直觉梯形模糊语言Frank算子及其在决策中的应用

Intuitionistic Trapezoidal Fuzzy Linguistic Frank Operator and Its Application in Decision Making

本文在直觉梯形模糊语言集的基础上,引入了Frank算子,提出一组新的算子——直觉梯形模糊语言Frank集结算子,并将其应用到多属性决策中。首先,本文提出了直觉梯形模糊语言集Frank算子的表达式,并给出相应的运算规则。然后提出了直觉梯形模糊语言Frank加权算术平均(ITr FLFWA)算子、直觉梯形模糊语言Frank加权几何平均(ITr FLFWG)算子、直觉梯形模糊语言Frank广义加权平均(ITr FLGFWA)算子等,并证明了其具有幂等性、有界性、单调性等性质。最后,通过实例验证了直觉梯形模糊语言Frank算子可以有效解决直觉梯形模糊语言环境下的多属性决策问题。

Based on the set of intuitionistic trapezoidal fuzzy linguistic, this paper introduces the Frank operator and proposes a new set of operators-intuitionistic trapezoidal fuzzy linguistic Frank assembly operators, and applies it to multi - attribute decision-making. Firstly, we give the concept of the formula, the corresponding operation rules, the scoring function, the exact function and the size comparison method of the Frank operator in the intuitionistic trapezoidal fuzzy linguistic environment. Then we propose the intuitionistic trapezoidal fuzzy lin- guistic Frank weighted arithmetic （ITrFLFWA）operator, intuitionistic trapezoidal fuzzy linguistic Frank weighted geometric（ ITrFLFWG ）operator, intuitionistic trapezoidal fuzzy linguistic generalized Frank weighted average （ITrFLGFWA） operator, etc., and prove its properties such as idempotency, boundedness, monotonicity. Finally, the decision-making method of the based and integrated operator is given, and the decision of the invest- ment bank is given, which proves the validity of the method we propose. This method can be widely used in vari- ous combinations of investment decisions, risk decisions, supplier selection, and so on.