Fuzzy Justification of Heuristic Methods in Inverse Problems and in Numerical Computations, with Applications to Detection of Business Cycles From Fuzzy and Intuitionistic Fuzzy Data

and the dependence of y on x into a Taylor series and neglect quadratic and higher order terms in this expansion. Thus, we have a linear dependence y = Ax + b (for some matrix A and vector b), and we get a linear equation that we have to solve in order to reconstruct x: Ax = c; where c = y \Gamma b, y is measured, A and b are known, and x has to be determined. For example, when we reconstruct how a single x depends on time x = x(t), we get a linear integral equation Z A(t; t 0 ) \Delta x(t 0 ) dt =<