A New Method for Decision Making Problems with Redundant and Incomplete Information Based on Incomplete Soft Sets: From Crisp to Fuzzy

This research is focused on decision-making problems with redundant and incomplete information under a fuzzy environment. Firstly, we present the definition of incomplete fuzzy soft sets and analyze their data structures. Based on that, binary relationships between each pair of objects and the “restricted/relaxed AND” operations in the incomplete fuzzy soft set are discussed. After that, the definition of incomplete fuzzy soft decision systems is proposed. To reduce the inconsistency caused by the redundant information in decision making, the significance of the attribute subset, the reduct attribute set, the optimal reduct attribute set and the core attribute in incomplete fuzzy soft decision systems is also discussed. These definitions can be applied in an incomplete fuzzy soft set directly, so there is no need to convert incomplete data into complete one in the process of reduction. Then a new decision-making algorithm based on the above definitions can be developed, which can deal with redundant information and incomplete information simultaneously, and is independent of some unreliable assumptions about the data generating mechanism to forecast the incomplete information. Lastly, the algorithm is applied in the problem of regional food safety evaluation in Chongqing, China, and the corresponding comparison analysis demonstrates the effectiveness of the proposed method.