Fuzzy Sets, Fuzzy Logic and Their Applications

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity

A specialised constraint approach for stable matching problems

Constraint programming is a generalised framework designed to solve combinatorial problems. This framework is made up of a set of predefined independent components and generalised algorithms. This is a very versatile structure which allows for a variety of rich combinatorial problems to be represented and solved relatively easily. Stable matching problems consist of a set of participants wishing to be matched into pairs or groups in a stable manner. A matching is said to be stable if there is no pair or group of participants that would rather make a private arrangement to improve their situation and thus undermine the matching. There are many important "real life" applications of stable matching problems across the world. Some of which includes the Hospitals/Residents problem in which a set of graduating medical students, also known as residents, need to be assigned to hospital posts. Some authorities assign children to schools as a stable matching problem. Many other such problems are also tackled as stable matching problems. A number of classical stable matching problems have efficient specialised algorithmic solutions. Constraint programming solutions to stable matching problems have been investigated in the past. These solutions have been able to match the theoretically optimal time complexities of the algorithmic solutions. However, empirical evidence has shown that in reality these constraint solutions run significantly slower than the specialised algorithmic solutions. Furthermore, their memory requirements prohibit them from solving problems which the specialised algorithmic solutions can solve in a fraction of a second. My contribution investigates the possibility of modelling stable matching problems as specialised constraints. The motivation behind this approach was to find solutions to these problems which maintain the versatility of the constraint solutions, whilst significantly reducing the performance gap between constraint and specialised algorithmic solutions. To this end specialised constraint solutions have been developed for the stable marriage problem and the Hospitals/Residents problem. Empirical evidence has been presented which shows that these solutions can solve significantly larger problems than previously published constraint solutions. For these larger problem instances it was seen that the specialised constraint solutions came within a factor of four of the time required by algorithmic solutions. It has also been shown that, through further specialisation, these constraint solutions can be made to run significantly faster. However, these improvements came at the cost of versatility. As a demonstration of the versatility of these solutions it is shown that, by adding simple side constraints, richer problems can be easily modelled. These richer problems add additional criteria and/or an optimisation requirement to the original stable matching problems. Many of these problems have been proven to be NP-Hard and some have no known algorithmic solutions. Included with these models are results from empirical studies which show that these are indeed feasible solutions to the richer problems. Results from the studies also provide some insight into the structure of these problems, some of which have had little or no previous study

Introduction to Real Analysis

Using a clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. This book is intended for those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.https://digitalcommons.trinity.edu/mono/1006/thumbnail.jp

Taking shape: The data science of elastic shape analysis with practical applications

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London.A mathematical curve can represent many different objects, both physical and abstract, from the outline curve of an artefact in an image to the weight of growing animal to the set of frequencies used in a sound. Regardless of these variations, the curves can almost always vary non-linearly. One way to study shapes and their potential variations is elastic shape analysis, a rich theory of which has developed over the past twenty years. However, methods of elastic shape analysis are seldom utilized in practical applications on real-world data, especially outside of the mathematical shape analysis community. Our aim in this thesis is to explore some practical applications of elastic shape analysis. To do this, we work with various types of shape data, the majority of which are based on image datasets. As our focus is on two-dimensional curves, it is important to be able to robustly extract contours from images, before we can apply elastic shape analysis tools. In order to analyse the shapes in a dataset, we turn to methods of machine learning, to investigate the applications of elastic shape analysis in classification. In this thesis, we introduce an anthology of projects, in order to emphasise and under- stand the potential of elastic shape analysis in practical applications. There are four main projects in this thesis: (i) Classification of objects using outlines and the comparisons between methods of elastic shape analysis, geometric morphometrics, and human experts, with a focus on ancient Greek vases, (ii) Mussel species identification and a demonstra- tion that shape may not be enough in some applications, (iii) A novel tool to monitor the development of k ̄ak ̄ap ̄o chicks, and (iv) Classifying individual kiwi based on acoustic data from their calls. By combining tools from computer vision and machine learning with methods of elastic shape analysis, we introduce a practical framework for the application of elastic shape analysis, through a data science lens

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...

Development and validation of the Euler-Lagrange formulation on a parallel and unstructured solver for large-eddy simulation

De nombreuses applications industrielles mettent en jeu des écoulements gaz-particules, comme les turbines aéronautiques et les réacteurs a lit fluidisé de l'industrie chimique. La prédiction des propriétés de la phase dispersée, est essentielle à l'amélioration et la conception des dispositifs conformément aux nouvelles normes européennes des émissions polluantes. L'objectif de cette these est de développer le formalisme Euler- Lagrange dans un solveur parallèle et non-structuré pour la simulation aux grandes échelles pour ce type d'écoulements. Ce travail est motivé par l'augmentation rapide de la puissance de calcul des machines massivement parallèles qui ouvre une nouvelle voie pour des simulations qui étaient prohibitives il y a une décennie. Une attention particulière a été portée aux structures de données afin de conserver une certaine simplicité et la portabilité du code sur des differentes architectures. Les développements sont validés pour deux configurations : un cas académique de turbulence homogène isotrope décroissante et un calcul polydisperse d'un jet turbulent recirculant chargé en particules. L'équilibrage de charges de particules est mis en évidence comme une solution prometteuse pour les simulations diphasiques Lagrangiennes afin d'améliorer les performances des calculs lorsque le déséquilibrage est trop important. ABSTRACT : Particle-laden flows occur in industrial applications ranging from droplets in gas turbines tofluidized bed in chemical industry. Prediction of the dispersed phase properties such as concentration and dynamics are crucial for the design of more efficient devices that meet the new pollutant regulations of the European community. The objective of this thesis is to develop an Euler-Lagrange formulation on a parallel and unstructured solver for large- eddy simulation. This work is motivated by the rapid increase in computing power which opens a new way for simulations that were prohibitive one decade ago. Special attention is taken to keep data structure simplicity and code portability. Developments are validated in two configurations : an academic test of a decaying homogeneous isotropic turbulence and a polydisperse two-phase flow of a confined bluff body. The use of load-balancing capabilities is highlighted as a promising solution in Lagrangian two-phase flow simulations to improve performance when strong imbalance of the dispersed phase is presen