Frank算子在广义正交梯形模糊语言环境下的应用  

Q-rung Orthopair Trapezoid Fuzzy Linguistic Frank Aggregation Operators and Their Application

作　　者：杜玉琴 李媛媛 杜向军 侯福均[4] 崔建新 DU Yuqin;LI Yuanyuan;DU Xiangjun;HOU Fujun;CUI Jianxin(School of Economics,University of Chinese Academy of Social Sciences,Beijing 102488,China;Department of Finance,Binhai College,Nankai University,Tianjin 300270,China;College of Mechanical Engineering,Tianjin Polytechnic University,Tianjin 300387,China;School of Management and Economics,Beijing Institute of Technology,Beijing 100081,China;China Railway Investment Group Limited,Beijing 100039,China)

机构地区：[1]中国社会科学院大学经济学院,北京102488 [2]南开大学滨海学院金融学系,天津300270 [3]天津工业大学机械工程学院,天津300387 [4]北京理工大学管理与经济学院,北京100081 [5]中铁投资集团有限公司,北京100039

出　　处：《复旦学报（自然科学版）》2023年第4期542-552,共11页Journal of Fudan University：Natural Science

基　　金：国家自然科学基金(71771025);教育部人文社会科学研究规划基金(22YJA630017);中国社会科学院大学校级卓越项目(校20220026);中国社会科学院大学校级拔尖项目(校20230031)。

摘　　要：基于广义正交梯形模糊语言变量及Frank T模和S模,定义了广义正交梯形模糊语言环境下的Frank T模和S模的运算规则。同时,给出了广义正交梯形模糊语言Frank加权算术平均算子、加权几何平均算子的具体表达形式,并证明了算子具有幂等性、有界性、单调性等性质。之后,将这些算子应用于属性权重已知且属性值以广义正交梯形模糊语言变量形式给出的多属性群决策问题中。最后,提出了两种不同的决策方法来处理多属性决策问题,并通过具体的示例验证了文中所提方法的正确性和可行性。Based on the q-rung orthopair trapezoidal fuzzy linguistic variables and Frank T-modules and S-modules,the q-rung orthopair trapezoid fuzzy linguistic Frank aggregation operator is proposed,and it is applied to multi-attribute decision problems.Firstly,the operation rules of Frank T-modules and S-modules in the q-rung orthopair trapezoid fuzzy linguistic environment are defined,and the q-rung orthopair trapezoid fuzzy linguistic Frank weighted arithmetic average operator and the q-rung orthopair trapezoid fuzzy linguistic Frank geometric average operator are given,and the idempotence,boundedness,and monotonicity for the proposed operators are proved.Afterwards,these operators are applied to deal with the multi-attribute group decision problem which the attribute weights are known and the attribute values are given in the form of q-rung orthopair trapezoid fuzzy linguistic variables.Based on the operators in this paper,two different decision-making methods are constructed to study the decision problem with q-rung orthopair trapezoid fuzzy linguistic variables.Finally,an example is given to illustrate the correctness and practicability of the proposed approaches.

关 键 词：广义正交模糊集 广义正交梯形模糊语言集 集结算子 Frank算子 

分 类 号：C934[经济管理—管理学]