Identification of general aggregation operators by Lipschitz approximation

Aggregation operators model various operations on fuzzy sets, such as conjunction, disjunction and aver aging. The choice of aggregation operators suitable for a particular problem is frequently done by fitting the parameters of the operator to the observed data. This paper examines fitting general aggregation operators by using a new method of Lipschitz approximation.

Multi-wavelets from B-spline super-functions with approximation order

Approximation order is an important feature of all wavelets. It implies that polynomials up to degree p−1 are in the space spanned by the scaling function(s). In the scalar case, the scalar sum rules determine the approximation order or the left eigenvectors of the infinite down-sampled convolution matrix H determine the combinations of scaling functions required to produce the desired polynomial. For multi-wavelets the condition for approximation order is similar to the conditions in the scalar case. Generalized left eigenvectors of the matrix H_f; a finite portion of H determines the combinations of scaling functions that produce the desired superfunction from which polynomials of desired degree can be reproduced. The superfunctions in this work are taken to be B-splines. However, any refinable function can serve as the superfunction. The condition of approximation order is derived and new, symmetric, compactly supported and orthogonal multi-wavelets with approximation orders one, two, three and four are constructed.

Shape preserving approximation using least squares splines

Least squares polynomial splines are an effective tool for data fitting, but they may fail to preserve essential properties of the underlying function, such as monotonicity or convexity. The shape restrictions are translated into linear inequality conditions on spline coefficients. The basis functions are selected in such a way that these conditions take a simple form, and the problem becomes non-negative least squares problem, for which effecitive and robust methods of solution exist. Multidimensional monotone approximation is achieved by using tensor-product splines with the appropriate restrictions. Additional inter polation conditions can also be introduced. The conversion formulas to traditional B-spline representation are provided.

Using Choquet integrals for kNN approximation and classification

k-nearest neighbors (kNN) is a popular method for function approximation and classification. One drawback of this method is that the nearest neighbors can be all located on one side of the point in question x. An alternative natural neighbors method is expensive for more than three variables. In this paper we propose the use of the discrete Choquet integral for combining the values of the nearest neighbors so that redundant information is canceled out. We design a fuzzy measure based on location of the nearest neighbors, which favors neighbors located all around x.

South Africa's transtion from apartheid : the role of professional closure in the experiences of black chartered accountants

As apartheid gave way to political freedom in South Africa in the last quarter of the 20th century, chartered accounting firms began to hire black South African trainees for the first time. The study examines the oral histories of black chartered accountants within the context of social closure theory and South Africa’s changing political and ideological landscape. The evidence indicates that processes of professional closure and credentialing excluded the majority population from the ranks of the profession on basis of race and class throughout the period 1976–2000.

HE community fights ALTC closure

While universities stand to lose more than twice as much from cuts to capital funding, it’s the abolition of the ALTC that really has the higher education community up in arms.