Tofigh Allahviranloo

Quantum Theory, Decision Making and Social Dynamics is an innovative exploration of the intersection of quantum theory, decision-making, and social networks. As quantum theory continues to permeate various fields, there is a growing need for accessible resources that elucidate its principles and applications. This book aims to fill that gap by illuminating the complex interplay between quantum theory and social dynamics, particularly in the context of decision-making. It addresses the challenges of understanding and applying quantum theory in social dynamics and equips readers with the knowledge to harness its potential in decision-making processes. The book is organized into nine chapters, each delving into a specific aspect of quantum theory and its applications. Chapter 1 provides an overview of quantum theory, tracing its historical development and key principles. Chapter 2 explores the integration of quantum theory with fuzzy systems, highlighting real-world applications and emerging trends. In Chapter 3, the focus shifts to the application of quantum theory in social networks, including quantum social network models and case studies. Chapter 4 examines decision-making processes within social networks, while Chapter 5 introduces and analyzes quantum decision-making models. Chapter 6 delves into quantum graph theory, discussing quantum graphs, walks, and algorithms. The subsequent chapters address the challenges and limitations of quantum decision-making (Chapter 7), future directions for the field (Chapter 8), and conclude with a summary of key points and final thoughts (Chapter 9). Quantum Theory, Decision Making and Social Dynamics is an invaluable resource for graduate students, researchers, and professionals in the fields of applied mathematics, computer science, physics, and social sciences interested in applying quantum approaches to the study of decision-making. These readers often face challenges in understanding complex quantum concepts, applying quantum theory to social networks, and utilizing quantum decision-making models. This book provides a solid foundation in quantum theory, introduces its applications in diverse areas, and prepares readers to navigate the quantum age with confidence. By offering a comprehensive overview and practical insights, this book empowers its audience to appreciate the profound impact of quantum theory on social network dynamics and decision-making.

This comprehensive book is designed for undergraduate, master's, and doctoral students in mathematics, as well as scholars interested in a deep understanding of fractional problems. The book covers a wide range of topics, including the existence and uniqueness of solutions, stability, optimal controllers, special functions, classical and fuzzy normed spaces, matrix functions, fuzzy matrix normed spaces, fixed-point theory, quality and certainty, and various numerical methods. The primary objective of this book is to analyze the existence and uniqueness of solutions for functional equations, analyze stability, and achieve the best possible results with minimal error. With a clear and direct approach, it presents advanced concepts in an accessible and comprehensible manner, enabling students to apply their knowledge to solving various problems. To prevent instability in fractional systems, methods based on fixed-point theory with the best approximation have been utilized. The stability analysis of fractional equations is conducted by considering classical and fuzzy normed spaces and employing special functions as optimal controllers. In fuzzy systems, the Z-number theory has been used to enhance results and improve quality. This theory enables the assessment of approximation accuracy and quality, providing the best possible approximation. The numerical analysis of fractional systems plays a crucial role in accurately modeling physical phenomena, simulations, and predicting complex systems. By presenting numerical results from fractional systems, which are essential in solving real-world problems and optimizing computational algorithms, this book serves as a valuable resource for both researchers and students.

The main target of this book is to present a new concept of Ulam-type stability, i.e., multi-stability, through the classical, well-known special functions and to obtain the best approximation error estimates by a different concept of perturbation stability including fuzzy approaches for uncertainty considerations. This stability allows us to obtain diverse approximations depending on various special functions that are initially chosen and to evaluate maximal stability and minimal error which enable us to obtain a unique optimal solution of functional equations, inequalities, and fractional equations. Stability analysis in the sense of the Ulam and its different kinds has received considerable attention from the researchers. However, how to effectively generalize the Ulam stability problems and to evaluate optimized controllability and stability are new issues. The multi-stability not only covers the previous concepts but also considers the optimization of the problem and provides a comprehensive discussion of optimizing the different types of the Ulam stabilities of mathematical models used in the natural sciences and engineering disciplines with fuzzy attitudes. Besides, this book also deals with nonlinear differential equations with various boundary conditions or initial value problems, based on the matrix Mittag-Leffler function, fixed point theory, as well as Babenko's approach to study uniqueness and existence of solutions. In general, the benefits for the readers can be concluded as follows: 1. Evaluates maximal stability with minimal error to get a unique optimal solution. 2. Discusses an optimal method of the alternative to study existence, uniqueness, and different types of Ulam stabilities under special consideration of the fuzzy approaches. 3. Delves into the new study of boundary value problems of fractional integro-differential equations with integral boundary conditions and variable coefficients.

