乘型一致性毕达哥拉斯模糊偏好关系

Multiplicative consistent Pythagorean fuzzy preference relation

毕达哥拉斯模糊偏好关系(PFPR)是直觉模糊偏好关系的推广,也是毕达哥拉斯模糊集的重要研究领域.相对于其他模糊偏好关系而言,毕达哥拉斯模糊偏好关系在表达决策者的模糊偏好时更加灵活有力.在乘型一致性区间模糊偏好关系和乘型一致性直觉模糊偏好关系研究成果的启发下,定义毕达哥拉斯模糊偏好关系的乘型一致性,并提出利用毕达哥拉斯模糊权重向量构造乘型一致性毕达哥拉斯模糊偏好关系的公式.以给定的毕达哥拉斯模糊偏好关系与构造的乘型一致性毕达哥拉斯模糊偏好关系的偏差最小为目标函数建立并求解优化模型,从而获取毕达哥拉斯模糊偏好关系的标准化权重向量,为方案排序提供一种可行的方法.计算实例分析表明,所提出方法是可行有效的.

As an expansion of the intuitionistic fuzzy preference relation, the Pythagorean fuzzy preference relation(PFPR) is an important research direction of Pythagorean fuzzy set. The Pythagorean fuzzy preference relation, which expresses fuzzy preference information of a decision maker, is more powerful than the other fuzzy preference relations.Inspired by the multiplicative consistent interval fuzzy preference relation and the multiplicative consistent intuitionistic fuzzy preference relation, the multiplicative consistency of Pythagorean fuzzy preference relation is defined, and a formula,which involves the underlying Pythagorean fuzzy weights of the PFPR, is proposed to construct such a multiplicative consistent PFPR. Then, the normalized weight vector of the PFPR is obtained by building and solving an optimization model, whose objective function is the deviation between the original PFPR and the multiplicative consistent PFPR constructed. An example is used to illustrate the feasibility and effectiveness of the proposed method.