改进的直觉模糊得分函数及其决策应用  

Improved Score Function of Intuitionistic Fuzzy Numbers and Its Application in Decision-Making

作　　者：方冰 朱江 白承森 FANG Bing;ZHU Jiang;BAI Chengsen(Army Command College of PLA,Nanjing 210045,China)

机构地区：[1]陆军指挥学院,江苏南京210045

出　　处：《陆军工程大学学报》2024年第5期40-48,共9页Journal of Army Engineering University of PLA

基　　金：国家自然科学基金(71401177)。

摘　　要：直觉模糊数之间的比较问题一直都是直觉模糊决策理论的核心课题。针对已有得分函数区分能力不足、构造过于复杂等问题,从全新视角出发,提出新的直觉模糊得分函数,并对其适用性进行必要拓展,定义了用于定量比较两个直觉模糊数区分程度的新可能度公式;基于所提公式,构建了适用于直觉模糊环境的新型多属性决策方法,并将其应用于具体的决策实践。理论分析和实验结果表明,新得分函数是对Ata-nassov偏序关系的精炼,能够在直觉模糊数集中建立起更为合理、可信的弱序关系;所提公式具有一定优势,能够有效拓展所提得分函数的适用性;基于可能度矩阵构建的直觉模糊多属性决策方法在决策过程中具有较强的自检能力,能够通过保证决策过程的正确性来确保最终结果的可靠性,且便于大规模决策运用。Comparison of intuitionistic fuzzy numbers(IFNs)is always the core issue of decision-making theory with intuitionistic fuzzy sets(IFSs).To address the issues of insufficient discrimination ability and overly complex construction in existing score functions,a new intuitionistic fuzzy score function is proposed from a fresh perspective,and its applicability is necessarily expanded by defining a new possibility degree formula for quantitatively comparing the degree of discrimination between two IFNs.Based on the proposed formula,a novel multi-attribute decision-making(MADM)method suitable for intuitionistic fuzzy environments is constructed and applied to specific decision-making practices.The theoretical analysis and experiment results indicate that the proposed score function has refined Atanassov's partial order and can construct a more reasonable admissible weak order among all IFNs,and the proposed possibility degree formula employs some nice properties and can effectively expand the usage of the proposed score function of the IFNs.Moreover,the proposed intuitionistic fuzzy MADM method,based on the possibility degree matrix,has a strong self-checking capability in the decision-making process and can ensure the validity of the final decision-making results by guaranteeing the calculation process,and is applicable for large-scale decision-making.

关 键 词：多属性决策 直觉模糊集 直觉模糊数 得分函数 可能度 可能度矩阵 模糊偏好关系 

分 类 号：C934[经济管理—管理学]