When we use linear programming in possibilistic regression analysis, some coefficients tend to become crisp because of the characteristic of linear programming. On the other hand, a quadratic programming approach gives more diverse spread coefficients than a linear programming one. Therefore, to overcome the crisp characteristic of linear programming, we propose interval regression analysis based on a quadratic programming approach. Another advantage of adopting a quadratic programming approach is to be able to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression. By changing the weights of the quadratic function, we can analyze the given data from different viewpoints. For data with crisp inputs and interval outputs, the possibility and necessity models can be considered. Therefore, the unified quadratic programming approach obtaining the possibility and necessity regression models simultaneously is proposed. Even though there always exist possibility estimation models, the existence of necessity estimation models is not guaranteed if we fail to assume a proper function fitting to the given data as a regression model. Thus, we consider polynomials as regression models since any curve can be represented by the polynomial approximation. Using polynomials, we discuss how to obtain approximation models which fit well to the given data where the measure of fitness is newly defined to gauge the similarity between the possibility and the necessity models. Furthermore, from the obtained possibility and necessity regression models, a trapezoidal fuzzy output can be constructed.

Interval regression analysis by quadratic programming approach

Identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters

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Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data

Least squares estimation of a linear regression model with LR fuzzy response

Fuzzy regression analysis using neural networks

Multidimensional least-squares fitting of fuzzy models

Solid propellant burning rate measurement in a closed bomb

Estimation of NMR function accuracies from least-squares fitting

Modified Governing Equations for Unsteady Compressible Flow in Ducts

: The report gives a correct formulation of the variational problem for the computation of maximum thrust nozzles. The relation between Rao's solution of the maximization problem and the correctly treated variational problem is clarified by demonstrating that Rao's family of characteristics is a special subset of the solutions of Euler's equations. It is shown further that other properly selected subsets as well as Rao's subset can be used to obtain the contour of a maximum thrust nozzle. Typical calculations of the thrust generated by maximum thrust nozzles and comparable conical nozzles show that properly dimensioned conical nozzles are adequate for most purposes Possible exceptions may be space rockets. (Author)

Aivars Celmins

Papers

Multidimensional least-squares fitting of fuzzy models

Solid propellant burning rate measurement in a closed bomb

Estimation of NMR function accuracies from least-squares fitting

Modified Governing Equations for Unsteady Compressible Flow in Ducts

Maximum Thrust Nozzles