Instituto Multidisciplinar de la Empresa (IME), Universidad de Salamanca, 37007, Salamanca, Spain.
Department of Mathematics and Statistics, Riphah International University, Hajj Complex I-14, Islamabad, Pakistan.
Sci Rep. 2022 Nov 10;12(1):19211. doi: 10.1038/s41598-022-20982-2.
The classical theory of rough set was established by Pawlak, which mainly focusses on the approximation of sets characterized by a single equivalence relation over the universe. However, most of the current single granulation structure models cannot meet the user demand or the target of solving problems. Multigranulation rough sets approach can better deal with the problems, where data might be spread over various locations. In this article, we present the idea of soft preference and soft dominance relation for the development of soft dominance rough set in an incomplete information system. Subsequently, several important structural properties and results of the proposed model are carefully analyzed. After employing soft dominance based rough set approach to it for any times, we can only get six different sets at most in an incomplete information system. That is to say, every rough set in a universe can be approximated by only six sets, where the lower and upper approximations of each set in the six sets are still lying among these six sets. The relationships among these six sets are established. Based on soft dominance relation, we introduce logical disjunction/conjunction soft dominance optimistic/pessimistic multigranulation decision theoretic rough approximations in an incomplete information. Meanwhile, to measure the uncertainty of soft dominance optimistic/pessimistic multigranulation decision theoretic rough approximation and some of their interesting properties are examined. Thereafter, a novel multi attribute with multi decision making problem approach based on logical disjunction/conjunction soft dominance optimistic/pessimistic multigranulation decision theoretic rough sets approach are developed to solve the selection of medicine to treat the coronavirus disease (COVID-19). The basic principle and the detailed steps of the decision making model (algorithms) are presented in detail. To demonstrate the applicability and potentiality of the proposed model, we present a practical example of a medical diagnosis is given to validate the practicality of the technique.
经典粗糙集理论由 Pawlak 建立，主要侧重于用单一等价关系来逼近整个论域上的集合。然而，当前大多数单粒化结构模型无法满足用户需求或解决问题的目标。多粒度粗糙集方法可以更好地处理数据可能分布在多个位置的问题。本文提出了一种软偏好和软优势关系的思想，用于开发不完全信息系统中的软优势粗糙集。随后，仔细分析了所提出模型的几个重要结构性质和结果。在一个不完全信息系统中，运用基于软优势的粗糙集方法对其进行任意次处理，最多只能得到六个不同的集合。也就是说，一个论域中的每个粗糙集都可以用这六个集合中的六个集合来逼近，而这六个集合中的每个集合的上下近似仍然在这六个集合中。建立了这六个集合之间的关系。基于软优势关系，我们在不完全信息中引入了逻辑析取/合取软优势乐观/悲观多粒度决策粗糙近似。同时，为了度量软优势乐观/悲观多粒度决策粗糙近似的不确定性，研究了其一些有趣的性质。此后，基于逻辑析取/合取软优势乐观/悲观多粒度决策粗糙集方法，开发了一种新的多属性多决策问题方法，用于解决治疗冠状病毒病（COVID-19）的药物选择问题。详细介绍了决策模型（算法）的基本原理和详细步骤。为了验证所提出模型的适用性和潜力，我们提供了一个医疗诊断的实际示例，以验证该技术的实用性。
