摘要
在直觉模糊集理论基础上,用梯形模糊数表示直觉模糊数的隶属度和非隶属度,进而提出了梯形直觉模糊数;然后定义了梯形直觉模糊数的运算法则,给出了相应的证明,并基于这些法则,给出了梯形直觉模糊加权算数平均算子(TIFWAA)、梯形直觉模糊数的加权二次平均算子(TIFWQA)、梯形直觉模糊数的有序加权二次平均算子(TIFOWQA)、梯形直觉模糊数的混合加权二次平均算子(TIFHQA)并研究了这些算子的性质;建立了不确定语言变量与梯形直觉模糊数的转化关系,并证明了转化的合理性;定义了梯形直觉模糊数的得分函数和精确函数,给出了梯形直觉模糊数大小比较方法;最后提供了一种基于梯形直觉模糊信息的决策方法,并通过实例结果证明了该方法的有效性。
On the foundation of the theory of the intuitionistic fuzzy set, trapezoid intuitionistic fuzzy number is proposed by using the trapezoid fuzzy number to denote the membership degree and the non-membership degree of the intuitionistic fuzzy number. Then, some operational laws of trapezoid intuitionistic fuzzy numbers are defined and proved. Based on these operational laws, some aggregation operators, including trapezoid intuitionistic fuzzy weighted arithmetic aggregation operator (TIFWAA), trapezoid intuitionistic fuzzy weighted quadratic average operator(TIFWQA),trapezoid intuitionistic fuzzy ordered weighted quadratic average operator (TIFOWQA) and trapezoid intuitionistic fuzzy hybrid quadratic average operator(TIFHQA), are proposed, and the properties of these operators are presented. The transformation relations from uncertain linguistic variable to trapezoidal intuitionistic fuzzy number are established and the rationality of conversion is proved. The score function and accuracy function of trapezoid intuitionistic fuzzy number are defined, and based on these two functions, a method for ranking trapezoid intuitionistic fuzzy numbers is presented. Finally, an approach for decision making with trapezoid intuitionistic fuzzy information is developed, and an illustrative example shows the effectiveness of the proposed approach.
出处
《模糊系统与数学》
CSCD
北大核心
2012年第3期127-138,共12页
Fuzzy Systems and Mathematics
基金
教育部人文社会科学研究项目(10YJA630073
09YJA630088)
山东省自然科学基金资助项目(ZR2011FM036)
关键词
梯形直觉模糊数
集成算子
多属性决策
Trapezoid Intuitionistic Fuzzy Number
Aggregation Operator
Decision Making