Weldon A. Lodwick

This book provides an essential introduction to the field of dynamical models. Starting from classical theories such as set theory and probability, it allows readers to draw near to the fuzzy case. On one hand, the book equips readers with a fundamental understanding of the theoretical underpinnings of fuzzy sets and fuzzy dynamical systems. On the other, it presents some concepts of derivatives, integrals and differential equations applied to the context of fuzzy functions. Each of the major topics is accompanied by examples, worked-out exercises, and exercises to be completed. Moreover, many applications to real problems are presented, mainly in biomathematics where the so-called p-fuzzy systems play an important role. The book has been developed on the basis of the authors’ lectures to university students and is accordingly primarily intended as a textbook for both upper-level undergraduates and graduates in applied mathematics, statistics, and engineering. It also offers a valuable resource for practitioners such as mathematical consultants and modelers, and for researchers alike, as it may provide both groups with new ideas and inspirations for projects in the fields of fuzzy logic and biomathematics. This thoroughly updated second edition includes a new chapter on fuzzy optimization, which also presents an application in carbon markets analysis and modeling

One of the primary objectives of this book is to highlight the profound difference between two types of AI that pursue distinct goals: emulative AI, which seeks to build machines whose output is similar to, or even superior to, that of the human brain, and investigative AI, whose purpose is to make invisible information within data visible by uncovering the laws through which individual behaviors self-organize into collective behaviors. The former is better known, as it serves as a useful tool for automating human labor and generating market profits; the latter is less widely recognized but is more scientifically oriented towards saving lives (in the medical field), explaining otherwise inexplicable phenomena (in the geophysical field), and enhancing our understanding of the material and abstract world. Both are valuable yet distinct: the emulative approach generates immediate profits and creates illusions of human-like power, while the investigative approach enhances fundamental scientific research and will yield its greatest benefits over time. The investigative approach presented in this volume seeks to rebuild the bridge between humanity and nature.

This book introduces the Topological Weighed Centroid approach and describes some applications in the study of the dynamics of various spatial phenomena with a special emphasis on the spatial analysis of the relationship, influence, and dynamics of geographical phenomena. Offering a comprehensive introduction to the theory and illustrative examples from various kinds of geographical data, this book also takes an in-depth look at more complex case studies, such as the applications of the topological weighed centroid approach in the study of epidemic patterns, cultural processes, criminality, and environmental phenomena.

This book provides an essential introduction to the field of dynamical models. Starting from classical theories such as set theory and probability, it allows readers to draw near to the fuzzy case. On one hand, the book equips readers with a fundamental understanding of the theoretical underpinnings of fuzzy sets and fuzzy dynamical systems. On the other, it presents some concepts of derivatives, integrals and differential equations applied to the context of fuzzy functions. Each of the major topics is accompanied by examples, worked-out exercises, and exercises to be completed. Moreover, many applications to real problems are presented, mainly in biomathematics where the so-called p-fuzzy systems play an important role. The book has been developed on the basis of the authors’ lectures to university students and is accordingly primarily intended as a textbook for both upper-level undergraduates and graduates in applied mathematics, statistics, and engineering. It also offers a valuable resource for practitioners such as mathematical consultants and modelers, and for researchers alike, as it may provide both groups with new ideas and inspirations for projects in the fields of fuzzy logic and biomathematics. This thoroughly updated second edition includes a new chapter on fuzzy optimization, which also presents an application in carbon markets analysis and modeling

This book introduces the Topological Weighed Centroid approach and describes some applications in the study of the dynamics of various spatial phenomena with a special emphasis on the spatial analysis of the relationship, influence, and dynamics of geographical phenomena. Offering a comprehensive introduction to the theory and illustrative examples from various kinds of geographical data, this book also takes an in-depth look at more complex case studies, such as the applications of the topological weighed centroid approach in the study of epidemic patterns, cultural processes, criminality, and environmental phenomena.

This book presents the theory and methods of flexible and generalized uncertainty optimization. Particularly, it describes the theory of generalized uncertainty in the context of optimization modeling. The book starts with an overview of flexible and generalized uncertainty optimization. It covers uncertainties that are both associated with lack of information and are more general than stochastic theory, where well-defined distributions are assumed. Starting from families of distributions that are enclosed by upper and lower functions, the book presents construction methods for obtaining flexible and generalized uncertainty input data that can be used in a flexible and generalized uncertainty optimization model. It then describes the development of the associated optimization model in detail. Written for graduate students and professionals in the broad field of optimization and operations research, this second edition has been revised and extended to include more worked examples and a section on interval multi-objective mini-max regret theory along with its solution method.

This book presents the theory and methods of flexible and generalized uncertainty optimization. Particularly, it describes the theory of generalized uncertainty in the context of optimization modeling. The book starts with an overview of flexible and generalized uncertainty optimization. It covers uncertainties that are both associated with lack of information and are more general than stochastic theory, where well-defined distributions are assumed. Starting from families of distributions that are enclosed by upper and lower functions, the book presents construction methods for obtaining flexible and generalized uncertainty input data that can be used in a flexible and generalized uncertainty optimization model. It then describes the development of the associated optimization model in detail. Written for graduate students and professionals in the broad field of optimization and operations research, this second edition has been revised and extended to include more worked examples and a section on interval multi-objective mini-max regret theory along with its solution method.

This book offers an introduction to artificial adaptive systems and a general model of the relationships between the data and algorithms used to analyze them. It subsequently describes artificial neural networks as a subclass of artificial adaptive systems, and reports on the backpropagation algorithm, while also identifying an important connection between supervised and unsupervised artificial neural networks. The book’s primary focus is on the auto contractive map, an unsupervised artificial neural network employing a fixed point method versus traditional energy minimization. This is a powerful tool for understanding, associating and transforming data, as demonstrated in the numerous examples presented here. A supervised version of the auto contracting map is also introduced as an outstanding method for recognizing digits and defects. In closing, the book walks the readers through the theory and examples of how the auto contracting map can be used in conjunction with another artificial neural network, the “spin-net,” as a dynamic form of auto-associative memory.

This book offers an introduction to artificial adaptive systems and a general model of the relationships between the data and algorithms used to analyze them. It subsequently describes artificial neural networks as a subclass of artificial adaptive systems, and reports on the backpropagation algorithm, while also identifying an important connection between supervised and unsupervised artificial neural networks. The book’s primary focus is on the auto contractive map, an unsupervised artificial neural network employing a fixed point method versus traditional energy minimization. This is a powerful tool for understanding, associating and transforming data, as demonstrated in the numerous examples presented here. A supervised version of the auto contracting map is also introduced as an outstanding method for recognizing digits and defects. In closing, the book walks the readers through the theory and examples of how the auto contracting map can be used in conjunction with another artificial neural network, the “spin-net,” as a dynamic form of auto-associative memory.

This book is a pedagogical presentation aimed at advanced undergraduate students, beginning graduate students and professionals who are looking for an introductory text to the field of Distance Geometry, and some of its applications. This versions profits from feedback acquired at undergraduate/graduate courses in seminars and a number of workshops.