Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches

Changing Choices

Changing choices psychological relativity theory unifying theory transformation parameters psychology psygologie koornstra choice dynamics The book contains a unifying theory on how the common object space is metrically transformed by individuals with different transformation parameters, due to their other previous experiences, to individually different psychological spaces for judgment on the one hand and preference on the other hand. Individual experiences also change generally, whereby the psychological spaces also change generally for each individual. The theory, therefore, is a psychological relativity theory of perception, judgment, preference, and choice dynamics. This book is a must read for all behavioural, economic, and social scientists with theoretical interest and some understanding of multidimensional data analyses. It integrates more than twenty theories on perception, judgment, preference, and risk decisions into one mathematical theory. Knowledge of advanced mathematics and modern geometry is not needed, because the mathematical subsections can be skipped without loss of understanding, due to their explanation and illustration by figures in the text

Decision-making and the role of feedback in complex tasks

This thesis investigates the process of decision-making in relation to complex tasks and considers the important role which dynamic information and real-time feedback play in shaping response behaviour and adaptation within such environments. Through empirical studies, the thesis explores the extent to which decision-makers can be said to act rationally when challenged by complex decision-making environments. Evidence relating to demand for information and the impact of feedback on behaviour is provided with two studies: The first uses a simulated auction platform to examine behaviour within overlapping auctions of short duration with close-to-identical items and minimal participation costs. Mouse tracking is used to capture data on relevant interactions of participants with the simulated online platform, including switching behaviour independent of bidding. The resulting data suggests that participants did behave in a manner consistent with utility maximisation, seeking to acquire the item at the lowest possible price and showing no bias in terms of auction preference. The impact of fixed-price offers in the form of a “Buy it Now” option is also examined with some evidence that participants again seek, and respond to, current information when deciding on their bidding strategy. The second study is a test of the impact of real-time feedback and demand for information within the context of financial markets. The study again uses a novel simulated environment which provides access to considerable amounts of relevant data which participants can choose to access. In addition, participants are exposed to regular feedback with regard to their own performance. Overall, demand for information is found to be dependent upon the type of feedback received and its context. Decision-makers then appear to behave objectively, apparently seeking the latest available information to support current decisions, although investor style is found to be important in determining overall trading propensity. The thesis starts by considering a number of the foundations and pathways which run through the judgment and decision-making literature. It is not a complete description, review or analysis of all of the prevailing lines of enquiry. Nevertheless, it seeks to achieve coherence in terms of bringing together some of the key themes dealing with risky choice under conditions of uncertainty and ambiguity. The field of judgment and decision-making is inevitably vast; its scope owing much to the fact that it transcends individual disciplines. The emergent behavioural sciences thus draw together important strands from various sources, notably Economics and Finance. In many areas, psychological traits can be applied to explain inconsistencies which are found in classical theory of rational behaviour. The recognition of behavioural traits has thus contributed greatly to the evolution of decisionmaking theories under conditions of uncertainty and ambiguity which are, in many cases, substantially more adaptable and robust than early normative theories of rational behaviour. The classical approach to rational decision making within Economics, together with some theoretical and empirical challenges to it, are considered in Chapter 1. It is here that we are introduced to the Rational Man. Like the mythical creatures found in Classical Antiquity, the Rational Man does not actually exist in the real world; he is nevertheless central to the concept of utility maximising rational choice which provided much of the foundation of Economics. Developments of expected utility theory (EUT) are considered, including its replacement of expected value, and the formalisation of rational behaviour within the context of axioms. When those logical axioms apply, decision-makers can be said to behave 'as if' they are utility maximises. The chapter ends with some empirical evidence, showing the types of approaches often used to explore rational decision-making. Some violations of EUT are explored, both in relation to notional gambles and consistency with regard to revealed preferences. Chapter 2 extends the narrative by considering rational decision-making in cases where there is no objective information about possible outcomes. Subjective utility theory (SEU) is then introduced, describing objective functions based upon preferences derived from combined utility and probability functions. The implications of the Allais’ and Ellsberg paradoxes are discussed, along with some possible solutions. It is here that we explore the concepts of uncertainty and ambiguity in more details and consider some theoretical formulations for addressing them. Chapter 3 covers the significant contribution to decision-making under conditions of uncertainty provided by Prospect Theory and, later, Cumulative Prospect Theory (CPT). Their evolution from the pioneering work of Markowitz is discussed within the context of reference points relative to which outcomes can be evaluated. The significance of stochastic dominance and rank dependence are explored. By this stage, we have examined numerous theories which have fundamentally transformed standard EUT into much more flexible and adaptable frameworks of rational choice. The core concepts of utility maximisation remain yet the initial, strictly concave utility function describing diminishing marginal utility is now substantially replaced by more complex weighted preference functions. From this theoretical base, the process of choice reduction and the application of heuristics in decision-making are considered. We again describe axiomatic behaviour compatible with rational choice. Therefore, decision-makers faced with multiple choices about which there may be little or no objective information about likely outcomes can nevertheless develop rational beliefs and expectations which can then be applied to reduce complex tasks to more manageable proportions. As well as considering these aspects from the point of view of actual choices, we also consider the processes by which decisions are taken. Thus, process tracing methods are introduced into the discussion. The chapter also explicitly considers the role of feedback in decision making. This includes a consideration of Bayesian inference as a process for updating probabilistic expectations subject to new information. From considering theoretical formulations form which we can judge rational behaviour, Chapter 5 looks at evidence for sub-optimal decision-making and bias. Bias with regard to probability assessments are considered along with empirical evidence of bias in relation to intertemporal discounting. Sunk cost bias is also considered as a clear example of irrational behaviour, leading in to a specific discussion about a number of persistent behavioural biases identified within financial markets. As an introduction to later chapters, this also covers the basic theoretical principles of market efficiency and evidence that real markets fail to adhere to those principles in important ways. Chapters 6 and 8 describe the empirical studies with Chapter 7 providing a more detailed introduction to the financial markets experiment, considering aspects of market efficiency, models of behaviour and other empirical evidence

