Some fuzzy neighborhood operators on fuzzy β-covering approximation space and their application in user preference evaluation

As a generalization of covering, fuzzy β-covering provides a more accurate and practical representation for incomplete information. This paper primarily proposes several fuzzy neighborhood operators based on diverse aggregation functions in an fuzzy β-covering approximation space (FβCAS) and develops a novel TOPSIS method to address the decision-making problem related to user preference factors. First, two classes of fuzzy neighborhood operators are introduced, derived from t-norms, overlap functions and their residual implications in an FβCAS, with their properties thoroughly analyzed. In addition, multiple fuzzy β-coverings are generated from the original fuzzy β-covering, and the classifications of fuzzy neighborhood operators, along with their partial order relationships, are examined. Based on these operators, two kinds of fuzzy β-covering-based rough sets (FβCRS) are established. Finally, an FβCRS-based fuzzy TOPSIS method is developed to evaluate user preference factors for fresh fruit, thereby demonstrating the rationality and feasibility of the proposed approach.