基于T-球形模糊熵和交叉熵的偏好
提取方法及其应用

杨雨欣1; 毛军军1; 2*; 黄慧鑫1; 庞星宇1

文章摘要

杨雨欣1 ，毛军军1,2* ，黄慧鑫1 ，庞星宇1.基于T-球形模糊熵和交叉熵的偏好提取方法及其应用[J].海南师范大学学报自科版,2025,38(1):54-63

基于T-球形模糊熵和交叉熵的偏好提取方法及其应用

Preference Extraction Method and Its Application Based on T-Spherical Fuzzy Entropy and Cross-Entropy

DOI：10.12051/j.issn.1674-4942.2025.01.008

中文关键词: T-球形模糊熵 T-球形模糊交叉熵改进的距离函数偏好提取多属性群决策

英文关键词: T-spherical fuzzy entropy T-spherical fuzzy cross-entropy improved distance function preference extraction multi-attribute group decision-making

基金项目:国家自然科学基金项目（72171002）；安徽省省级质量工程项目（2023jyxm0101）；安徽省省级研究生教育项目（2022jyjxggyj135）

作者	单位
杨雨欣1 ，毛军军1,2* ，黄慧鑫1 ，庞星宇1	1. 安徽大学大数据与统计学院，安徽合肥 230601； 2. 安徽大学计算智能与信号处理教育部重点实验室，安徽合肥 230601

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中文摘要:

由于决策环境的日益复杂，专家和属性的偏好信息在决策过程中至关重要。因此为了更加客观地识别信息，提出了一种基于T-球形模糊熵和交叉熵的偏好提取方法并将其用于多属性群决策问题中。首先针对模糊熵不满足现实意义以及交叉熵不满足非负性的问题，提出了新的T- 球形模糊熵和交叉熵，用以客观准确地确定专家和属性的偏好信息，并证明了其相关性质；其次，针对以往有些研究中定义的距离函数不满足三角不等式的缺点，提出了基于新T-球形模糊交叉熵的距离函数，并将其与新提出的T-球形模糊熵和交叉熵用于TOPSIS方法对方案进行排序；最后通过一个计算机辅助工程（CAE）仿真软件的选择实例说明了所提方法的可行性和有效性，为解决T- 球形模糊环境下的多属性群决策问题提供了一种新的思路。

英文摘要:

As the decision-making environment becomes increasingly complex, the preference information of experts and attributes plays a crucial role in the decision-making process. Therefore, to identify information more objectively, a preference extraction method based on T-spherical fuzzy entropy and cross-entropy is proposed and applied to multi-attribute group decision-making problems. Firstly, addressing the issues of fuzzy entropy not satisfying practical significance and cross-entropy not satisfying non-negativity, new T-spherical fuzzy entropy and cross-entropy are proposed to objectively and accurately determine the preference information of experts and attributes, and their relevant properties are proved. Secondly, addressing the shortcomings of some previous studies where the defined distance functions do not satisfy the triangle inequality, a distance function based on the new T-spherical fuzzy cross-entropy is proposed and used together with the newly proposed T-spherical fuzzy entropy and cross-entropy in the TOPSIS method to rank alternatives. Finally, the feasibility and effectiveness of the proposed method are demonstrated through an example of selecting computer-aided engineering (CAE) simulation software, providing a new approach to solve multi-attribute group decision-making problems in a T-spherical fuzzy environment.

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