TY - JOUR
A2 - Sessa, Salvatore
AU - Perfilieva, Irina
AU - Kreinovich, Vladik
PY - 2011
DA - 2011/08/02
TI - Towards an (Even More) Natural Probabilistic Interpretation of Fuzzy Transforms (and of Fuzzy Modeling)
SP - 719256
VL - 2011
AB - In many practical applications, it turns out to be useful to use the notionof fuzzy transform: once we have functions A1(x)≥0,...,An≥0,with∑i=1nAi(x)=1, we can then represent each function f(x) by the coefficientsFi=(∫f(x)·Ai(x)dx)/(∫Ai(x)dx). Once we know the coefficients Fi, we can(approximately) reconstruct the original function f(x) as ∑i=1nFi·Ai(x). The original motivation for this transformation came from fuzzy modeling,but the transformation itself is a purely mathematical transformation. Thus, the empirical successes of this transformation suggest thatthis transformation can be also interpreted in more traditional (nonfuzzy)mathematics as well. Such an interpretation is presented in this paper. Specifically, we showthat the 2002 probabilistic interpretation of fuzzy modeling by Sánchezet al. can be modified into a natural probabilistic explanation of fuzzytransform formulas.
SN - 1687-7101
UR - https://doi.org/10.1155/2011/719256
DO - 10.1155/2011/719256
JF - Advances in Fuzzy Systems
PB - Hindawi Publishing Corporation
KW -
ER -