Authored by a leading expert in the field, this book introduces an innovative methodology that harnesses the power of fuzzy logic to enhance decision-making in multi-attribute scenarios. In a world of complexity and uncertainty, effective decision-making is paramount. Springer proudly presents a cutting-edge publication that revolutionizes decision analysis: "Fuzzy Decision Analysis: Multi-attribute Decision-Making Approach." This book stands at the forefront of decision analysis, introducing the integration of fuzzy logic into multi-attribute decision-making. It is a transformative journey into the realm of advanced decision analysis. It book not only equips you with the knowledge to comprehend the theoretical underpinnings but also empowers you to apply these insights in practical scenarios. This book serves as your indispensable companion. Its comprehensive coverage serves as a beacon, guiding you through the intricate maze of fuzzy logic and multi-attribute decision-making, ultimately empowering you to embrace innovation and master the art of making well-informed decisions in an ever-changing world.

The combination of DEA and ratio analysis is introduced as a suitable field for evaluating the performance of DMUs. In this regard, DEA-R is also proposed as a hybrid technique for calculating efficiency, ranking DMUs, and finding efficient faces. Therefore, the relationship between DEA and DEA-R provides a suitable field for researchers in the field of evaluating the performance of DMUs. The audience of this book is not limited to researchers in mathematics fields, but experts and students in industrial engineering and management fields also benefit from the topics of this book.

Numerical analysis forms a cornerstone of numeric computing and optimization, in particular recently, interval numerical computations play an important role in these topics. The interest of researchers in computations involving uncertain data, namely interval data opens new avenues in coping with real-world problems and deliver innovative and efficient solutions. This book provides the basic theoretical foundations of numerical methods, discusses key technique classes, explains improvements and improvements, and provides insights into recent developments and challenges.The theoretical parts of numerical methods, including the concept of interval approximation theory, are introduced and explained in detail. In general, the key features of the book include an up-to-date and focused treatise on error analysis in calculations, in particular the comprehensive and systematic treatment of error propagation mechanisms, considerations on the quality of data involved in numerical calculations, and a thorough discussion of interval approximation theory.Moreover, this book focuses on approximation theory and its development from the perspective of linear algebra, and new and regular representations of numerical integration and their solutions are enhanced by error analysis as well. The book is unique in the sense that its content and organization will cater to several audiences, in particular graduate students, researchers, and practitioners.

This book presents the theory and application of the models presented in this regard and establishes a meaningful relationship between data envelopment analysis and multi-attribute decision making. The issue of "choice" using the aggregation of voters' votes is one of the most important group decision-making issues that are always considered by decision makers in electoral systems. Voting is a method of group decision making in a democratic society that expresses the will of the majority. Voting is perhaps the simplest way to gather the opinions of experts, and this ease of application has made it a multi-attribute decision-making method in group decisions. Preferential voting is a type of voting that may refer to electoral systems or groups of the electoral system. In preferential voting, voters vote for multiple candidates, and how the candidates are arranged on the ballot is important. Researchers have made many efforts to provide models of voter aggregation, and one of the bestresults of these efforts is the aggregation of votes based on the policy of data envelopment analysis. Thus, in group decisions, the opinions of experts are obtained in a simple structure and consolidated in an interactive and logical structure, and the results can be a powerful tool for decision support.This book provides a complete set of voting models based on data envelopment analysis and expressing its various applications in industry and society. However, most decision-making methods do not use the opinions of experts or reduce the motivation of experts to participate in complex interactions and time, while voting methods do not have this shortcoming.This book is suitable for graduate students in the fields of industrial management, business management, industrial engineering, applied mathematics, and economics. It can also be a good source for researchers in decision science, decision support systems, data envelopment analysis, supply chain management, healthcare management, and others. The methods presented in this book can not only offer a comprehensive framework for solving the problems of these areas but also can inspire researchers to pursue new innovative hybrid methods.

The authors of this book tried to make these experiences available to those interested, considering the experience of several years of training, research, and implementation of projects in the supply chain performance evaluation field.This book intends to identify the current performance and competitive position of that supply chain compared to other supply chains by presenting and reviewing the techniques and models for measuring the efficiency and performance of the supply chain. Determining the performance of a supply chain is a good description of the status quo (what is). Determining the performance of a supply chain is useful for describing the past and present of supply chain processes, and on the other hand, it can be used to set performance goals and initiate the improvement process. To realize this, a strategic framework or model is needed to be able to extract indicators related to the efficiency of the supply chain and design the appropriate model.

