三角犹豫模糊Heronian平均算子及其在多属性决策中的应用

Hesitant Triangular Fuzzy Heronian Mean Operators and Their Application in Multiple Attribute Decision Making

针对属性间含有关联信息的三角犹豫模糊多属性决策问题,提出一种基于三角犹豫模糊Heronian平均算子的决策方法。首先,考虑已有Heronian平均算子仅适用输入变量为两参数的情形,进一步定义三参数加权Heronian平均(TPWHM)和三参数加权几何Heronian平均(TPWGHM)算子,证明所提算子具有还原性、幂等性、单调性和有界性等性质,并研究它们的几种特例。其次,将TPWHM和TPWGHM算子推广至三角犹豫模糊决策环境下,提出三角犹豫模糊三参数加权Heronian平均(HTFTPWHM)和三角犹豫模糊三参数加权几何Heronian平均(HTFTPWGHM)算子,并证明算子的优良性质。在此基础上,提出基于两种算子的决策分析方法,并用来解决三角犹豫模糊决策问题。最后,通过算例验证所提方法的可行性和合理性。

For solving the multiple attribute decision making problems in which the attribute values are in the form of hesitant triangular fuzzy elements and the attributes are associated with each other, some approaches to multiple attribute decision making are proposed based on hesitant triangular fuzzy Heronian mean operators. Firstly, considering that the existing Heronian mean operators only consider the correlations of any two aggregated arguments, we develop the new three parameters weighted Heronian mean(TPWHM)and three parameters weighted geometric Heronian mean(TPWGHM)operators, and have proved some desirable properties of these proposed operators, such as reducibility, idempotency, monotonicity and boundedness. Some special cases are discussed. Then because hesitant triangular fuzzy sets can easily express fuzzy information, we investigate the hesitant triangular fuzzy three parameters weighted Heronian mean(HTFTPWHM)and hesitant triangular fuzzy three parameters weighted geometric Heronian mean(HTFTPWGHM)operators, and discuss some properties of the proposed operators. Moreover, some approaches based on the developed operators are proposed. Finally, we give an example to illustrate the feasibility and rationality of the proposed approaches.