What are Fuzzy integrals?

Question

How could you define "Fuzzy Integral"? Could you recomended me any interesting book to self study about Fuzzy integrals?

Thanks

Answer 1

You can check the book

Zhenyuan Wang and George J. Klir , Fuzzy measure theory, Springer, 1992

The authors provide a rigorous mathematical development of fuzzy (Sugeno) integrals in Chapter 7.

Answer 2

As a rough definition, a fuzzy integral is a generalization of traditional integration techniques (e.g. the Lebesgue integral), but where the measure used is non-additive or fuzzy . For practical use, it's a way of summing up or averaging a set of inputs in a way that takes into account interaction or other relationships between input sources.

Some introductory videos here: Fuzzy integrals YouTube playlist

Then the following books:

An introduction to aggregation functions in R - A fairly simple introductory book on aggregation functions. Has fuzzy integrals as the last chapter - this is if you're interested in these functions from a data summary/machine learning perspective.

Discrete Fuzzy Measures - Or a more in-depth introduction, including a chapter on some different fuzzy integrals and their history.