Exploring object reduction approaches for optimizing decision-making in linguistic concept formal context

Knowledge reduction is a crucial research topic in formal concept analysis. Given the ability of three-way concept analysis to capture attribute information in a more comprehensive and detailed manner, this paper focuses on investigating object reduction methods and their applications based on three-way concept lattice. We achieve this by integrating necessity and possibility operators in a formal context containing linguistic data. Our proposed approach involves constructing an attribute-induced three-way object-oriented linguistic concept lattice to classify the object set into three regions based on three-way decision. Additionally, we introduce an approach of attribute-induced three-way object-oriented linguistic granular reduction, which employs granular concepts, granular discernibility functions, and granular consistent sets to enhance the efficiency of extracting uncertainty information. We obtain the relationships between the five consistent sets of attribute-induced three-way object-oriented linguistic concepts and further analyze the corresponding object reduction relations. To demonstrate the feasibility and validity of our proposed method, we apply it to address optimization decision-making challenges in corporate projects using different attribute-induced three-way object-oriented linguistic concepts.