Ibrahim Hariwan Z, Al-Shami Tareq M, Arar Murad, Hosny M
Department of Mathematics, College of Education, University of Zakho, Zakho, Kurdistan Region, Iraq.
Department of Mathematics, Sana'a University, Sana'a, Yemen.
PLoS One. 2025 May 13;20(5):e0319757. doi: 10.1371/journal.pone.0319757. eCollection 2025.
The newly introduced nth power root fuzzy set is a useful tool for expressing ambiguity and vagueness. It has an improved ability to manage uncertain situations compared to intuitionistic fuzzy set and Pythagorean fuzzy set theories, making nth power root fuzzy sets applicable in various everyday decision-making contexts. The notions of nth power root fuzzy sets and complex fuzzy sets are integrated in this study to offer complex nth power root fuzzy sets (CnPR-FSs), explaining its fundamental ideas and useful applications. The proposed CnPR-FS integrates the advantages of nth power root fuzzy set and captures both quantitative and qualitative analyses of decision-makers. It is shown that CnPR-FSs are a crucial tool that can describe uncertain data better than complex intuitionistic fuzzy sets and complex Pythagorean fuzzy sets. A key characteristic of CnPR-FSs is a constraint that guarantees the summation of the nth power of the real (and imaginary) part of the complex-valued membership degree and the 1/n power of the real (and imaginary) part of the complex-valued non-membership degree to be equal to or less than one. This allows for a broader representation of uncertain information. The study also explores the creation of customized comparison techniques, accuracy functions, and scoring functions for two complex nth power root fuzzy numbers. Furthermore, it investigates novel aggregation operators by providing in-depth descriptions of their characteristics, such as complex nth power root fuzzy weighted averaging (CnPR-FWA) as well as complex nth power root fuzzy weighted geometric (CnPR-FWG) operators based on CnPR-FSs. Through an in-depth analysis, this paper aims to determine the selection of the most suitable caterer and optimal venue for corporate events. The study's outcomes highlight the suggested method's effectiveness and practical application as compared to other approaches, providing insight into its practical applicability and efficacy.
新引入的n次幂根模糊集是表达模糊性和不确定性的有用工具。与直觉模糊集和毕达哥拉斯模糊集理论相比，它在处理不确定情况方面具有更强的能力，使得n次幂根模糊集适用于各种日常决策环境。本研究将n次幂根模糊集和复模糊集的概念相结合，提出了复n次幂根模糊集（CnPR-FSs），并阐述了其基本思想和实际应用。所提出的CnPR-FS整合了n次幂根模糊集的优点，兼顾了决策者的定量和定性分析。结果表明，CnPR-FSs是一种比复直觉模糊集和复毕达哥拉斯模糊集更能有效描述不确定数据的关键工具。CnPR-FSs的一个关键特性是一个约束条件，它保证复值隶属度的实部（和虚部）的n次幂与复值非隶属度的实部（和虚部）的1/n次幂之和等于或小于1。这使得对不确定信息有更广泛的表示。该研究还探索了针对两个复n次幂根模糊数的定制比较技术、精度函数和评分函数的创建。此外，通过深入描述其特性，研究了新型聚合算子，如基于CnPR-FSs的复n次幂根模糊加权平均（CnPR-FWA）算子和复n次幂根模糊加权几何（CnPR-FWG）算子。通过深入分析，本文旨在确定公司活动最合适的餐饮供应商和最佳场地的选择。研究结果突出了所建议方法与其他方法相比的有效性和实际应用价值，为其实际适用性和功效提供了见解。
