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.<br /

Dynamic fuzzy rule interpolation and its application to intrusion detection

Fuzzy rule interpolation (FRI) offers an effective approach for making inference possible in sparse rule-based systems (and also for reducing the complexity of fuzzy models). However, requirements of fuzzy systems may change over time and hence, the use of a static rule base may affect the accuracy of FRI applications. Fortunately, an FRI system in action will produce interpolated rules in abundance during the interpolative reasoning process. While such interpolated results are discarded in existing FRI systems, they can be utilized to facilitate the development of a dynamic rule base in supporting subsequent inference. This is because the otherwise relinquished interpolated rules may contain possibly valuable information, covering regions that were uncovered by the original sparse rule base. This paper presents a dynamic fuzzy rule interpolation (D-FRI) approach by exploiting such interpolated rules in order to improve the overall system's coverage and efficacy. The resulting D-FRI system is able to select, combine, and generalize informative, frequently used interpolated rules for merging with the existing rule base while performing interpolative reasoning. Systematic experimental investigations demonstrate that D-FRI outperforms conventional FRI techniques, with increased accuracy and robustness. Furthermore, D-FRI is herein applied for network security analysis, in devising a dynamic intrusion detection system (IDS) through integration with the Snort software, one of the most popular open source IDSs. This integration, denoted as D-FRI-Snort hereafter, delivers an extra amount of intelligence to predict the level of potential threats. Experimental results show that with the inclusion of a dynamic rule base, by generalising newly interpolated rules based on the current network traffic conditions, D-FRI-Snort helps reduce both false positives and false negatives in intrusion detection

BEMDEC: An Adaptive and Robust Methodology for Digital Image Feature Extraction

The intriguing study of feature extraction, and edge detection in particular, has, as a result of the increased use of imagery, drawn even more attention not just from the field of computer science but also from a variety of scientific fields. However, various challenges surrounding the formulation of feature extraction operator, particularly of edges, which is capable of satisfying the necessary properties of low probability of error (i.e., failure of marking true edges), accuracy, and consistent response to a single edge, continue to persist. Moreover, it should be pointed out that most of the work in the area of feature extraction has been focused on improving many of the existing approaches rather than devising or adopting new ones. In the image processing subfield, where the needs constantly change, we must equally change the way we think. In this digital world where the use of images, for variety of purposes, continues to increase, researchers, if they are serious about addressing the aforementioned limitations, must be able to think outside the box and step away from the usual in order to overcome these challenges. In this dissertation, we propose an adaptive and robust, yet simple, digital image features detection methodology using bidimensional empirical mode decomposition (BEMD), a sifting process that decomposes a signal into its two-dimensional (2D) bidimensional intrinsic mode functions (BIMFs). The method is further extended to detect corners and curves, and as such, dubbed as BEMDEC, indicating its ability to detect edges, corners and curves. In addition to the application of BEMD, a unique combination of a flexible envelope estimation algorithm, stopping criteria and boundary adjustment made the realization of this multi-feature detector possible. Further application of two morphological operators of binarization and thinning adds to the quality of the operator

Development of soft computing and applications in agricultural and biological engineering

Soft computing is a set of “inexact” computing techniques, which are able to model and analyze very complex problems. For these complex problems, more conventional methods have not been able to produce cost-effective, analytical, or complete solutions. Soft computing has been extensively studied and applied in the last three decades for scientific research and engineering computing. In agricultural and biological engineering, researchers and engineers have developed methods of fuzzy logic, artificial neural networks, genetic algorithms, decision trees, and support vector machines to study soil and water regimes related to crop growth, analyze the operation of food processing, and support decision-making in precision farming. This paper reviews the development of soft computing techniques. With the concepts and methods, applications of soft computing in the field of agricultural and biological engineering are presented, especially in the soil and water context for crop management and decision support in precision agriculture. The future of development and application of soft computing in agricultural and biological engineering is discussed

Adaptive fuzzy interpolation

Fuzzy interpolative reasoning strengthens the power of fuzzy inference by the enhancement of the robustness of fuzzy systems and the reduction of the systems' complexity. However, after a series of interpolations, it is possible that multiple object values for a common variable are inferred, leading to inconsistency in interpolated results. Such inconsistencies may result from defective interpolated rules or incorrect interpolative transformations. This paper presents a novel approach for identification and correction of defective rules in interpolative transformations, thereby removing the inconsistencies. In particular, an assumption-based truth-maintenance system (ATMS) is used to record dependences between interpolations, and the underlying technique that the classical general diagnostic engine (GDE) employs for fault localization is adapted to isolate possible faulty interpolated rules and their associated interpolative transformations. From this, an algorithm is introduced to allow for the modification of the original linear interpolation to become first-order piecewise linear. The approach is applied to a realistic problem, which predicates the diarrheal disease rates in remote villages, to demonstrate the potential of this study

Feasible Form Parameter Design of Complex Ship Hull Form Geometry

This thesis introduces a new methodology for robust form parameter design of complex hull form geometry via constraint programming, automatic differentiation, interval arithmetic, and truncated hierarchical B- splines. To date, there has been no clearly stated methodology for assuring consistency of general (equality and inequality) constraints across an entire geometric form parameter ship hull design space. In contrast, the method to be given here can be used to produce guaranteed narrowing of the design space, such that infeasible portions are eliminated. Furthermore, we can guarantee that any set of form parameters generated by our method will be self consistent. It is for this reason that we use the title feasible form parameter design. In form parameter design, a design space is represented by a tuple of design parameters which are extended in each design space dimension. In this representation, a single feasible design is a consistent set of real valued parameters, one for every component of the design space tuple. Using the methodology to be given here, we pick out designs which consist of consistent parameters, narrowed to any desired precision up to that of the machine, even for equality constraints. Furthermore, the method is developed to enable the generation of complex hull forms using an extension of the basic rules idea to allow for automated generation of rules networks, plus the use of the truncated hierarchical B-splines, a wavelet-adaptive extension of standard B-splines and hierarchical B-splines. The adaptive resolution methods are employed in order to allow an automated program the freedom to generate complex B-spline representations of the geometry in a robust manner across multiple levels of detail. Thus two complementary objectives are pursued: ensuring feasible starting sets of form parameters, and enabling the generation of complex hull form geometry