首页|基于后悔理论的图模糊LINMAP多属性决策方法及应用

基于后悔理论的图模糊LINMAP多属性决策方法及应用

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针对图模糊多属性决策方法基于未知属性权重且往往只考虑客观属性信息的不足,提出一种基于后悔理论的图模糊LINMAP多属性决策方法.首先,依据后悔理论的思想,定义图模糊后悔-欣喜函数,给出方案感知效用值的计算方法;然后,设计图模糊偏好信息集,用其表示属性间的相互影响关系,并提出方案对序列和决策者事先给定偏好信息的图模糊一致性程度和非一致性程度;接着,通过图模糊得分函数和精确度函数构建含有参数的目标函数,并设置图模糊阈值,使得非一致性程度最小化且一致性程度与非一致性程度差别至少不小于该图模糊阈值,据此建立新的优化模型,获得备选方案的属性权重向量和模糊理想点,进而利用感知效用值对备选方案进行排序择优;最后,通过算例分析验证所提出方法的合理性,并通过灵敏度分析和对比分析表明所提出方法的灵活性和优点.
Picture fuzzy LINMAP multiple attribute decision making method based on regret theory and its application
The picture fuzzy multiple attribute decision making methods are based on unknown attribute weights,and mostly only consider objective attribute information.To overcome these defects,a picture fuzzy LINMAP multiple attribute decision making method based on the regret theory is developed,in which the decision maker's regret aversion behavior and the influence relationships among attributes are considered.Firstly,a picture fuzzy regret-rejoice function is defined on the basis of the regret theory and the computational formula of perceived utility value is given.Secondly,the picture fuzzy preference information set is proposed to represent the interaction between attributes,and the picture fuzzy consistency and inconsistency between pair-wise rankings of alternatives and the preference information assumed apriori given by decision makers are proposed.Thirdly,the objective function with parameters is established by the picture fuzzy score function and accuracy function,and the picture fuzzy threshold is designed so that inconsistent degree is minimized and the difference between the consistent degree and inconsistent degree is at least not less than the proposed picture fuzzy threshold.Base on this,a new optimization model is established to solve the weights and fuzzy ideal points of different attributes of each alternative,and then the perceived utility values of each alternative are calculated and the alternatives are ranked also.Finally,the rationality of the developed method is illustrated by an example,and the flexibility and merits of the proposed method are demonstrated by sensitivity analysis and comparative analysis.

picture fuzzy setregret theorypicture fuzzy preferencepicture fuzzy LINMAP methodperceived utility valuesmultiple attribute decision making

王磊、苑博荣

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辽宁工程技术大学基础教学部,辽宁葫芦岛 125105

辽宁工程技术大学理学院,辽宁阜新 123000

图模糊集 后悔理论 图模糊偏好 图模糊LINMAP方法 感知效用值 多属性决策

辽宁省教育厅科学研究经费项目教育部研究规划基金项目辽宁省社会科学规划基金项目

LJ2020JCL01821YJCZH204L22BGL028

2024

10.13195/j.kzyjc.2022.2179

控制与决策
东北大学

控制与决策

CSTPCD北大核心
影响因子：1.227
ISSN：1001-0920
年,卷(期)：2024.39(8)