犹豫模糊语言Heronian平均算子在多属性决策中的应用

Hesitant Fuzzy Linguistic Heronian Mean Operators and Their Application to Multiple Attribute Decision Making

针对输入变量之间的相互影响以及评价值为犹豫模糊语言信息的多属性决策问题,提出一种基于犹豫模糊语言Heronian平均算子的多属性决策方法。由于Heronian平均(HM)算子具有能够反映输入变量之间相互关联的良好特性,在犹豫模糊语言信息环境下,提出了两种新的集成算子,即犹豫模糊语言Heronian平均(HFLHM)算子和犹豫模糊语言几何Heronian平均(HFLGHM)算子,同时研究了它们的一些特性。考虑到输入变量具有不同的重要程度,还定义了犹豫模糊语言加权Heronian平均(HFLWHM)算子和犹豫模糊语言加权几何Heronian平均(HFLWGHM)算子。最后提出了基于HFLWHM算子和HFLWGHM算子的犹豫模糊语言多属性决策方法,并通过实例验证了这些算子的合理性和可行性。

For solving multiple attribute decision making（MADM） problems when the evaluation values are in the form of hesitant fuzzy linguistic sets（HFLS） and the input arguments are associated with each other, an approach based on the Heronian mean （HM）operator is proposed to aggregate the hesitant fuzzy linguistic information. Due to the desirable properties of Heronian mean （HM）operator and geometric Heronian mean （GHM）operator that they can capture the interrelationship between input arguments, a hesitant fuzzy linguistic Heronian mean（HFL- HM） operator and a hesitant fuzzy linguistic geometric Heronian mean （HFLGHM）operator are proposed. Furthermore, some desirable properties and special cases of these operators are studied in detail. Considering the input arguments with different importance, the hesitant fuzzy linguistic weighted Heronian mean （HFLWHM） operator and the hesitant fuzzy linguistic weighted geometric Heronian mean （HFLWGHM）operator are defined. Moreover, based on these proposed aggregation operators, we develop an approach to deal with multiple attribute decision making problems under hesitant fuzzy linguistic to illustrate the practicality and validity of the proposed environment. Finally, a numerical example is provided method.