新定义的钻石毕达哥拉斯模糊CODAS方法通过多标准决策问题的应用
Muhammad Bilal Khan1,2, Miguel Vivas Cortez3, Bandar Bin-Mohsin4
1Department of Mathematics and Computer Science, Transilvania University of Brasov, Brasov, Romania.
PloS one
|December 12, 2025
概括
本研究介绍了钻石毕达哥拉斯模糊集 (Dia-PyFS),增强了与多位专家的决策. Dia-PyFS为复杂的选择提供了一个强大的框架,改进了现有的模糊集合理论.
科学领域:
- 决策科学 决策科学 决策科学
- 模糊的集合理论 模糊的集合理论
- 采用多个标准做出决定
背景情况:
- 传统的决策模式与来自多个决策者的多样性投入作斗争.
- 现有的毕达哥拉斯模糊集合 (PyFS) 和区间值 PyFS (IVPyFS) 在捕捉复杂决策动态方面存在局限性.
- 直觉模糊集 (IFS) 已经扩展到PyFS,表明进一步进步的潜力.
研究的目的:
- 介绍钻石毕达哥拉斯模糊集 (Dia-PyFS) 作为PyFS的新扩展.
- 定义和分析Dia-PyFS的代数和算术运算.
- 开发新的聚合运营商,并将Dia-PyFS与CODAS方法进行决策支持.
主要方法:
- 定义Dia-PyFS模型,扩展钻石直觉模糊集和PyFS.
- 为Dia-PyFS制定基本的代数运算 (结合,交叉) 和算术运算 (加法,乘法,标量乘法).
- 发展加权平均和几何总和运算符,并应用三角形t-规范和t-规范.
- 将Dia-PyFS与使用欧几里德和汉明距离的结合式基于距离的评估 (CODAS) 方法集成.
主要成果:
- 在多专家场景中,Dia-PyFS模型为决策值提供了更全面的表示.
- 定义的操作和属性确保了Dia-PyFS框架的数学稳定性.
- 拟议的聚合运算符和CODAS集成证明了在选择问题中的实际实用性.
- 对比分析验证了Dia-PyFS方法的可行性和适用性.
结论:
- 迪亚-PyFS在模糊集合理论中为多标准决策提供了重大进展.
- 开发的框架和方法为处理涉及多个利益相关者的复杂决策问题提供了有效的工具.
- 在选择最佳替代方案时,Dia-PyFS方法显示出强大的实际应用潜力.
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