Hussain Abrar, Liu Yu, Ullah Kifayat, Rashid Muhammad, Senapati Tapan, Moslem Sarbast
Department of Mathematics, Riphah International University (Lahore Campus), 54000, Lahore, Pakistan.
College of Economics and Management, Hebei Agricultural University, Baoding, 071001, China.
Heliyon. 2024 Mar 10;10(6):e27548. doi: 10.1016/j.heliyon.2024.e27548. eCollection 2024 Mar 30.
Aggregation operators (AOs) are well-known and efficient mathematical tools that are utilized to overcome the impact of imprecise and vague information during the aggregation process. The theoretical concepts of Aczel Alsina aggregation expressions are an extension of triangular norms and become a hot research topic in the environment of the fuzzy framework. The power operators provide a smooth approximation and are used to mitigate the influence of redundant or insufficient information on the attributes or criteria. Some robust aggregation approaches are developed by combining two different theories, like power operators and Aczel Alsina aggregation tools. This article aims to explore the theory of picture fuzzy sets (PFSs), an extended version of fuzzy sets, and intuitionistic fuzzy sets. Some robust operations of Aczel Alsina aggregation tools are also present in light of the picture fuzzy environment. We established a class of new methodologies in the light of picture fuzzy information, including picture fuzzy Aczel Alsina power weighted average (PFAAPWA) and picture fuzzy Aczel Alsina power ordered weighted average (PFAAPOWA) operators. We also developed an appropriate approach like picture fuzzy Aczel Alsina power weighted geometric (PFAAPWG) and picture fuzzy Aczel Alsina power ordered weighted geometric (PFAAPOWG) operators. Notable properties and characteristics of proposed methodologies are also demonstrated. Our invented approaches not only aggregate complicated information but can clearly define interrelationships among several arguments. Moreover, we establish an algorithm for the multi-attribute group decision-making (MAGDM) problem to handle the impact of redundant and vague information on human opinions. Finally, we study an experimental case study to evaluate an appropriate optimal option from available options. To reveal consistency and effectiveness of developed approaches, influence study by changing various parametric values and comparative study by comparing results of existing approaches.
聚合算子（AOs）是众所周知的高效数学工具，用于在聚合过程中克服不精确和模糊信息的影响。阿泽尔·阿尔西纳（Aczel Alsina）聚合表达式的理论概念是三角范数的扩展，在模糊框架环境中成为一个热门研究课题。幂算子提供了一种平滑逼近，用于减轻冗余或不足信息对属性或准则的影响。通过结合两种不同的理论，如幂算子和阿泽尔·阿尔西纳聚合工具，开发了一些稳健的聚合方法。本文旨在探索图像模糊集（PFSs）理论，它是模糊集和直觉模糊集的扩展版本。还根据图像模糊环境给出了阿泽尔·阿尔西纳聚合工具的一些稳健运算。我们根据图像模糊信息建立了一类新方法，包括图像模糊阿泽尔·阿尔西纳幂加权平均（PFAAPWA）和图像模糊阿泽尔·阿尔西纳幂有序加权平均（PFAAPOWA）算子。我们还开发了一种合适的方法，如图像模糊阿泽尔·阿尔西纳幂加权几何（PFAAPWG）和图像模糊阿泽尔·阿尔西纳幂有序加权几何（PFAAPOWG）算子。还展示了所提方法的显著性质和特点。我们发明的方法不仅能聚合复杂信息，还能清晰地定义几个参数之间的相互关系。此外，我们针对多属性群决策（MAGDM）问题建立了一种算法，以处理冗余和模糊信息对人类意见的影响。最后，我们研究了一个实验案例，以从可用选项中评估合适的最优选项。为了揭示所开发方法的一致性和有效性，通过改变各种参数值进行影响研究，并通过比较现有方法的结果进行对比研究。
