The focus of this book is on establishing theories and methods of both decision and game analysis in management using intuitionistic fuzzy sets. It proposes a series of innovative theories, models and methods such as the representation theorem and extension principle of intuitionistic fuzzy sets, ranking methods of intuitionistic fuzzy numbers, non-linear and linear programming methods for intuitionistic fuzzy multi-attribute decision making and (interval-valued) intuitionistic fuzzy matrix games. These theories and methods form the theory system of intuitionistic fuzzy decision making and games, which is not only remarkably different from those of the traditional, Bayes and/or fuzzy decision theory but can also provide an effective and efficient tool for solving complex management problems. Since there is a certain degree of inherent hesitancy in real-life management, which cannot always be described by the traditional mathematical methods and/or fuzzy set theory, this book offers an effective approach to using the intuitionistic fuzzy set expressed with membership and non-membership functions. This book is addressed to all those involved in theoretical research and practical applications from a variety of fields/disciplines: decision science, game theory, management science, fuzzy sets, operational research, applied mathematics, systems engineering, industrial engineering, economics, etc.

An introduction to game theory and its application to the study of politics, designed by a leading authority for students without advanced mathematical training.

The progress of society can only happen through interpersonal cooperation, because only cooperation can bring about mutual benefit, thus bringing happiness to each person. This should be our collective rationality, but we often see it conflicts with individual interests, which leads to the so-called "Prisoners' Dilemma" and does not bring happiness to all. From a game theoretical perspective, this book addresses the issue of how people can cooperate better. It has two objectives. The first is to use common language to systematically introduce the basic methodologies and core conclusions of Game Theory, including the Nash equilibrium, multiple equilibriums, dynamic games, etc. Mathematics and theoretical models are used to the minimum necessary scope too, to make this book get access to ordinary readers with elementary mathematical training. The second objective is to utilize these methods and conclusions to analyze various Chinese social issues and institutional arrangements, with a focus on the reasons people exhibit non-cooperative behaviors as well as the institutions and cultures that promote interpersonal cooperation. In addition to economics, specialists in sociology, law, history, politics and management will also be attracted by this book for its insightful analysis on the issue of cooperation in these fields. Also, readers curious about Chinese society will benefit from this book.

The Presidential Election Game may change the way you think about presidential elections and, for that matter, American politics in general. It is not filled with statistics about the voting behavior of citizens, nor does it give detailed histories of past campaigns. Rather, it is an analytic treatment of strategy in the race for the presidency, from the primaries to the general election. Using modern game theory and decision theory, Brams demonstrates why certain campaign strategies are more effective than others and supports his analysis with historical evidence.

Mathematics in Games, Sports, and Gambling: The Games People Play, Second Edition demonstrates how discrete probability, statistics, and elementary discrete mathematics are used in games, sports, and gambling situations. With emphasis on mathematical thinking and problem solving, the text draws on numerous examples, questions, and problems to explain the application of mathematical theory to various real-life games.This updated edition of a widely adopted textbook considers a number of popular games and diversions that are mathematically based or can be studied from a mathematical perspective. Requiring only high school algebra, the book is suitable for use as a textbook in seminars, general education courses, or as a supplement in introductory probability courses.New in this Edition: Many new exercises, including basic skills exercises More answers in the back of the book Expanded summary exercises, including writing exercises More detailed examples, especially in the early chapters An expansion of the discrete adjustment technique for binomial approximation problems New sections on chessboard puzzles that encourage students to develop graph theory ideas New review material on relations and functions Exercises are included in each section to help students understand the various concepts. The text covers permutations in the two-deck matching game so derangements can be counted. It introduces graphs to find matches when looking at extensions of the five-card trick and studies lexicographic orderings and ideas of encoding for card tricks.The text also explores linear and weighted equations in the section on the NFL passer rating formula and presents graphing to show how data can be compared or displayed. For each topic, the author includes exercises based on real games and actual sports data.

Despite the proliferation of video games in the twenty-first century, the theory of game design is largely underdeveloped, leaving designers on their own to understand what games really are. Helping you produce better games, Game Design Theory: A New Philosophy for Understanding Games presents a bold new path for analyzing and designing games. The author offers a radical yet reasoned way of thinking about games and provides a holistic solution to understanding the difference between games and other types of interactive systems. He clearly details the definitions, concepts, and methods that form the fundamentals of this philosophy. He also uses the philosophy to analyze the history of games and modern trends as well as to design games. Providing a robust, useful philosophy for game design, this book gives you real answers about what games are and how they work. Through this paradigm, you will be better equipped to create fun games.

