Approximation Theory and Related Applications

In recent years, we have seen a growing interest in various aspects of approximation theory. This happened due to the increasing complexity of mathematical models that require computer calculations and the development of the theoretical foundations of the approximation theory. Approximation theory has broad and important applications in many areas of mathematics, including functional analysis, differential equations, dynamical systems theory, mathematical physics, control theory, probability theory and mathematical statistics, and others. Approximation theory is also of great practical importance, as approximate methods and estimation of approximation errors are used in physics, economics, chemistry, signal theory, neural networks and many other areas. This book presents the works published in the Special Issue "Approximation Theory and Related Applications". The research of the world’s leading scientists presented in this book reflect new trends in approximation theory and related topics

Sustainability ranking of desalination plants using Mamdani Fuzzy Logic Inference Systems

As water desalination continues to expand globally, desalination plants are continually under pressure to meet the requirements of sustainable development. However, the majority of desalination sustainability research has focused on new desalination projects, with limited research on sustainability performance of existing desalination plants. This is particularly important while considering countries with limited resources for freshwater such as the United Arab Emirates (UAE) as it is heavily reliant on existing desalination infrastructure. In this regard, the current research deals with the sustainability analysis of desalination processes using a generic sustainability ranking framework based on Mamdani Fuzzy Logic Inference Systems. The fuzzy-based models were validated using data from two typical desalination plants in the UAE. The promising results obtained from the fuzzy ranking framework suggest this more in-depth sustainability analysis should be beneficial due to its flexibility and adaptability in meeting the requirements of desalination sustainability

Decision tree learning for intelligent mobile robot navigation

The replication of human intelligence, learning and reasoning by means of computer algorithms is termed Artificial Intelligence (Al) and the interaction of such algorithms with the physical world can be achieved using robotics. The work described in this thesis investigates the applications of concept learning (an approach which takes its inspiration from biological motivations and from survival instincts in particular) to robot control and path planning. The methodology of concept learning has been applied using learning decision trees (DTs) which induce domain knowledge from a finite set of training vectors which in turn describe systematically a physical entity and are used to train a robot to learn new concepts and to adapt its behaviour. To achieve behaviour learning, this work introduces the novel approach of hierarchical learning and knowledge decomposition to the frame of the reactive robot architecture. Following the analogy with survival instincts, the robot is first taught how to survive in very simple and homogeneous environments, namely a world without any disturbances or any kind of "hostility". Once this simple behaviour, named a primitive, has been established, the robot is trained to adapt new knowledge to cope with increasingly complex environments by adding further worlds to its existing knowledge. The repertoire of the robot behaviours in the form of symbolic knowledge is retained in a hierarchy of clustered decision trees (DTs) accommodating a number of primitives. To classify robot perceptions, control rules are synthesised using symbolic knowledge derived from searching the hierarchy of DTs. A second novel concept is introduced, namely that of multi-dimensional fuzzy associative memories (MDFAMs). These are clustered fuzzy decision trees (FDTs) which are trained locally and accommodate specific perceptual knowledge. Fuzzy logic is incorporated to deal with inherent noise in sensory data and to merge conflicting behaviours of the DTs. In this thesis, the feasibility of the developed techniques is illustrated in the robot applications, their benefits and drawbacks are discussed

Variable Precision Rough Set Approximations in Concept Lattice

The notions of variable precision rough set and concept lattice are can be shared by a basic notion, which is the definability of a set of objects based on a set of properties. The two theories of rough set and concept lattice can be compared, combined and applied to each other based on definability. Based on introducing the definitions of variable precision rough set and concept lattice, this paper shows that any extension of a concept in concept lattice is an equivalence class of variable precision rough set. After that, we present a definition of lower and upper approximations in concept lattice and generate the lower and upper approximations concept of concept lattice. Afterwards, we discuss the properties of the new lower and upper approximations. Finally, an example is given to show the validity of the properties that the lower and upper approximations have

Decision Support System for Managing Reverse Supply Chain

Reverse logistics are becoming more and more important in the overall Industry area because of the environment and business factors. Planning and implementing a suitable reverse logistics network could bring more profit, customer satisfaction, and an excellent social picture for companies. But, most of the logistics networks are not equipped to handle the return products in reverse channels. Reverse logistics processes and plans rely heavily on reversing the supply chain so that companies can correctly identify and categorize returned products for disposition, an area that offers many opportunities for additional revenue. The science of reverse logistics includes return policy administration, product recall protocols, repairs processing, product repackaging, parts management, recycling, product disposition management, maximizing liquidation values and much more. The focus of this project is to develop a reverse logistics management system/ tools (RLMS). The proposed tools are demonstrated in the following order. First, we identify the risks involved in the reverse supply chain. Survey tool is used to collect data and information required for analysis. The methodologies that are used to identify key risks are the six sigma tools, namely Define, Measure, Analyse, Improve and Control (DMAIC), SWOT analysis, cause and effect, and Risk Mapping. An improved decision-making method using fuzzy set theory for converting linguistic data into numeric risk ratings has been attempted. In this study, the concept of ‘Left and Right dominance approach’(Chen and Liu, 2001) and Method of ‘In center of centroids’ (Thoran et al., 2012a,b) for generalized trapezoidal fuzzy numbers has been used to quantify the ‘degree of risk’ in terms of crisp ratings. After the analysis, the key risks are identified are categorized, and an action requirement plan suggested for providing guidelines for the managers to manage the risk successfully in the context of reverse logistics. Next, from risk assessment findings, information technology risk presents the highest risk impact on the performance of the reverse logistics, especially lack of use of a decision support system (DSS). We propose a novel multi-attribute decision (MADM) support tool that can categorizes return products and make the best alternative selection of recovery and disposal option using carefully considered criteria using MADM decision making methodologies such as fuzzy MOORA and VIKOR. The project can be applied to all types of industries. Once the returned products are collected and categorized at the retailers/ Points of return (PoR), an optimized network is required to determine the number of reprocessing centres to be opened and the optimized optimum material flow between retailers, reprocessing, recycling and disposal centers at minimum costs. The research develops a mixed integer linear programming model for two scenarios, namely considering direct shipping from retailer/ PoR to the respective reprocessing centers and considering the use of centralized return centers (CRC). The models are solved using LINGO 15 software and excel solver tools respectively. The advantage of the implementation of our solution is that it will help improve performance and reduce time. This benefits the company by having a reduction in their cost due to uncertainties and also contributes to better customer satisfaction. Implementation of these tools at ABZ computer distributing company demonstrates how the reverse logistics management tools can used in order to be beneficial to the organization. The tool is designed to be easily implemented at minimal cost and serves as a valuable tool for personnel faced with significant and costly decisions regarding risk assessment, decision making and network optimization in the reverse supply chain practices

Workshop on Fuzzy Control Systems and Space Station Applications

The Workshop on Fuzzy Control Systems and Space Station Applications was held on 14-15 Nov. 1990. The workshop was co-sponsored by McDonnell Douglas Space Systems Company and NASA Ames Research Center. Proceedings of the workshop are presented