The main target of this book is to present a new concept of Ulam-type stability, i.e., multi-stability, through the classical, well-known special functions and to obtain the best approximation error estimates by a different concept of perturbation stability including fuzzy approaches for uncertainty considerations. This stability allows us to obtain diverse approximations depending on various special functions that are initially chosen and to evaluate maximal stability and minimal error which enable us to obtain a unique optimal solution of functional equations, inequalities, and fractional equations. Stability analysis in the sense of the Ulam and its different kinds has received considerable attention from the researchers. However, how to effectively generalize the Ulam stability problems and to evaluate optimized controllability and stability are new issues. The multi-stability not only covers the previous concepts but also considers the optimization of the problem and provides a comprehensive discussion of optimizing the different types of the Ulam stabilities of mathematical models used in the natural sciences and engineering disciplines with fuzzy attitudes. Besides, this book also deals with nonlinear differential equations with various boundary conditions or initial value problems, based on the matrix Mittag-Leffler function, fixed point theory, as well as Babenko's approach to study uniqueness and existence of solutions. In general, the benefits for the readers can be concluded as follows: 1. Evaluates maximal stability with minimal error to get a unique optimal solution. 2. Discusses an optimal method of the alternative to study existence, uniqueness, and different types of Ulam stabilities under special consideration of the fuzzy approaches. 3. Delves into the new study of boundary value problems of fractional integro-differential equations with integral boundary conditions and variable coefficients.

Authored by a leading expert in the field, this book introduces an innovative methodology that harnesses the power of fuzzy logic to enhance decision-making in multi-attribute scenarios. In a world of complexity and uncertainty, effective decision-making is paramount. Springer proudly presents a cutting-edge publication that revolutionizes decision analysis: "Fuzzy Decision Analysis: Multi-attribute Decision-Making Approach." This book stands at the forefront of decision analysis, introducing the integration of fuzzy logic into multi-attribute decision-making. It is a transformative journey into the realm of advanced decision analysis. It book not only equips you with the knowledge to comprehend the theoretical underpinnings but also empowers you to apply these insights in practical scenarios. This book serves as your indispensable companion. Its comprehensive coverage serves as a beacon, guiding you through the intricate maze of fuzzy logic and multi-attribute decision-making, ultimately empowering you to embrace innovation and master the art of making well-informed decisions in an ever-changing world.

The combination of DEA and ratio analysis is introduced as a suitable field for evaluating the performance of DMUs. In this regard, DEA-R is also proposed as a hybrid technique for calculating efficiency, ranking DMUs, and finding efficient faces. Therefore, the relationship between DEA and DEA-R provides a suitable field for researchers in the field of evaluating the performance of DMUs. The audience of this book is not limited to researchers in mathematics fields, but experts and students in industrial engineering and management fields also benefit from the topics of this book.

This book presents the theory and application of the models presented in this regard and establishes a meaningful relationship between data envelopment analysis and multi-attribute decision making. The issue of "choice" using the aggregation of voters' votes is one of the most important group decision-making issues that are always considered by decision makers in electoral systems. Voting is a method of group decision making in a democratic society that expresses the will of the majority. Voting is perhaps the simplest way to gather the opinions of experts, and this ease of application has made it a multi-attribute decision-making method in group decisions. Preferential voting is a type of voting that may refer to electoral systems or groups of the electoral system. In preferential voting, voters vote for multiple candidates, and how the candidates are arranged on the ballot is important. Researchers have made many efforts to provide models of voter aggregation, and one of the bestresults of these efforts is the aggregation of votes based on the policy of data envelopment analysis. Thus, in group decisions, the opinions of experts are obtained in a simple structure and consolidated in an interactive and logical structure, and the results can be a powerful tool for decision support.This book provides a complete set of voting models based on data envelopment analysis and expressing its various applications in industry and society. However, most decision-making methods do not use the opinions of experts or reduce the motivation of experts to participate in complex interactions and time, while voting methods do not have this shortcoming.This book is suitable for graduate students in the fields of industrial management, business management, industrial engineering, applied mathematics, and economics. It can also be a good source for researchers in decision science, decision support systems, data envelopment analysis, supply chain management, healthcare management, and others. The methods presented in this book can not only offer a comprehensive framework for solving the problems of these areas but also can inspire researchers to pursue new innovative hybrid methods.