Collected Papers (on Physics, Artificial Intelligence, Health Issues, Decision Making, Economics, Statistics), Volume XI

This eleventh volume of Collected Papers includes 90 papers comprising 988 pages on Physics, Artificial Intelligence, Health Issues, Decision Making, Economics, Statistics, written between 2001-2022 by the author alone or in collaboration with the following 84 co-authors (alphabetically ordered) from 19 countries: Abhijit Saha, Abu Sufian, Jack Allen, Shahbaz Ali, Ali Safaa Sadiq, Aliya Fahmi, Atiqa Fakhar, Atiqa Firdous, Sukanto Bhattacharya, Robert N. Boyd, Victor Chang, Victor Christianto, V. Christy, Dao The Son, Debjit Dutta, Azeddine Elhassouny, Fazal Ghani, Fazli Amin, Anirudha Ghosha, Nasruddin Hassan, Hoang Viet Long, Jhulaneswar Baidya, Jin Kim, Jun Ye, Darjan Karabašević, Vasilios N. Katsikis, Ieva Meidutė-Kavaliauskienė, F. Kaymarm, Nour Eldeen M. Khalifa, Madad Khan, Qaisar Khan, M. Khoshnevisan, Kifayat Ullah,, Volodymyr Krasnoholovets, Mukesh Kumar, Le Hoang Son, Luong Thi Hong Lan, Tahir Mahmood, Mahmoud Ismail, Mohamed Abdel-Basset, Siti Nurul Fitriah Mohamad, Mohamed Loey, Mai Mohamed, K. Mohana, Kalyan Mondal, Muhammad Gulfam, Muhammad Khalid Mahmood, Muhammad Jamil, Muhammad Yaqub Khan, Muhammad Riaz, Nguyen Dinh Hoa, Cu Nguyen Giap, Nguyen Tho Thong, Peide Liu, Pham Huy Thong, Gabrijela Popović‬‬‬‬‬‬‬‬‬‬, Surapati Pramanik, Dmitri Rabounski, Roslan Hasni, Rumi Roy, Tapan Kumar Roy, Said Broumi, Saleem Abdullah, Muzafer Saračević, Ganeshsree Selvachandran, Shariful Alam, Shyamal Dalapati, Housila P. Singh, R. Singh, Rajesh Singh, Predrag S. Stanimirović, Kasan Susilo, Dragiša Stanujkić, Alexandra Şandru, Ovidiu Ilie Şandru, Zenonas Turskis, Yunita Umniyati, Alptekin Ulutaș, Maikel Yelandi Leyva Vázquez, Binyamin Yusoff, Edmundas Kazimieras Zavadskas, Zhao Loon Wang.‬‬‬

Innovations in Quantitative Risk Management

Quantitative Finance; Game Theory, Economics, Social and Behav. Sciences; Finance/Investment/Banking; Actuarial Science

Dynamic Programming: Finite States

This book is about dynamic programming and its applications in economics, finance, and adjacent fields. It brings together recent innovations in the theory of dynamic programming and provides applications and code that can help readers approach the research frontier. The book is aimed at graduate students and researchers, although most chapters are accessible to undergraduate students with solid quantitative backgrounds