The main idea of statistical convergence is to demand convergence only for a majority of elements of a sequence. This method of convergence has been investigated in many fundamental areas of mathematics such as: measure theory, approximation theory, fuzzy logic theory, summability theory, and so on. In this monograph we consider this concept in approximating a function by linear operators, especially when the classical limit fails. The results of this book not only cover the classical and statistical approximation theory, but also are applied in the fuzzy logic via the fuzzy-valued operators. The authors in particular treat the important Korovkin approximation theory of positive linear operators in statistical and fuzzy sense. They also present various statistical approximation theorems for some specific real and complex-valued linear operators that are not positive. This is the first monograph in Statistical Approximation Theory and Fuzziness. The chapters are self-contained and several advanced courses can be taught. The research findings will be useful in various applications including applied and computational mathematics, stochastics, engineering, artificial intelligence, vision and machine learning. This monograph is directed to graduate students, researchers, practitioners and professors of all disciplines.

There are many invaluable books available on data mining theory and applications. However, in compiling a volume titled “DATA MINING: Foundations and Intelligent Paradigms: Volume 3: Medical, Health, Social, Biological and other Applications” we wish to introduce some of the latest developments to a broad audience of both specialists and non-specialists in this field.

The monograph offers a view on Rough Mereology, a tool for reasoning under uncertainty, which goes back to Mereology, formulated in terms of parts by Lesniewski, and borrows from Fuzzy Set Theory and Rough Set Theory ideas of the containment to a degree. The result is a theory based on the notion of a part to a degree. One can invoke here a formula Rough: Rough Mereology : Mereology = Fuzzy Set Theory : Set Theory. As with Mereology, Rough Mereology finds important applications in problems of Spatial Reasoning, illustrated in this monograph with examples from Behavioral Robotics. Due to its involvement with concepts, Rough Mereology offers new approaches to Granular Computing, Classifier and Decision Synthesis, Logics for Information Systems, and are--formulation of well--known ideas of Neural Networks and Many Agent Systems. All these approaches are discussed in this monograph. To make the exposition self--contained, underlying notions of Set Theory, Topology, and Deductive and Reductive Reasoning with emphasis on Rough and Fuzzy Set Theories along with a thorough exposition of Mereology both in Lesniewski and Whitehead--Leonard--Goodman--Clarke versions are discussed at length. It is hoped that the monograph offers researchers in various areas of Artificial Intelligence a new tool to deal with analysis of relations among concepts.

In presented book the Intelligent Open Learning Systems (IOLS) are proposed, described, discussed, and evaluated. The IOLS is a system in which traditional methods of online teaching are enhanced through the use of artificial intelligence and cognitive science. This is the main topic of the book. It consists of ten chapters and is divided into three parts. The first part concentrates on the Open Learning System (OLS) analysis, in particular: the social and educational meanings of the OLS, the new role of the teacher and the new requirements regarding the structure of didactic material. Moreover, the cybernetic model of student, teacher and computer collaboration is presented, the teaching-learning process content and its main characteristics are discussed, and the system based approach to the OLS design is proposed. The second part is focused on the problem of knowledge modeling in the OLS based on the ontology and the competence approaches and leading to the learning object concept and competence management in open systems. The third part describes applications of the OLS in the virtual laboratory for competence transfer, the community-built system of distance learning network, and the AGH student city – the real-life application of the OLS concept. The authors’ research findings presented in the book should be useful in various applications related to knowledge management, e-learning systems and information systems.

The book puts special stress on the contemporary techniques for reasoning-based image processing and analysis: learning based image representation and advanced video coding; intelligent image processing and analysis in medical vision systems; similarity learning models for image reconstruction; visual perception for mobile robot motion control, simulation of human brain activity in the analysis of video sequences; shape-based invariant features extraction; essential of paraconsistent neural networks, creativity and intelligent representation in computational systems. The book comprises 14 chapters. Each chapter is a small monograph, representing resent investigations of authors in the area. The topics of the chapters cover wide scientific and application areas and complement each-other very well. The chapters’ content is based on fundamental theoretical presentations, followed by experimental results and comparison with similar techniques. The size of the chapters is well-ballanced which permits a thorough presentation of the investigated problems. The authors are from universities and R&D institutions all over the world; some of the chapters are prepared by international teams. The book will be of use for university and PhD students, researchers and software developers working in the area of digital image and video processing and analysis.

