勾股模糊偏好關系及其在群體決策中的應用

摘要： 以區(qū)間模糊偏好關系(IVFPR)和直覺模糊偏好關系(IFPR)的理論框架為依據(jù),將勾股模糊數(shù)(PFN)引入偏好關系中,定義勾股模糊偏好關系(PFPR)和加性一致性PFPR.然后,提出標準化勾股模糊權重向量(PFWV)的概念,并給出構造加性一致性PFPR的轉換公式.為獲取任意給定的PFPR的權重向量,建立以給定的PFPR與構造的加性一致性PFPR偏差最小為目標的優(yōu)化模型.針對多個勾股模糊偏好關系的集結,利用能夠有效處理極端值并滿足關于序關系單調的勾股模糊加權二次(PFWQ)算子作為集結工具.進一步,聯(lián)合PFWQ算子和目標優(yōu)化模型提出一種群體決策方法.最后,通過案例分析表明所提出方法的實用性和可行性.
Based on the theoretical framework of interval-valued fuzzy preference relation(IVFPR) and intuitionistic fuzzy preference relation(IFPR), the Pythagorean fuzzy number(PFN) is introduced into the preference relation, and the concepts of Pythagorean fuzzy preference relation(PFPR) and additive consistent PFPR are proposed. Then, the definition of normalized Pythagorean fuzzy weight vector(PFWV) is proposed, and a conversion formula is provided to convert this PFWV into the additive consistent PFPR. For any given PFPR, a goal programming model is developed to obtain its Pythagorean fuzzy weights by minimizing its deviation from the constructed additive consistent PFPR. Because the Pythagorean fuzzy weighted quadratic(PFWQ) operator can effectively deal with extremes and satisfy the monotonicity with respect to the order relation, it is used for the aggregation of multiple PFPRs. A group decision making approach is proposed by using the PFWQ operator and the goal programming model, and a practice example is given to illustrate the practicability and feasibility of the proposed approach.