The H control has been one of the important robust control approaches since the 1980s. This book extends the area to nonlinear stochastic H2/H control, and studies more complex and practically useful mixed H2/H controller synthesis rather than the pure H control. Different from the commonly used convex optimization method, this book applies the Nash game approach to give necessary and sufficient conditions for the existence and uniqueness of the mixed H2/H control. Researchers will benefit from our detailed exposition of the stochastic mixed H2/H control theory, while practitioners can apply our efficient algorithms to address their practical problems.

This book presents a wide range of optimization methods and their applications to various electrical power system problems such as economical load dispatch, demand supply management in microgrids, levelized energy pricing, load frequency control and congestion management, and reactive power management in radial distribution systems. Problems related to electrical power systems are often highly complex due to the massive dimensions, nonlinearity, non-convexity and discontinuity associated with objective functions. These systems also have a large number of equality and inequality constraints, which give rise to optimization problems that are difficult to solve using classical numerical methods. In this regard, nature inspired optimization algorithms offer an effective alternative, due to their ease of use, population-based parallel search mechanism, non-dependence on the nature of the problem, and ability to accommodate non-differentiable, non-convex problems. The analytical model of nature inspired techniques mimics the natural behaviors and intelligence of life forms. These techniques are mainly based on evolution, swarm intelligence, ecology, human intelligence and physical science.

This book considers a range of problems in operations research, which are formulated through various mathematical models such as complementarity, variational inequalities, multiobjective optimization, fixed point problems, noncooperative games and inverse optimization. Moreover, the book subsumes all these models under a common structure that allows them to be formulated in a unique format: the Ky Fan inequality. It subsequently focuses on this unifying equilibrium format, providing a comprehensive overview of the main theoretical results and solution algorithms, together with a wealth of applications and numerical examples. Particular emphasis is placed on the role of nonlinear optimization techniques - e.g. convex optimization, nonsmooth calculus, proximal point and descent algorithms - as valuable tools for analyzing and solving Ky Fan inequalities.

This book presents a selection of advanced case studies that cover a substantial range of issues and real-world challenges and applications in space engineering. Vital mathematical modeling, optimization methodologies and numerical solution aspects of each application case study are presented in detail, with discussions of a range of advanced model development and solution techniques and tools. Space engineering challenges are discussed in the following contexts: *Advanced Space Vehicle Design *Computation of Optimal Low Thrust Transfers *Indirect Optimization of Spacecraft Trajectories *Resource-Constrained Scheduling, *Packing Problems in Space *Design of Complex Interplanetary Trajectories *Satellite Constellation Image Acquisition *Re-entry Test Vehicle Configuration Selection *Collision Risk Assessment on Perturbed Orbits *Optimal Robust Design of Hybrid Rocket Engines *Nonlinear Regression Analysis in Space Engineering *Regression-Based Sensitivity Analysis and Robust Design *Low-Thrust Multi-Revolution Orbit Transfers *Modeling and Optimization of Balance Layout Problems *Pilot-Induced Oscillations Alleviation *Modeling and Optimization of Hybrid Transfers to Near-Earth Objects *Probabilistic Safety Analysis of the Collision Between Space Debris and Satellite *Flatness-based Low-thrust Trajectory Optimization for Spacecraft Proximity Operations The contributing authors are expert researchers and practitioners in either the space engineering and/or in the applied optimization fields. Researchers and practitioners working in various applied aspects of space engineering will find this book practical and informative. Academics, graduate and post-graduate students in aerospace engineering, applied mathematics, operations research, optimization, and optimal control, will find this book useful.

This book presents the latest insights and developments in the field of socio-cultural inspired algorithms. Akin to evolutionary and swarm-based optimization algorithms, socio-cultural algorithms belong to the category of metaheuristics (problem-independent computational methods) and are inspired by natural and social tendencies observed in humans by which they learn from one another through social interactions. This book is an interesting read for engineers, scientists, and students studying/working in the optimization, evolutionary computation, artificial intelligence (AI) and computational intelligence fields.

