Methods of construction of OWA operators from data

This paper investigates the problem of obtaining the weights of the ordered weighted aggregation (OWA) operators from observations. The problem is formulated as a restricted least squares and uniform approximation problems. We take full advantage of the linearity of the problem. In the former case, a well known technique of non-negative least squares is used. In a case of uniform approximation, we employ a recently developed cutting angle method of global optimisation. Both presented methods give results superior to earlier approaches, and do not require complicated nonlinear constructions. Additional restrictions, such as degree of orness of the operator, can be easily introduced

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.

Review of applications of the Cutting Angle methods

The theory of abstract convexity provides us with the necessary tools for building accurate one-sided approximations of functions. Cutting angle methods have recently emerged as a tool for global optimization of families of abstract convex functions. Their applicability have been subsequently extended to other problems, such as scattered data interpolation. This paper reviews three different applications of cutting angle methods, namely global optimization, generation of nonuniform random variates and multivatiate interpolation.

New methods for objective evaluation of fabric pilling by frequency domain image processing

Fabric pilling is a serious problem for the apparel industry. Resistance to pilling is normally tested by simulated accelerated wear and manual assessment of degree of pilling based on a visual comparison of the sample to a set of test images. A number of automated systems based on image analysis have been developed. The authors propose new methods of image analysis based on the two-dimensional wavelet transform to objectively measure the pilling intensity in sample images. Initial work employed the detail coefficients of the two-dimensional discrete wavelet transform (2DDWT) as a measure of the pilling intensity of woven/knitted fabrics.

This method is shown to be robust to image translation and brightness variation. Using the approximation coefficients of the 2DDWT, the method is extended to non-woven pilling image sets. Wavelet texture analysis (WTA) combined with principal components analysis are shown to produce a richer texture description of pilling for analysis and classification. Finally, employing the two-dimensional dual-tree complex wavelet transform as the basis for the WTA feature vector is shown to produce good automated classification on a range of standard pilling image sets.

Fuzzy concepts and formal methods

It has been recognised that formal methods are useful as a modelling tool in requirements engineering. Specification languages such as Z permit the precise and unambiguous modelling of system properties and behaviour. However some system problems, particularly those drawn from the information systems problem domain, may be difficult to model in crisp or precise terms. It may also be desirable that formal modelling should commence as early as possible, even when our understanding of parts of the problem domain is only approximate. This thesis suggests fuzzy set theory as a possible representation scheme for this imprecision or approximation. A fuzzy logic toolkit that defines the operators, measures and modifiers necessary for the manipulation of fuzzy sets and relations is developed. The toolkit contains a detailed set of laws that demonstrate the properties of the definitions when applied to partial set membership. It also provides a set of laws that establishes an isomorphism between the toolkit notation and that of conventional Z when applied to boolean sets and relations. The thesis also illustrates how the fuzzy logic toolkit can be applied in the problem domains of interest. Several examples are presented and discussed including the representation of imprecise concepts as fuzzy sets and relations, system requirements as a series of linguistically quantified propositions, the modelling of conflict and agreement in terms of fuzzy sets and the partial specification of a fuzzy expert system. The thesis concludes with a consideration of potential areas for future research arising from the work presented here.

A review on computational intelligence methods for controlling traffic signal timing

Urban traffic as one of the most important challenges in modern city life needs practically effective and efficient solutions. Artificial intelligence methods have gained popularity for optimal traffic light control. In this paper, a review of most important works in the field of controlling traffic signal timing, in particular studies focusing on Q-learning, neural network, and fuzzy logic system are presented. As per existing literature, the intelligent methods show a higher performance compared to traditional controlling methods. However, a study that compares the performance of different learning methods is not published yet. In this paper, the aforementioned computational intelligence methods and a fixed-time method are implemented to set signals times and minimize total delays for an isolated intersection. These methods are developed and compared on a same platform. The intersection is treated as an intelligent agent that learns to propose an appropriate green time for each phase. The appropriate green time for all the intelligent controllers are estimated based on the received traffic information. A comprehensive comparison is made between the performance of Q-learning, neural network, and fuzzy logic system controller for two different scenarios. The three intelligent learning controllers present close performances with multiple replication orders in two scenarios. On average Q-learning has 66%, neural network 71%, and fuzzy logic has 74% higher performance compared to the fixed-time controller.

Approximation of centroid end-points and switch points for replacing type reduction algorithms

Despite several years of research, type reduction (TR) operation in interval type-2 fuzzy logic system (IT2FLS) cannot perform as fast as a type-1 defuzzifier. In particular, widely used Karnik-Mendel (KM) TR algorithm is computationally much more demanding than alternative TR approaches. In this work, a data driven framework is proposed to quickly, yet accurately, estimate the output of the KM TR algorithm using simple regression models. Comprehensive simulation performed in this study shows that the centroid end-points of KM algorithm can be approximated with a mean absolute percentage error as low as 0.4%. Also, switch point prediction accuracy can be as high as 100%. In conjunction with the fact that simple regression model can be trained with data generated using exhaustive defuzzification method, this work shows the potential of proposed method to provide highly accurate, yet extremely fast, TR approximation method. Speed of the proposed method should theoretically outperform all available TR methods while keeping the uncertainty information intact in the process.