Fuzzy sensitivity analysis and its application

In this study, we are concerned with the concept, properties and algorithms of differentiation of the Choquet integral. The differentiation of the Choquet integral of a nonnegative measurable function is studied in the setting of sensitivity analysis. It is shown that the differentiation of Choquet integral reflects a way in which the aggregation is sensitive to the function being aggregated. The aggregation function using fuzzy integral could be viewed central to data-mining, the business process mining, web-marketing, e-commerce and the other pattern-matching problems in economics. Next, the differentiation of the Choquet integral is extended to the differentiation of the generalized t-conorm integral. Four types of the differentiation of the generalized t-conorm integrals (namely, Choquet integral, Sugeno integral, and the other generalized t-conorm integrals) are discussed and compared with regard to their sensitivity properties. Lastly, the Choquet integral is applied to the credit risk analysis (long-term debt rating) to make clear the significance of them, especially, this differentiation is shown to be an effective sensitivity analysis tool which gives us how much evaluation of each index influence to the total evaluation on the corporations.