As the title of the question suggest. Is there any tool that generalizes all mathematical operations, like adding, subtracting, dividing or even integrating, deriving or making a matrix transformation. The most accurate example that I can think of now is the generalized Stoke's Theorem or in a similar way that of a Physicist that makes a model to explain many phenomena of nature.
I don't know if this question sounds pedantic and little scientific, but I would like to know it, just for divulgative propose.
Think about set-theoretic (crisp) operations. Zadeh's extension principle extends these operations to fuzzy sets.