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

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.