Multidimensional Least Squares Fitting of Fuzzy Models.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 10, 1987
- Accession Number
- ADA185148
Entities
People
- Aivars K. R. Celmins
Organizations
- Ballistic Research Laboratory