A Circular Intuitionistic Fuzzy Set-Based Three-Way Decision Model with FCM-Optimized Probabilities and Three-Reference-Solution-Guided Relative Loss Functions
摘要
Circular intuitionistic fuzzy sets (CIFS) extends intuitionistic fuzzy sets (IFS) by simulating the structure of a circle, which allows for a more precise representation of decision uncertainty and efficient aggregation of multi-expert information. The three-way decisions (3WD) approach offers an effective method for classifying multi-attribute decision problems into three categories: acceptance, non-commitment, and rejection, based on the principle of risk minimization. However, there is currently significant controversy regarding the calculation of two key elements: the conditional probability and the loss function. This study proposes a novel 3WD model that combines CIFS, fuzzy C-means (FCM) optimization, and loss functions guided by three reference solutions. First, CIFS models decision attribute information. Then, conditional probabilities are derived by minimizing the FCM objective function. Importantly, six relative loss functions are dynamically constructed using distances to three reference solutions (Good, Medium, Bad), enabling adaptive threshold determination based on their relative positions. These three reference solutions naturally correspond to the three decision domains: acceptance, non-commitment, and rejection. Experimental results show that the proposed approach outperforms others in classification and ranking tasks for multi-attribute group decision-making problems. Finally, a case study confirms the practical effectiveness of the method in real-world applications.