Publication Date




Published in Proceedings of the 2nd Conference of the European Society for Fuzzy Logic and Technology EUSFLAT'01, Leicester, England, September 5-7, 2001, pp. 402-405


In many practical problems, we must combine ("fuse") data represented in different formats, e.g., statistical, fuzzy, etc. The simpler the data, the easier to combine them. Therefore, to combine complex data, it is desirable to "decompose" this complex data into simpler (easy-to-combine) data chunks.

It is well known that when we have n random variables x1, ..., xn with a joint Gaussian distribution, then we can reduce them to n independent variables by an appropriate linear transformation x1, ..., xn --> y1 = f1(x1,...,xn), ..., yn = fn(x1,...,xn). It is not so well known but also true that when we have x1, ..., xn with a known joint probability distribution (not necessarily Gaussian), then we can always reduce them to n independent variables by an appropriate non-linear transformation. In this paper, we show that a similar result holds for fuzzy uncertainty as well.