Yahya Muhammad, Abdullah Saleem, Khan Faisal, Safeen Kashif, Ali Rafiaqat
Department of Mathematics, Abdul Wali Khan University Mardan, KP, Pakistan.
Department of Electrical and Electronic Engineering, College of Sciences and Engineering, National University of Ireland Galway (UCG), Ireland.
Heliyon. 2024 Feb 7;10(4):e25818. doi: 10.1016/j.heliyon.2024.e25818. eCollection 2024 Feb 29.
As the increasing environmental issues, various companies have take initiatives to produce green products or to select green suppliers which maximize the business performance and minimize the environmental pollution. The real numbers data have imbiguity and uncertainty due to described by classical tools. Therefore, we consider a new type of fuzzy set, fuzzy credibility rough sets. In fuzzy credibility rough set has credibility membership of positive membership and they reduced the imbiguity in data information. In this paper we have defined a new set called fuzzy credibility rough set (FCRS), after that we defined Frank operational laws for FCRS information. Using these operational laws, we defined a series of aggregation operators that is fuzzy credibility Frank rough weigthed averaging aggregation operators, fuzzy credibility Frank rough ordered weigthed averaging aggregation operators, fuzzy credibility Frank rough hybrid weigthed averaging aggregation operators and its basic properties like boundedness, monotonicity and idempotency. As there is no work which is based on Frank norms aggregation operators under FCRS information. So, we defined a series of aggregation operators that can help us to collect the data for various green suppliers management. We developed a new set called fuzzy credibility rough set (FCRS). We developed a new Frank norms operational laws under FCRS information. We developed a series of aggregation operators. We developed and extend various steps of GRA, VIKOR and TOPSIS method under FCRS information. We explained the application of our proposed work to a real life decision making problem (green supplier management). All the proposed work is to applied to real life decision making problems (green supplier management) to find the best optimal result. Firstly we can collect the data from the decision makers using the proposed aggregation operators and then we applied all the steps of developed method to find the solution in case of green supplier management.
随着环境问题日益严重，各公司纷纷采取举措生产绿色产品或选择绿色供应商，以实现业务绩效最大化和环境污染最小化。由于经典工具对实际数据的描述存在模糊性和不确定性，因此，我们考虑一种新型模糊集——模糊可信度粗糙集。在模糊可信度粗糙集中，具有正隶属度的可信度隶属关系减少了数据信息中的模糊性。本文定义了一种名为模糊可信度粗糙集（FCRS）的新集合，之后为FCRS信息定义了弗兰克运算定律。利用这些运算定律，我们定义了一系列聚合算子，即模糊可信度弗兰克粗糙加权平均聚合算子、模糊可信度弗兰克粗糙有序加权平均聚合算子、模糊可信度弗兰克粗糙混合加权平均聚合算子及其诸如有界性、单调性和幂等性等基本性质。由于目前尚无基于FCRS信息下弗兰克范数聚合算子的研究，所以，我们定义了一系列聚合算子，以帮助我们收集各种绿色供应商管理的数据。我们开发了一种名为模糊可信度粗糙集（FCRS）的新集合。我们在FCRS信息下开发了新的弗兰克范数运算定律。我们开发了一系列聚合算子。我们在FCRS信息下开发并扩展了灰色关联分析（GRA）、多准则妥协解排序法（VIKOR）和逼近理想解排序法（TOPSIS）方法的各个步骤。我们阐述了所提工作在实际决策问题（绿色供应商管理）中的应用。所有所提工作都应用于实际决策问题（绿色供应商管理）以获得最佳最优结果。首先，我们可以使用所提聚合算子从决策者那里收集数据，然后应用所开发方法的所有步骤来求解绿色供应商管理问题。
