Palanikumar Murugan, Kausar Nasreen, Pamucar Dragan, Simic Vladimir, Tolasa Fikadu Tesgera
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, 602105, India.
Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Esenler, Istanbul, 34220, Turkey.
Sci Rep. 2024 Aug 29;14(1):20073. doi: 10.1038/s41598-024-70020-6.
This paper describes a generalized Diophantine fuzzy sets, which can be seen as a generalization of both Diophantine fuzzy sets and Pythagorean fuzzy sets. We define the basic properties of generalized Diophantine fuzzy set, as well as their relationships and distances. We compare Diophantine fuzzy sets with other Diophantine Pythagorean fuzzy sets to demonstrate their importance in the literature. We introduce new operators including necessity, possibility, accuracy function and score function. Furthermore, we discuss the new distance between normalized Euclidean distance and normalized Hamming distance. For a generalized Diophantine fuzzy relation, image and inverse image functions are defined. Numerous real-world applications can be found for the prevalent ideas of intuitionistic fuzzy sets, Pythagorean fuzzy sets, Diophantine fuzzy sets and q-rung orthopair fuzzy sets. Regretfully, these theories about the membership and non-membership grades have their own limits. We provide a new idea the generalized Diophantine fuzzy set that eliminates these limitations by including reference parameters. Compared to other kinds of fuzzy sets, there are more applications for generalized Diophantine fuzzy sets. We offer practical examples that show how different enhanced distances might be used in everyday situations. Additionally, to demonstrate the effectiveness of the suggested approach, flowchart based multi-criteria decision-making is provided and used to a numerical example. The outcomes are assessed for various parameter values. Furthermore, a comparative analysis developed to demonstrate the superiority of the suggested technique over current methodologies.
本文描述了一种广义丢番图模糊集，它可被视为丢番图模糊集和毕达哥拉斯模糊集的一种推广。我们定义了广义丢番图模糊集的基本性质，以及它们之间的关系和距离。我们将丢番图模糊集与其他丢番图毕达哥拉斯模糊集进行比较，以证明它们在文献中的重要性。我们引入了新的算子，包括必要性、可能性、准确性函数和得分函数。此外，我们讨论了归一化欧几里得距离和归一化汉明距离之间的新距离。对于广义丢番图模糊关系，定义了像函数和逆像函数。直觉模糊集、毕达哥拉斯模糊集、丢番图模糊集和q阶正交对模糊集的普遍概念有许多实际应用。遗憾的是，这些关于隶属度和非隶属度等级的理论都有其局限性。我们提出了广义丢番图模糊集这一新概念，通过纳入参考参数消除了这些局限性。与其他类型的模糊集相比，广义丢番图模糊集有更多的应用。我们提供了实际例子，展示了不同的增强距离在日常情况中可能如何使用。此外，为了证明所提方法的有效性，提供了基于流程图的多准则决策方法并将其用于一个数值例子。对各种参数值的结果进行了评估。此外，还进行了比较分析，以证明所提技术相对于现有方法的优越性。
