Akula Naveen Kumar, S Sharief Basha, Tarakaramu Nainaru, Ramesh Obbu, Askar Sameh, Rayudu Uma Maheswari, Ahmad Hijaz, Khan M Ijaz
Department of Mathematics, Mother Theresa Institute of Engineering and Technology, Palamaner, A.P, 517408, India.
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, 632014, Vellore, Tamilnadu, India.
Sci Rep. 2024 Aug 3;14(1):18000. doi: 10.1038/s41598-024-68371-1.
Group decision-making (GDM) is crucial in various components of graph theory, management science, and operations research. In particular, in an intuitionistic fuzzy group decision-making problem, the experts communicate their preferences using intuitionistic fuzzy preference relations (IFPRs). This approach is a way that decision-makers rank or select the most desirable alternatives by gathering criteria-based information to estimate the best alternatives using a wider range of knowledge and experience. This article proposes a new statistical measure in a fuzzy environment when the data is ambiguous or unreliable to solve a decision-making problem. This study uses the variation coefficient measure combined with intuitionistic fuzzy graphs (IFG) and Laplacian energy (LE) to solve a GDM problem that utilizes intuitionistic fuzzy preference relations (IFPRs) to select a reliable alliance partner. Initially, the Laplacian energy determines the weight of individual standards, and the obtained weight average further estimates the overall criterion weight vector. We establish the authority criteria weights using the variation coefficient measure and then ultimately rank the alternatives for each criterion using the same measure. We examine four distinct companies Alpha, Beta, Delta, and Zeta to conduct a realistic GDM to choose which alliance partner would be ideal. We successfully implemented the suggested technique, determining that Alpha satisfies company standards and is ranked first among other companies. Moreover, this technique is useful for all kinds of Intuitionistic fuzzy group decision-making problems to select optimal ones.
群体决策（GDM）在图论、管理科学和运筹学的各个组成部分中都至关重要。特别是在直觉模糊群体决策问题中，专家们使用直觉模糊偏好关系（IFPRs）来表达他们的偏好。这种方法是决策者通过收集基于标准的信息，利用更广泛的知识和经验来估计最佳备选方案，从而对最理想的备选方案进行排序或选择的一种方式。本文提出了一种在数据模糊或不可靠的模糊环境下的新统计度量，以解决决策问题。本研究使用变异系数度量结合直觉模糊图（IFG）和拉普拉斯能量（LE）来解决一个利用直觉模糊偏好关系（IFPRs）选择可靠联盟伙伴的群体决策问题。首先，拉普拉斯能量确定各个标准的权重，所获得的权重平均值进一步估计总体标准权重向量。我们使用变异系数度量建立权威标准权重，然后最终使用相同的度量对每个标准的备选方案进行排序。我们考察了四家不同的公司Alpha、Beta、Delta和Zeta，以进行实际的群体决策，来选择哪个联盟伙伴是理想的。我们成功地实施了所建议的技术，确定Alpha符合公司标准，在其他公司中排名第一。此外，该技术对各类直觉模糊群体决策问题选择最优方案都很有用。