This proceedings volume convenes selected, peer-reviewed papers presented at the 3rd International Conference on Mathematics and its Applications in Science and Engineering - ICMASE 2022, which was held on July 4-7, 2022 by the Technical University of Civil Engineering of Bucharest, Romania. Works in this volume cover new developments in applications of mathematics in science and engineering, with emphasis on mathematical and computational modeling of real-world problems. Topics range from the use of differential equations to model mechanical structures to the employ of number theory in the development of information security and cryptography. Educational issues specific to the acquisition of mathematical competencies by engineering and science students at all university levels are also touched on. Researchers and university students are the natural audiences for this book, which can be equally appealing to practitioners seeking up-to-date techniques in mathematical applications to different contexts and disciplines.

The satellite range scheduling (SRS) problem, an important operations research problem in the aerospace industry consisting of allocating tasks among satellites and Earth-bound objects, is examined in this book. SRS principles and solutions are applicable to many areas, including: Satellite communications, where tasks are communication intervals between sets of satellites and ground stations Earth observation, where tasks are observations of spots on the Earth by satellites Sensor scheduling, where tasks are observations of satellites by sensors on the Earth. This self-contained monograph begins with a structured compendium of the problem and moves on to explain the optimal approach to the solution, which includes aspects from graph theory, set theory, game theory and belief networks. This book is accessible to students, professionals and researchers in a variety of fields, including: operations research, optimization, scheduling theory, dynamic programming and game theory. Taking account of the distributed, stochastic and dynamic variants of the problem, this book presents the optimal solution to the fixed interval SRS problem and how to migrate results into more complex cases. Reference algorithms and traditional algorithms for solving the scheduling problems are provided and compared with examples and simulations in practical scenarios.

The solitaire game "The Tower of Hanoi" was invented in the 19th century by the French number theorist Edouard Lucas. The book presents its mathematical theory and offers a survey of the historical development from predecessors up to recent research. In addition to long-standing myths, it provides a detailed overview of the essential mathematical facts with complete proofs, and also includes unpublished material, e.g., on some captivating integer sequences. The main objects of research today are the so-called Hanoi graphs and the related Sierpinski graphs. Acknowledging the great popularity of the topic in computer science, algorithms, together with their correctness proofs, form an essential part of the book. In view of the most important practical applications, namely in physics, network theory and cognitive (neuro)psychology, the book also addresses other structures related to the Tower of Hanoi and its variants. The updated second edition includes, for the first time in English, the breakthrough reached with the solution of the "The Reve's Puzzle" in 2014. This is a special case of the famed Frame-Stewart conjecture which is still open after more than 75 years. Enriched with elaborate illustrations, connections to other puzzles and challenges for the reader in the form of (solved) exercises as well as problems for further exploration, this book is enjoyable reading for students, educators, game enthusiasts and researchers alike. Excerpts from reviews of the first edition: "The book is an unusual, but very welcome, form of mathematical writing: recreational mathematics taken seriously and serious mathematics treated historically. I don't hesitate to recommend this book to students, professional research mathematicians, teachers, and to readers of popular mathematics who enjoy more technical expository detail." Chris Sangwin, The Mathematical Intelligencer 37(4) (2015) 87f. "The book demonstrates that the Tower of Hanoi has a very rich mathematical structure, and as soon as we tweak the parameters we surprisingly quickly find ourselves in the realm of open problems." Laszlo Kozma, ACM SIGACT News 45(3) (2014) 34ff. "Each time I open the book I discover a renewed interest in the Tower of Hanoi. I am sure that this will be the case for all readers." Jean-Paul Allouche, Newsletter of the European Mathematical Society 93 (2014) 56.

Most textbooks on modern heuristics provide the reader with detailed descriptions of the functionality of single examples like genetic algorithms, genetic programming, tabu search, simulated annealing, and others, but fail to teach the underlying concepts behind these different approaches.

The author takes a different approach in this textbook by focusing on the users' needs and answering three fundamental questions: First, he tells us which problems modern heuristics are expected to perform well on, and which should be left to traditional optimization methods. Second, he teaches us to systematically design the "right" modern heuristic for a particular problem by providing a coherent view on design elements and working principles. Third, he shows how we can make use of problem-specific knowledge for the design of efficient and effective modern heuristics that solve not only small toy problems but also perform well on large real-world problems.

This book is written in an easy-to-read style and it is aimed at students and practitioners in computer science, operations research and information systems who want to understand modern heuristics and are interested in a guide to their systematic design and use.

This book is written in an easy-to-read style and it is aimed at students and practitioners in computer science, operations research and information systems who want to understand modern heuristics and are interested in a guide to their systematic design and use.

This book is written in an easy-to-read style and it is aimed at students and practitioners in computer science, operations research and information systems who want to understand modern heuristics and are interested in a guide to their systematic design and use.