The authors of this book tried to make these experiences available to those interested, considering the experience of several years of training, research, and implementation of projects in the supply chain performance evaluation field.This book intends to identify the current performance and competitive position of that supply chain compared to other supply chains by presenting and reviewing the techniques and models for measuring the efficiency and performance of the supply chain. Determining the performance of a supply chain is a good description of the status quo (what is). Determining the performance of a supply chain is useful for describing the past and present of supply chain processes, and on the other hand, it can be used to set performance goals and initiate the improvement process. To realize this, a strategic framework or model is needed to be able to extract indicators related to the efficiency of the supply chain and design the appropriate model.

This book suggests that the numerical analysis subjects’ matter are the important tools of the book topic, because numerical errors and methods have important roles in solving integral equations. Therefore, all needed topics including a brief description of interpolation are explained in the book. The integral equations have many applications in the engineering, medical, and economic sciences, so the present book contains new and useful materials about interval computations including interval interpolations that are going to be used in interval integral equations. The concepts of integral equations are going to be discussed in two directions, analytical concepts, and numerical solutions which both are necessary for these kinds of dynamic systems. The differences between this book with the others are a full discussion of error topics and also using interval interpolations concepts to obtain interval integral equations. All researchers and students in the field of mathematical, computer, and also engineering sciences can benefit the subjects of the book.

This book delivers a concise and carefully structured introduction to probability and random variables. It aims to build a linkage between the theoretical conceptual topics and the practical applications, especially in the undergraduate engineering area. The book motivates the student to gain full understanding of the fundamentals of probability theory and help acquire working problem-solving skills and apply the theory to engineering applications. Each chapter includes solved examples at varying levels (both introductory and advanced) in addition to problems that demonstrate the relevance of the probability and random variables in engineering. As authors, we focused on to find out the optimum ways in order to introduce the topics in probability and random variables area.

Numerical analysis forms a cornerstone of numeric computing and optimization, in particular recently, interval numerical computations play an important role in these topics. The interest of researchers in computations involving uncertain data, namely interval data opens new avenues in coping with real-world problems and deliver innovative and efficient solutions. This book provides the basic theoretical foundations of numerical methods, discusses key technique classes, explains improvements and improvements, and provides insights into recent developments and challenges.The theoretical parts of numerical methods, including the concept of interval approximation theory, are introduced and explained in detail. In general, the key features of the book include an up-to-date and focused treatise on error analysis in calculations, in particular the comprehensive and systematic treatment of error propagation mechanisms, considerations on the quality of data involved in numerical calculations, and a thorough discussion of interval approximation theory.Moreover, this book focuses on approximation theory and its development from the perspective of linear algebra, and new and regular representations of numerical integration and their solutions are enhanced by error analysis as well. The book is unique in the sense that its content and organization will cater to several audiences, in particular graduate students, researchers, and practitioners.

This book suggests that the numerical analysis subjects’ matter are the important tools of the book topic, because numerical errors and methods have important roles in solving integral equations. Therefore, all needed topics including a brief description of interpolation are explained in the book. The integral equations have many applications in the engineering, medical, and economic sciences, so the present book contains new and useful materials about interval computations including interval interpolations that are going to be used in interval integral equations. The concepts of integral equations are going to be discussed in two directions, analytical concepts, and numerical solutions which both are necessary for these kinds of dynamic systems. The differences between this book with the others are a full discussion of error topics and also using interval interpolations concepts to obtain interval integral equations. All researchers and students in the field of mathematical, computer, and also engineering sciences can benefit the subjects of the book.

This book delivers a concise and carefully structured introduction to probability and random variables. It aims to build a linkage between the theoretical conceptual topics and the practical applications, especially in the undergraduate engineering area. The book motivates the student to gain full understanding of the fundamentals of probability theory and help acquire working problem-solving skills and apply the theory to engineering applications. Each chapter includes solved examples at varying levels (both introductory and advanced) in addition to problems that demonstrate the relevance of the probability and random variables in engineering. As authors, we focused on to find out the optimum ways in order to introduce the topics in probability and random variables area.

This book contains new and useful materials concerning fuzzy fractional differential and integral operators and their relationship. As the title of the book suggests, the fuzzy subject matter is one of the most important tools discussed. Therefore, it begins by providing a brief but important and new description of fuzzy sets and the computational calculus they require. Fuzzy fractals and fractional operators have a broad range of applications in the engineering, medical and economic sciences. Although these operators have been addressed briefly in previous papers, this book represents the first comprehensive collection of all relevant explanations. Most of the real problems in the biological and engineering sciences involve dynamic models, which are defined by fuzzy fractional operators in the form of fuzzy fractional initial value problems. Another important goal of this book is to solve these systems and analyze their solutions both theoretically and numerically. Given the content covered, the book will benefit all researchers and students in the mathematical and computer sciences, but also the engineering sciences.