Computer Engineering Commons^™

Second-Order Uncertainty As A Bridge Between Probabilistic And Fuzzy Approaches, Hung T. Nguyen, Vladik Kreinovich, Luc Longpre

Departmental Technical Reports (CS)

On the example of physics, we show that the traditional one-level description is not completely adequate. For a more adequate structure, a hierarchical description of uncertainty is necessary, which supplements the more traditional first-order uncertainty with second-order, third-order and more sophisticated models. In particular, the second-order approach seems to provide a bridge between probabilistic and fuzzy approaches to uncertainty.

Reduction To Independent Variables: From Normal Distribution To General Statistical Case To Fuzzy, Mourad Oussalah, Hung T. Nguyen, Vladik Kreinovich

Departmental Technical Reports (CS)

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 …