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

In 2014, winner of "Outstanding Book Award" by The Japan Society for Fuzzy Theory and Intelligent Informatics. Covering in detail both theoretical and practical perspectives, this book is a self-contained and systematic depiction of current fuzzy stochastic optimization that deploys the fuzzy random variable as a core mathematical tool to model the integrated fuzzy random uncertainty. It proceeds in an orderly fashion from the requisite theoretical aspects of the fuzzy random variable to fuzzy stochastic optimization models and their real-life case studies. The volume reflects the fact that randomness and fuzziness (or vagueness) are two major sources of uncertainty in the real world, with significant implications in a number of settings. In industrial engineering, management and economics, the chances are high that decision makers will be confronted with information that is simultaneously probabilistically uncertain and fuzzily imprecise, and optimization in the form of a decision must be made in an environment that is doubly uncertain, characterized by a co-occurrence of randomness and fuzziness. This book begins by outlining the history and development of the fuzzy random variable before detailing numerous optimization models and applications that include the design of system controls for a dam.

In the modern world the theory of probability is used extensively in mathematics, science, engineering, medicine and, of course, gambling. A proposition bet is one that involves the use of probability -both estimated and actual -where an individual makes an apparently attractive bet to someone who is easily deceived by the odds, which are at first glance in his favor. The Book of Proposition Bets gathers together, and reveals the true mathematics behind, over 50 classic and original proposition bets. From the famous Three Card Monty (really an exercise in the Monty Hall Paradox), to probabilities based on rolling dice and pulling playing cards, or whether or not a mark can guess 3 correct digits of a one dollar bill's serial number (spoiler: the odds are against it), author Owen O'Shea here compiles a fascinating and engaging survey of prop bets. In addition, Part 2 of the book contains a brief history of the theory of probability and some examples of cons and scams perpetrated on the general public to this day around the world, (plus a few more mathematical proposition bets!). Whether to learn the intricacies used by hustlers, or borrow a couple of tricks for yourself, we wager that there is a high probability that readers will enjoy this entertaining and illuminating book!

This book is dedicated to applied gamification in the areas of education and business, while also covering pitfalls to avoid and guidelines needed to successfully implement for a project. Using different theoretical backgrounds from various areas including behavioral economics, game theory, and complex adaptive systems, the contributors aim to help readers avoid common problems and difficulties that they could face with poor implementation. The book's contributors are scholars and academics from the many areas where the key theory of gamification typically comes from. Ultimately, the book's goal is to help bring together the theories from these different disciplines to the field of practice in education and business. The book is divided into four parts: Theory, Education, Business, and Use Cases. Part I provides a foundation on the theory of gamification and offers insight into some of the outstanding questions that have yet to be addressed. In Part II, the application and value that gamification can bring within the education sector is examined. The book then changes focus in Part III to spotlight the use of gamification within business environments. The topics also cover educational aspects like improved learning outcomes, motivation, and learning retention at the workplace. Finally Part IV concentrates on the applications and use of gamification through a series of case studies and key elements that are used in real situations to drive real results.

This textbook offers graduate students a concise introduction to the classic notions of convex optimization. Written in a highly accessible style and including numerous examples and illustrations, it presents everything readers need to know about convexity and convex optimization. The book introduces a systematic three-step method for doing everything, which can be summarized as "conify, work, deconify". It starts with the concept of convex sets, their primal description, constructions, topological properties and dual description, and then moves on to convex functions and the fundamental principles of convex optimization and their use in the complete analysis of convex optimization problems by means of a systematic four-step method. Lastly, it includes chapters on alternative formulations of optimality conditions and on illustrations of their use. "The author deals with the delicate subjects in a precise yet light-minded spirit... For experts in the field, this book not only offers a unifying view, but also opens a door to new discoveries in convexity and optimization...perfectly suited for classroom teaching." Shuzhong Zhang, Professor of Industrial and Systems Engineering, University of Minnesota

In today's confrontational and connected world, communication is the key strategic act. This book uses drama theory-a radical extension of game theory-to show how best to communicate so as to manage the emotionally charged confrontations occurring in any worthwhile relationship. Alongside a toolset that provides a systematic framework for analysing conflicts, drama theory explains why people need to listen to, and rely on, their feelings to help shake themselves out of fixed, unproductive positions and to find new ways of solving tough problems. This guide provides a sufficient grounding in the approach to enable you to apply it immediately for your own benefit and for the benefit of those with whom you work. A host of inspirational examples are included based upon actual situations in social and personal relations, business and organisational relations, defence and political management. These will give you an entirely fresh way of seeing how power is exercised in everyday interpersonal exchanges and a greater critical awareness of such factors as subtext and plotholes in public narratives. Using this approach you will be able to overcome the dilemmas of credibility and disbelief to build compelling messages that underpin your strategic intent. Moving beyond the vague platitudes of concepts like emotional intelligence, drama theory will also help you to avoid the pathologies that bedevil the process of managing conflicts and find ways of achieving authentic resolutions.

