梯形直觉模糊数集成算子及在决策中的应用研究

发布时间：2018-08-26 20:52

【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。
[Abstract]:On the basis of intuitionistic fuzzy set theory, the membership degree and non-membership degree of intuitionistic fuzzy number are expressed by trapezoid fuzzy number, and then the trapezoid intuitionistic fuzzy number is proposed, and the arithmetic of trapezoid intuitionistic fuzzy number is defined, and the corresponding proof is given. And based on these laws, In this paper, the weighted quadratic average operator of (TIFWAA), trapezoid intuitionistic fuzzy number is given. The ordered weighted quadratic average operator (TIFOWQA), trapezoid intuitionistic fuzzy number of (TIFWQA), trapezoid intuitionistic fuzzy numbers is given. The mixed weighted quadratic average of (TIFOWQA), trapezoid intuitionistic fuzzy numbers is given. (TIFHQA) operators and the properties of these operators are studied. The transformation relationship between uncertain language variables and trapezoid intuitionistic fuzzy numbers is established, and the rationality of the transformation is proved, the score function and accurate function of trapezoid intuitionistic fuzzy numbers are defined, and the comparison method of trapezoid intuitionistic fuzzy numbers is given. Finally, a decision method based on trapezoid intuitionistic fuzzy information is presented, and the effectiveness of the method is proved by an example.
【作者单位】：山东财经大学管理科学与工程学院;
【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)
【分类号】：C934

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