School of Mathematical Sciences, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China.
Department of Mathematics, University of Management and Technology, Lahore, 54770, Pakistan.
Sci Rep. 2023 Apr 20;13(1):6511. doi: 10.1038/s41598-023-32818-8.
Infrastructure development and the economy heavily rely on the construction industry. However, decision-making in construction projects can be intricate and difficult due to conflicting standards and requirements. To address this challenge, the q-rung orthopair fuzzy soft set (q-ROFSS) has emerged as a useful tool incorporating fuzzy and uncertain contractions. In many cases, further characterization of attributes is necessary as their values are not mutually exclusive. The prevalent q-ROFSS structures cannot resolve this state. The q-rung orthopair fuzzy hypersoft sets (q-ROFHSS) is a leeway of q-ROFSS that use multi-parameter approximation functions to scare the scarcities of predominant fuzzy sets structures. The fundamental objective of this research is to introduce the Einstein weighted aggregation operators (AOs) for q-rung orthopair fuzzy hypersoft sets (q-ROFHSS), such as q-rung orthopair fuzzy hypersoft Einstein weighted average and geometric operators, and discuss their fundamental properties. Mathematical explanations of decision-making (DM) contractions is present to approve the rationality of the developed approach. Einstein AOs, based on predictions, carried an animated multi-criteria group decision (MCGDM) method with the most substantial significance with the prominent MCGDM structures. Moreover, we utilize our proposed MCGDM model to select the most suitable construction company for a given construction project. The proposed method is evaluated through a statistical analysis, which helps ensure the DM process's efficiency. This analysis demonstrates that the proposed method is more realistic and reliable than other DM approaches. Overall, the research provides valuable insights for decision-makers in the construction industry who seek to optimize their DM processes and improve the outcomes of their projects.
基础设施的发展和经济的繁荣在很大程度上依赖于建筑行业。然而,由于标准和要求的冲突,建筑项目的决策可能会变得复杂和困难。为了解决这一挑战,q-阶数对偶模糊软集(q-ROFSS)作为一种有用的工具应运而生,它结合了模糊和不确定收缩。在许多情况下,由于它们的值不是相互排斥的,因此需要进一步描述属性。流行的 q-ROFSS 结构无法解决这种情况。q-阶数对偶模糊超软集(q-ROFHSS)是 q-ROFSS 的一种扩展,它使用多参数逼近函数来克服主要模糊集结构的不足。本研究的基本目标是引入 q-阶数对偶模糊超软集(q-ROFHSS)的爱因斯坦加权聚合算子(AOs),如 q-阶数对偶模糊超软爱因斯坦加权平均和几何算子,并讨论它们的基本性质。提出了决策(DM)收缩的数学解释,以证明所提出方法的合理性。基于预测的爱因斯坦 AOs 用于携带具有突出 MCGDM 结构的具有最显著意义的 q-阶数对偶模糊超软 Einstein 加权平均和几何算子。此外,我们利用我们提出的 MCGDM 模型来为给定的建筑项目选择最合适的建筑公司。通过统计分析评估所提出的方法,这有助于确保 DM 过程的效率。该分析表明,与其他 DM 方法相比,所提出的方法更现实和可靠。总的来说,该研究为建筑行业的决策者提供了有价值的见解,他们寻求优化他们的 DM 过程并改善他们的项目结果。