„Between Certainty & Uncertainty” is a one-of–a-kind short course on statistics for students, engineers and researchers. It is a fascinating introduction to statistics and probability with notes on historical origins and 80 illustrative numerical examples organized in the five units: · Chapter 1 Descriptive Statistics: Compressing small samples, basic averages - mean and variance, their main properties including God’s proof; linear transformations and z-scored statistics . · Chapter 2 Grouped data: Udny Yule’s concept of qualitative and quantitative variables. Grouping these two kinds of data. Graphical tools. Combinatorial rules and qualitative variables. Designing frequency histogram. Direct and coded evaluation of quantitative data. Significance of percentiles. · Chapter 3 Regression and correlation: Geometrical distance and equivalent distances in two orthogonal directions as a prerequisite to the concept of two regression lines. Misleading in interpreting two regression lines. Derivation of the two regression lines. Was Hubble right? Houbolt’s cloud. What in fact measures the correlation coefficient? · Chapter 4 Binomial distribution: Middle ages origins of the binomials; figurate numbers and combinatorial rules. Pascal’s Arithmetical Triangle. Bernoulli’s or Poisson Trials? John Arbuthnot curing binomials. How Newton taught S. Pepys probability. Jacob Bernoulli’s Weak Law of Large Numbers and others. · Chapter 5 Normal distribution and binomial heritage – Tables of the normal distribution. Abraham de Moivre and the second theorem of de Moivre-Laplace. · Chapter 1 Descriptive Statistics: Compressing small samples, basic averages - mean and variance, their main properties including God’s proof; linear transformations and z-scored statistics . · Chapter 2 Grouped data: Udny Yule’s concept of qualitative and quantitative variables. Grouping these two kinds of data. Graphical tools. Combinatorial rules and qualitative variables. Designing frequency histogram. Direct and coded evaluation of quantitative data. Significance of percentiles. · Chapter 3 Regression and correlation: Geometrical distance and equivalent distances in two orthogonal directions as a prerequisite to the concept of two regression lines. Misleading in interpreting two regression lines. Derivation of the two regression lines. Was Hubble right? Houbolt’s cloud. What in fact measures the correlation coefficient? · Chapter 4 Binomial distribution: Middle ages origins of the binomials; figurate numbers and combinatorial rules. Pascal’s Arithmetical Triangle. Bernoulli’s or Poisson Trials? John Arbuthnot curing binomials. How Newton taught S. Pepys probability. Jacob Bernoulli’s Weak Law of Large Numbers and others. · Chapter 5 Normal distribution and binomial heritage – Tables of the normal distribution. Abraham de Moivre and the second theorem of de Moivre-Laplace. · Chapter 5 Normal distribution and binomial heritage – Tables of the normal distribution. Abraham de Moivre and the second theorem of de Moivre-Laplace.

The study of complex systems attracts the attention of many researchers in diverse fields. Complex systems are characterized by a high number of entities and a high degree of interactions. One of the most important features is that they do not involve a central organizing authority, but the various elements that make up the systems are self-organized. Moreover, some complex systems possess an emergency priority: climate change and sustainable development research, studies of public health, ecosystem habitats, epidemiology, and medicine, among others. Unfortunately, a great number of today’s overlapping approaches fail to meet the needs of decision makers when managing complex domains. Indeed, the design of complex systems often requires the integration of a number of artificial intelligence tools and techniques. The problem can be viewed in terms of goals, states, and actions, choosing the best action to move the system toward its desired state or behavior. This is why agent-based approaches are used to model complex systems. The main objective of this book is to bring together existing methods for decision support systems creation within a coherent agent-based framework and to provide an interdisciplinary and flexible methodology for modeling complex and systemic domains.