Abstract: The main goal of this paper is to study the interactive multi-attribute decision making problem where the attribute value is described by interval-valued Pythagorean fuzzy number and the information about criteria weight is incomplete. Firstly, the projection of the weighted score vector of every alternative on the Pythagorean fuzzy positive and negative ideal points is obtained by using the score function of interval-valued Pythagorean fuzzy number, and an optimization model is established to obtain the criteria weights. Secondly, a single objective programming model is obtained by using the objective information of alternatives and the subjective requirements provided by the decision maker, and the process of interactive decision making is implemented by giving and revising the satisfactory degree of alternative. Finally, an illustrated example is given to verify the effectiveness and feasibility of the proposed method.

Key words: multi-attribute decision making, interval-valued Pythagorean fuzzy number, projection, satisfactory degree, interactive

摘要： 研究了权重信息部分已知，评价信息为区间Pythagorean模糊数的交互式多准则决策问题。利用区间Pythagorean模糊数得分函数，计算各方案的加权得分向量在Pythagorean模糊正理想点和Pythagorean模糊负理想点上的投影，构建基于方案满意度最大的非线性规划准则权重确定模型。根据决策者的主观偏好并结合现有客观信息建立单目标规划模型，通过对方案满意度的给定与修正来实现交互决策。通过算例说明模型及方法的可行性和有效性。

关键词: 多准则决策, 区间Pythagorean模糊数, 投影, 满意度, 交互