Accession Number : ADA185148

Title :   Multidimensional Least Squares Fitting of Fuzzy Models.

Descriptive Note : Technical rept. Jun 85-Jun 86,

Corporate Author : ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD

Personal Author(s) : Celmins, Aivars K R

PDF Url : ADA185148

Report Date : 10 Apr 1987

Pagination or Media Count : 54

Abstract : We describe a new method for the fitting of differentiable fuzzy model functions to crisp data. The model functions can be either scalar or multi-dimensional and need not be linear. The data are n-component vectors. An efficient algorithm is achieved by restricting the fuzzy model functions to sets which depend on fuzzy parameter vector and assuming that the vector has a conical membership function. A fuzzy model function, equated to zero, defines in the n-space a fuzzy hypersurface. Simple properties of such surfaces are established and a structure in the space of fuzzy manifolds is introduced by defining a discord and collocation between any two fuzzy manifolds. Using these concepts and the restriction to conical membership functions, we derive a simple spread propagation formula for arbitrary functions of fuzzy variables. The model fitting is done in a least squares sense by minimizing the squares of the deviations from one of the membership values of the fitted hypersurface at the observations. Under the outlined restriction, the problem can be reduced to an ordinary least squares formulation for which software is available.

Descriptors :   *LEAST SQUARES METHOD, *MATHEMATICAL MODELS, *FITTING FUNCTIONS(MATHEMATICS), VARIABLES, ALGORITHMS, EFFICIENCY, PARAMETERS, CHARTS, CRATERS, SIZES(DIMENSIONS)

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE