基于一种新得分函数和累积前景理论的毕达哥拉斯模糊TOPSIS法
作者:
作者单位:

福州大学

作者简介:

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中图分类号:

C934

基金项目:

国家自然科学基金项目(71872047);福建省社会科学规划项目(FJ2018B029,FJ2019B086);福建省高校领军人才资助


Pythagorean fuzzy TOPSIS based on a novel score function and cumulative prospect theory
Author:
Affiliation:

Fuzhou university

Fund Project:

The National Natural Science Foundation of China (71872047);Social Science Planning Fund project of Fujian Province(FJ2018B029,FJ2019B086);Funding for leading talents in Fujian universities

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    摘要:

    针对属性权重未知,评价信息为毕达哥拉斯模糊数的多属性决策问题.本文首先对毕达哥拉斯模糊集的得分函数进行深入分析,为解决现有得分函数中存在的不足,提出了一种新的得分函数,通过证明其相关定理,分析了新得分函数的性质.其次,将新的得分函数运用到毕达哥拉斯模糊多属性决策问题中,以帮助决策者更好地处理模糊的决策信息.此外,针对现有大多数毕达哥拉斯模糊多属性决策方法基于决策者是完全理性的假设,忽略了决策者在面临风险时的不同主观价值感受的问题,引入累积前景理论,提出了基于新得分函数和累积前景理论的毕达哥拉斯模糊TOPSIS法,该方法用前景价值来代替各方案与正负理想解之间的距离测度,避免了忽略不同属性间的相关性对决策结果造成的影响,同时将各属性的灰靶贡献度近似看作对应指标对评价结果的重要程度以确定各属性的权重大小.最后,通过实例分析验证了所提得分函数及相关定理的正确性,并且通过仿真数据进一步验证了本文所提方法的有效性和可行性.

    Abstract:

    Due to the deficiencies of the existing score function in Pythagorean fuzzy sets, a novel score function is proposed, and the relevant theorems are proved to analyze the properties of the novel score function. Then, the novel score function is introduced to Pythagorean fuzzy multi-attribute decision making methods to help decision maker (DM) process the fuzzy decision information. Additionally, most Pythagorean fuzzy decision methods are based on expected utility theory, which assumes that DM has perfect knowledge about the decision environment associated with perfectly rational when making decisions, and the subjective value perception of DM is ignored when facing losses and gains. Therefore, the cumulative prospect theory is introduced to reflect the subjective value perception of DM and the prospect values are used to replace the distance measure between alternatives and ideal solution for avoiding the effects of correlation between different attributes, then the Pythagorean fuzzy TOPSIS method based on the novel score function and cumulative prospect theory is proposed, where the attribute weights are known and attribute values are in the form of Pythagorean fuzzy number (PFN), and the weights of attributes are determined by the contributing degree of grey target theory.Finally, an example is given to illustrate the validity of the proposed score function, and then several sets of simulation data are used to verify the effectiveness and feasibility of the proposed method.

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历史
  • 收稿日期:2020-07-09
  • 最后修改日期:2020-10-21
  • 录用日期:2020-11-05
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