基于隶属度与非隶属度交叉影响的直觉模糊集运算法则及其应用

Operations Laws for the Intuitionistic Fuzzy Sets and Their Application Based on Interaction between Membership Function and Non-membership Function

考虑到不同直觉模糊集的隶属度与非隶属度之间可能存在着某些关联和相互影响,本文提出了直觉模糊集上的改进的加法运算、数乘运算、乘积运算和幂运算。在这些运算的基础上,我们重新给出了直觉模糊加权算术平均算子、直觉模糊有序加权算术平均算子、直觉模糊加权几何平均算子和直觉模糊有序加权几何平均算子的表达式,并研究了他们的一些性质。最后通过实例,说明了新的集成算子在决策应用中的有效性。

There may also exist some interactions between membership function and non- membership function of different intuitionistic fuzzy sets . We propose the improved operations laws over intuitionistic fuzzy sets, including addition, scalar multiplication, multiplication and power operations. Based on which, we give the expression for the intuitionistic fuzzy weighted arithmetic average operator, the intuitionistic fuzzy ordered weighted arithmetic average operator, the intuitionistic fuzzy weighted geometric average operator and the intuitionistic fuzzy ordered weighted geometric average operator. We also study the properties of these operators. Finally, an example shows the feasibility and validity of the new operator in the application of decision making problems.