Akram Muhammad, Amjad Umaira, Alcantud José Carlos R, Santos-García Gustavo
Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan.
BORDA Research Unit and IME, University of Salamanca, 37007 Salamanca, Spain.
J Ambient Intell Humaniz Comput. 2023;14(7):8765-8798. doi: 10.1007/s12652-021-03629-4. Epub 2022 Feb 4.
Decision-making methods play an important role in the real-life of human beings and consist of choosing the best options from a set of possible choices. This paper proposes the notion of complex Fermatean fuzzy -soft set (S) which, by means of ranking parameters, is capable of handling two-dimensional information related to the degree of satisfaction and dissatisfaction implicit in the nature of human decisions. We define the fundamental set-theoretic operations of S and elaborate the S associated with threshold. The algebraic and Yager operations on numbers are also defined. Several algorithms are proposed to demonstrate the applicability of S to multi-attribute decision making. The advanced algorithms are described and accomplished by several numerical examples. Then, a comparative study manifests the validity, feasibility, and reliability of the proposed model. This method is compared with the Fermatean fuzzy Yager weighted geometric (G) and the Fermatean fuzzy Yager weighted average (A) operators. Further, we developed a remarkable -TOPSIS approach by applying innovative weighted average operator and distance measure. The presented technique is fantastically designed for the classification of the most favorable alternative by examining the closeness of all available choices from particular ideal solutions. Afterward, we demonstrate the amenability of the initiated approach by analyzing its tremendous potential to select the best city in the USA for farming. An integrated comparative analysis with existing Fermatean fuzzy TOPSIS technique is rendered to certify the terrific capability of the established approach. Further, we decisively investigate the rationality and reliability of the presented S and -TOPSIS approach by highlighting its advantages over the existent models and TOPSIS approaches. Finally, we holistically describe the conclusion of the whole work.
决策方法在人类现实生活中起着重要作用，包括从一组可能的选择中挑选出最佳选项。本文提出了复费尔马模糊软集（S）的概念，借助排序参数，它能够处理与人类决策本质中隐含的满意度和不满意度相关的二维信息。我们定义了S的基本集合论运算，并阐述了与阈值相关的S。还定义了数的代数运算和亚格尔运算。提出了几种算法来证明S在多属性决策中的适用性。通过几个数值例子描述并完成了先进算法。然后，一项比较研究表明了所提出模型的有效性、可行性和可靠性。将该方法与费尔马模糊亚格尔加权几何（G）算子和费尔马模糊亚格尔加权平均（A）算子进行了比较。此外，我们通过应用创新的加权平均算子和距离测度开发了一种卓越的逼近理想解排序法（TOPSIS）方法。所提出的技术通过检查所有可用选择与特定理想解的接近程度，出色地设计用于对最有利的备选方案进行分类。之后，我们通过分析其在美国选择最佳农业城市的巨大潜力来证明所提出方法的适用性。与现有的费尔马模糊TOPSIS技术进行了综合比较分析，以证明所建立方法的卓越能力。此外，我们通过突出其相对于现有模型和TOPSIS方法的优势，果断地研究了所提出的S和TOPSIS方法的合理性和可靠性。最后，我们全面描述了整个工作的结论。
