Applying a generalized choquet integral with signed fuzzy measure based on the complexity to evaluate the overall satisfaction of the patients

The weighted arithmetic mean method and the regression method are the most commonly used operators to aggregate criteria in decision making problems without further considering the interactions among criteria. The discrete Choquet integral respect to a fuzzy measure is proved to be an adequate aggregation operator by further taking into accounts the interactions among criteria. A signed fuzzy measure is needed when the gain and loss must be considered in the same time. In this study, we propose a signed fuzzy measure based on the complexity method to construct a signed fuzzy measure needed by the discrete generalized Choquet integral and a real questionnaire data is analyzed. The advantage of the complexity-based method is that no population probability is to be estimated such that the error of estimating the population probability is reduced and it is easily to construct a signed fuzzy measure based on the complexity method. Four methods, including the discrete Choquet integral with fuzzy measure based on the entropy method, the discrete Choquet integral with fuzzy measure based on the complexity method, the discrete generalized Choquet integral with signed fuzzy measure based on the cardinality method, and our proposed discrete generalized Choquet integral with signed fuzzy measure based on the complexity method, are used in this study to evaluate the overall satisfaction of the patients. The results show that our proposed applying a discrete generalized Choquet integral with signed fuzzy measure based on the complexity method to evaluate the overall satisfaction is the best among the four methods.