Fuzzified Choquet integral with a fuzzy-valued integrand and its application on temperature prediction

In this paper, the original Choquet integral is generalized as a Fuzzified Choquet Integral with a Fuzzy-valued Integrand (FCIFI), which supports a fuzzy-valued integrand and an integration result. The calculation of the FCIFI is established on the Choquet integral with an interval-valued integrand (CIII). The definitions, properties, and calculation algorithms of the CIII and the FCIFI are discussed and proposed in this paper. As a specific application scheme, we designed a CIII regression model for the regression problems involving interval-valued data. This CIII regression model has a self-learning ability through a double genetic algorithm. Finally, a daily temperature predictor based on the CIII regression model is discussed, where a series of experiments is implemented to validate the performance of the predictor by real weather records from the Hong Kong Observatory.