"Decision Systems and Non-stochastic Randomness" presents the first mathematical formalization of the statistical regularities of non-stochastic randomness and demonstrates how these regularities extend the standard probability-based model of decision making under uncertainty, allowing for the description of uncertain mass events that do not fit standard stochastic models. The formalism of statistical regularities developed in this book will have a significant influence on decision theory and information theory as well as numerous other disciplines.

In this volume, the authors close the gap between abstract mathematical approaches, such as abstract algebra, number theory, nonlinear functional analysis, partial differential equations, methods of nonlinear and multi-valued analysis, on the one hand, and practical applications in nonlinear mechanics, decision making theory and control theory on the other. Readers will also benefit from the presentation of modern mathematical modeling methods for the numerical solution of complicated engineering problems in hydromechanics, geophysics and mechanics of continua. This compilation will be of interest to mathematicians and engineers working at the interface of these field. It presents selected works of the open seminar series of Lomonosov Moscow State University and the National Technical University of Ukraine “Kyiv Polytechnic Institute”. The authors come from Germany, Italy, Spain, Russia, Ukraine, and the USA.

Starting with numerical algorithms resulting in new kinds of amazing fractal patterns on the sphere, this book describes the theory underlying these phenomena and indicates possible future applications. The book also explores the following questions:

Traceability describes the ability of stakeholders to understand and follow relationships between artifacts that play some role in software development. It is essential for many development tasks, e.g., quality assurance, requirements management, or software maintenance. Aiming to overcome various deficiencies of existing traceability concepts, this book presents a universal approach describing required features of traceability solutions. This includes a technology-independent, generic template for the definition of semantically rich traceability relationship types and technology-independent patterns for the retrieval of traceability information, reflecting generic problems common to traceability applications. The universal approach is implemented on the basis of two concrete technologies which facilitate comprehensive traceability: the TGraph approach and OWL ontologies. The applicability of the approach is shown by three case studies dealing with the reuse of software artifacts, process model refinement, and requirements management, respectively.

This book describes a comprehensive approach to applying systems science formally to the deep analysis of a wide variety of complex systems. Detailed ‘how-to’ examples of the three phases (analysis-modeling-design) of systems science are applied to systems of various types (machines, organic (e.g. ecosystem), and supra-organic (e.g. business organizations and government). The complexity of the global system has reached proportions that seriously challenge our abilities to understand the consequences of our use of technology, modification of natural ecosystems, or even how to govern ourselves. For this reason, complex mathematics is eschewed when simpler structures will suffice, allowing the widest possible audience to apply and benefit from the available tools and concepts of systems science in their own work. The book shows, in detail, how to functionally and structurally deconstruct complex systems using a fundamental language of systems. It shows how to capture the discovered details in a structured knowledge base from which abstract models can be derived for simulation. The knowledge base is also shown to be a basis for generating system design specifications for human-built artifacts, or policy recommendations/policy mechanisms for socio-economic-ecological systems management. The book builds on principles and methods found in the authors’ textbook Principles of Systems Science (co-authored with Michael Kalton), but without prerequisites. It will appeal to a broad audience that deals with complex systems every day, from design engineers to economic and ecological systems managers and policymakers.

Uncertainties due to randomness and fuzziness comprehensively exist in control and decision support systems.

This book is a printed edition of the Special Issue "Fuzzy Mathematics" that was published in Mathematics