CnPR-F decision table.

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.新近提出的n次根模糊集（nth power root fuzzy set）是表达歧义与模糊性的有效工具。相较于直觉模糊集（intuitionistic fuzzy set）与毕达哥拉斯模糊集（Pythagorean fuzzy set）理论，其在处理不确定场景时具备更优异的性能，使得n次根模糊集可应用于各类日常决策场景。本研究将n次根模糊集与复模糊集（complex fuzzy sets）的概念相结合，提出复n次根模糊集（complex nth power root fuzzy sets，CnPR-FSs），并阐释其核心思想与实际应用价值。所提出的CnPR-FS融合了n次根模糊集的优势，能够同时捕捉决策者的定量与定性分析维度。研究表明，相较于复直觉模糊集与复毕达哥拉斯模糊集，CnPR-FSs可更精准地刻画不确定数据，是一项至关重要的工具。CnPR-FSs的核心约束为：复值隶属度的实部（及虚部）的n次幂，与复值非隶属度的实部（及虚部）的1/n次幂之和小于或等于1，该约束可实现不确定信息的更广泛表征。本研究还针对两类复n次根模糊数，构建了定制化的比较方法、精度函数与得分函数。此外，本文基于CnPR-FSs提出了新型聚合算子，包括复n次根模糊加权平均（complex nth power root fuzzy weighted averaging，CnPR-FWA）算子与复n次根模糊加权几何（complex nth power root fuzzy weighted geometric，CnPR-FWG）算子，并对其性质展开了深入剖析。通过深入的案例分析，本文旨在遴选企业活动的最优餐饮服务商与举办场地。研究结果显示，相较于其他方法，所提方法具备良好的有效性与实用性，可为其实际应用效能提供理论参考与实践指引。