Surya A N, Vimala J, Kausar Nasreen, Stević Željko, Shah Mohd Asif
Department of Mathematics, Alagappa University, Karaikudi, Tamilnadu, India.
Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Esenler, 34220, Istanbul, Turkey.
Sci Rep. 2024 Mar 8;14(1):5770. doi: 10.1038/s41598-024-56252-6.
A notable advancement in fuzzy set theory is the q-rung linear diophantine fuzzy set. The soft set theory was expanded into the hypersoft set theory. By combining both the q-rung linear diophantine fuzzy set and hypersoft set, this study describes the notion of q-rung linear diophantine fuzzy hypersoft set that can handle multi sub-attributed q-rung linear diophantine fuzzy situations in the real world. Furthermore, some of its algebraic operations such as union, intersection and complement are described in this study. In addtion, the entropy measure of the q-rung linear diophantine fuzzy hypersoft set is established as it is helpful in determining the degree of fuzziness of q-rung linear diophantine fuzzy hypersoft sets. A multi-attribute decision making algorithm based on suggested entropy is presented in this study along with a numerical example of selecting a suitable wastewater treatment technology to demonstrate the effectiveness of the proposed algorithm in real-life situations. A comparative study was undertaken that describes the validity, robustness and superiority of the proposed algorithm and notions by discussing the advantages and drawbacks of existing theories and algorithms. Overall, this study describes a novel fuzzy extension that prevails over the existing ones and contributes to the real world with a valid real-life multi-attribute decision making algorithm that can cover many real-world problems that are unable to be addressed by the existing methodology.
模糊集理论的一个显著进展是q阶线性丢番图模糊集。软集理论已扩展为超软集理论。通过结合q阶线性丢番图模糊集和超软集，本研究描述了q阶线性丢番图模糊超软集的概念，它能够处理现实世界中多子属性的q阶线性丢番图模糊情况。此外，本研究还描述了其一些代数运算，如并集、交集和补集。另外，建立了q阶线性丢番图模糊超软集的熵测度，因为它有助于确定q阶线性丢番图模糊超软集的模糊程度。本研究提出了一种基于所建议熵的多属性决策算法，并给出了一个选择合适废水处理技术的数值例子，以证明所提算法在实际情况中的有效性。通过讨论现有理论和算法的优缺点，进行了一项比较研究，描述了所提算法和概念的有效性、稳健性和优越性。总体而言，本研究描述了一种优于现有方法的新型模糊扩展，并通过一种有效的现实生活多属性决策算法为现实世界做出贡献，该算法可以涵盖许多现有方法无法解决的现实世界问题。
