3D roll-forming of hat-profile with variable depth and width

The use of roll-formed products in automotive, furniture, buildings etc. increases every year due to the low part-production cost and the complicated cross-sections that can be produced. The limitation with roll-forming until recent years is that one could only produce profiles with a constant cross-section in the longitudinal direction. About eight years ago ORTIC AB [1] developed a machine in which it was possible to produce profiles with a variable width (“3D roll-forming”) for the building industry. Experimental equipment was recently built for research and prototyping of profiles with variable cross-section in both width and depth for the automotive industry. The objective with the current study is to investigate the new tooling concept that makes it possible to roll-form hat-profiles, made of ultra high strength steel, with variable cross-section in depth and width. The result shows that it is possible to produce 3D roll-formed profiles with close tolerances.

A Note on Proxy Variables and Instrument Variable Regression

This is a note about proxy variables and instruments for identification of structural parameters in regression models. We have experienced that in the econometric textbooks these two issues are treated separately, although in practice these two concepts are very often combined. Usually, proxy variables are inserted in instrument variable regressions with the motivation they are exogenous. Implicitly meaning they are exogenous in a reduced form model and not in a structural model. Actually if these variables are exogenous they should be redundant in the structural model, e.g. IQ as a proxy for ability. Valid proxies reduce unexplained variation and increases the efficiency of the estimator of the structural parameter of interest. This is especially important in situations when the instrument is weak. With a simple example we demonstrate what is required of a proxy and an instrument when they are combined. It turns out that when a researcher has a valid instrument the requirements on the proxy variable is weaker than if no such instrument exists

Appropriate choice of aggregation operators in fuzzy decision support systems

Fuzzy logic provides a mathematical formalism for a unified treatment of vagueness and imprecision that are ever present in decision support and expert systems in many areas. The choice of aggregation operators is crucial to the behavior of the system that is intended to mimic human decision making. This paper discusses how aggregation operators can be selected and adjusted to fit empirical data—a series of test cases. Both parametric and nonparametric regression are considered and compared. A practical application of the proposed methods to electronic implementation of clinical guidelines is presented

Monotone approximation of aggregation operators using least squares splines

The need for monotone approximation of scattered data often arises in many problems of regression, when the monotonicity is semantically important. One such domain is fuzzy set theory, where membership functions and aggregation operators are order preserving. Least squares polynomial splines provide great flexbility when modeling non-linear functions, but may fail to be monotone. Linear restrictions on spline coefficients provide necessary and sufficient conditions for spline monotonicity. The basis for splines is selected in such a way that these restrictions take an especially simple form. The resulting non-negative least squares problem can be solved by a variety of standard proven techniques. Additional interpolation requirements can also be imposed in the same framework. The method is applied to fuzzy systems, where membership functions and aggregation operators are constructed from empirical data.

How to build aggregation operators from data

This article discusses a range of regression techniques specifically tailored to building aggregation operators from empirical data. These techniques identify optimal parameters of aggregation operators from various classes (triangular norms, uninorms, copulas, ordered weighted aggregation (OWA), generalized means, and compensatory and general aggregation operators), while allowing one to preserve specific properties such as commutativity or associativity. © 2003 Wiley Periodicals, Inc.

Fitting generated aggregation operators to empirical data

This paper treats the problem of fitting general aggregation operators with unfixed number of arguments to empirical data. We discuss methods applicable to associative operators (t-norms, t-conorms, uninorms and nullnorms), means and Choquet integral based operators with respect to a universal fuzzy measure. Special attention is paid to k-order additive symmetric fuzzy measures.

Decision aggregation in an agent-based financial investment planning system

Agent technology provides a new way to model many complex problems like financial investment planning. With this observation in mind, a financial investment planning system was developed from agent perspectives with 12 different agents integrated. Some of the agents have similar problem solving and decision making capabilities. The results from these agents require to be combined. Ordered Weighted Averaging (OWA) operator was chosen to aggregate different results. Details on how OWA was applied as well as appropriate evaluation are presented.