Choquet积分算子及其决策应用

Intuitionistic Fuzzy Interaction Choquet Integrals Operators and Applications in Decision Making

直觉模糊Choquet积分集成算子能有效解决属性关联的直觉模糊决策问题,直觉模糊数交叉影响运算能反映出不同直觉模糊数的隶属度和非隶属度之间的交叉影响.通过将直觉模糊Choquet积分平均算子与直觉模糊数交叉影响运算相结合,定义了直觉模糊交叉影响Choquet积分集成算子,包括直觉模糊交叉影响Choquet积分平均算子(IFICIA)和直觉模糊交叉影响Choquet积分几何算子(IFICIG),推导出它们的计算公式,讨论了它们的性质.通过研究直觉模糊交叉影响Choquet积分集成算子的特殊形式,发现直觉模糊交叉加权平均算子(IFIWA)和有序加权平均算子(IFIOWA)、直觉模糊交叉加权几何算子(IFIWG)和有序加权几何算子(IFIOWG)等均为它们的特例。最后,提出了基于直觉模糊交叉影响Choquet积分集成算子的决策方法,通过决策实例说明其可行性和稳定性。

Intuitionistic fuzzy Choquet integral aggregation operators can effectively solve intuitionistic fuzzy decision making problems,which exist interactions among decision making criteria. Intuitionistic fuzzy interaction operations can reflect some interactions between membership function and non- membership function. To Combine intuitionistic fuzzy interaction operations with intuitionistic fuzzy Choquet integral aggregation operators, the intuitionistic fuzzy interaction Choquet integral aggrega- tion operators are defined, including the intuitionistic fuzzy interaction Choquet integral averaging operator （IFICIA） and the intuitionistic fuzzy interaction Choquet integrals geometric operator （IFICIG）, and the mathematical expressions of their operators are obtained by derivation and some properties of the operator are discussed. It is worth pointing that some intuitionistic fuzzy aggregations operators, such as IFIWA operator, IFIOWA operator, IFIWG operator and IFIOWG operator, can be regarded as the special cases of the intuitionistic fuzzy interaction Choquet integral aggregation operators.Finally, an approach for decision making based on the intuitionistic fuzzy interaction Choquet integrals aggregation operators is presented, and an illustrative example is given to demonstrate the stability and feasibility of the developed method.