This booksurveys state-of-the-art optimization modeling for design, analysis, and management of wireless networks, such as cellular and wireless local area networks (LANs), and the services they deliver. The past two decades have seen a tremendous growth in the deployment and use of wireless networks. The current-generation wireless systems can provide mobile users with high-speed data services at rates substantially higher than those of the previous generation. As a result, the demand for mobile information services with high reliability, fast response times, and ubiquitous connectivity continues to increase rapidly. The optimization of system performance has become critically important both in terms of practical utility and commercial viability, and presents a rich area for research.

In the editors' previous work on traditional wired networks, we have observed that designing low cost, survivable telecommunication networks involves extremely complicated processes. Commercial products available to help with this task typically have been based on simulation and/or proprietary heuristics. As demonstrated in this book, however, mathematical programming deserves a prominent place in the designer's toolkit. Convenient modeling languages and powerful optimization solvers have greatly facilitated the implementation of mathematical programming theory into the practice of commercial network design.

These points are equally relevant and applicable in today's world of wireless network technology and design. But there are new issues as well: many wireless network design decisions, such as routing and facility/element location, must be dealt with in innovative ways that are unique and distinct from wired (fiber optic) networks. The book specifically treats the recent research and the use of modeling languages and network optimization techniques that are playing particularly important and distinctive roles in the wireless domain. "

Complex Social Networks is a newly emerging (hot) topic with applications in a variety of domains, such as communication networks, engineering networks, social networks, and biological networks. In the last decade, there has been an explosive growth of research on complex real-world networks, a theme that is becoming pervasive in many disciplines, ranging from mathematics and computer science to the social and biological sciences. Optimization of complex communication networks requires a deep understanding of the interplay between the dynamics of the physical network and the information dynamics within the network. Although there are a few books addressing social networks or complex networks, none of them has specially focused on the optimization perspective of studying these networks. This book provides the basic theory of complex networks with several new mathematical approaches and optimization techniques to design and analyze dynamic complex networks. A wide range of applications and optimization problems derived from research areas such as cellular and molecular chemistry, operations research, brain physiology, epidemiology, and ecology.

Throughout the evolutionary history of this planet, biological systems have been able to adapt, survive and ?ourish despite the turmoils and upheavals of the environment. This ability has long fascinated and inspired people to emulate and adapt natural processes for application in the arti?cial world of human endeavours. The realm of optimisation problems is no exception. In fact, in recent years biological systems have been the inspiration of the majority of meta-heuristic search algorithms including, but not limited to, genetic algorithms, particle swarmoptimisation, ant colony optimisation and extremal optimisation. This book presentsa continuum ofbiologicallyinspired optimisation, from the theoretical to the practical. We begin with an overview of the ?eld of biologically-inspired optimisation, progress to presentation of theoretical analysesandrecentextensionstoavarietyofmeta-heuristicsand?nallyshow application to a number of real-worldproblems. As such, it is anticipated the book will provide a useful resource for reseachers and practitioners involved in any aspect of optimisation problems. The overviewof the ?eld is provided by two works co-authored by seminal thinkers in the ?eld. Deb's "Evolution's Niche in Multi-Criterion Problem Solving," presents a very comprehensive and complete overview of almost all major issues in Evolutionary Multi-objective Optimisation (EMO). This chapter starts with the original motivation for developing EMO algorithms and provides an account of some successful problem domains on which EMO has demonstrated a clear edge over their classical counterparts.

This is the first of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses basic principles of computation, and fundamental numerical algorithms that will serve as basic tools for the subsequent two volumes. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 80 examples, 324 exercises, 77 algorithms, 35 interactive JavaScript programs, 391 references to software programs and 4 case studies. Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in LAPACK, GSLIB and MATLAB. This book could be used for an introductory course in numerical methods, for either upper level undergraduates or first year graduate students. Parts of the text could be used for specialized courses, such as principles of computer languages or numerical linear algebra.