Abstract: This paper studies the multi-attribute group decision making problems where the attribute values are triangular intuitionistic fuzzy numbers (TIFNs), and proposes a new decision making method on the basis of weight function. Firstly, this paper introduces the concept, arithmetic operations and cut sets of TIFNs. Secondly, this paper defines the crisp value and ambiguities of the membership function and the non-membership function for TIFNs as well as the crisp value-index and ambiguity-index, then develops a crisp value and ambiguity based ranking method and uses the method to solve multi-attribute decision making problems. Thirdly, this paper gives the steps of triangular intuitionistic multiple attribute decision making. Finally, an illustrative example shows the effectiveness of the proposed method.

Key words: triangular intuitionistic fuzzy number, decision making, ranking

摘要： 研究了属性值为三角直觉模糊数的多属性决策问题，提出了一种基于权重函数的决策方法。给出了三角直觉模糊数的定义、运算法则和截集；定义了三角直觉模糊数关于隶属函数和非隶属函数的精确值和模糊度，以及精确值的指标和模糊度的指标，给出了三角直觉模糊数的排序方法，并将其应用到属性值为三角直觉模糊数的多属性决策问题中；给出了属性值为三角直觉模糊数的多属性决策的步骤；通过数值算例分析和验证了该方法的有效性。

关键词: 三角直觉模糊数, 决策, 排序