A kernel intersection defined on intervals

One of the main benefits using kernels in classification tasks and learning machines is its effective capacity to work in spaces that do not have an Euclidean structure defined: texts, images, qualitative labels, etc. This work shows that the intersection operation can be interpreted as a kernel on the space of intervals. The simplicity of this kernel can be taken advantage of when defining an implicit structure in the interval's space and to use learning machines with interval variables. A variation of this kernel based on the concept of influence function is presented and analyzed. This influence function will consider the proximity of the intervals and makes it possible to deal simultaneously with intervals and real variables. The methodology used in this work leads to new interesting ways for the application of learning methods with qualitative and fuzzy data.