Uncertain Computation Based Decision Theory

Uncertain computation is a system of computation and reasoning in which the objects of computation are not values of variables but restrictions on values of variables. This compendium includes uncertain computation examples based on interval arithmetic, probabilistic arithmetic, fuzzy arithmetic, Z-number arithmetic, and arithmetic with geometric primitives. The principal problem with the existing decision theories is that they do not have capabilities to deal with such environment. Up to now, no books where decision theories based on all generalizations level of information are considered. Thus, this self-containing volume intends to overcome this gap between real-world settings' decisions and their formal analysis. Contents: Decision EnvironmentAnalysis of the Existing Decision TheoriesInterval ComputationProbabilistic ArithmeticFuzzy Type-1 and Fuzzy Type-2 ComputationsComputation with Z-NumbersComputation with U-NumbersFuzzy Geometry Based ComputationsInterval Granular-Based Decision MakingDecision Making in Fuzzy EnvironmentThe Z-Restriction Centered Decision TheorySimulation and Applications Readership: Researchers, academics, professionals and graduate students in fuzzy logic, decision sciences and mathematical economics. Keywords: Uncertain Computation;Decision Making;Interval Arithmetic;Fuzzy Arithmetic;Z-Number;Combined State;Fuzzy EconomicsReview:0

Uncertain computation is a system of computation and reasoning in which the objects of computation are not values of variables but restrictions on values of variables. --

Uncertain computation is a system of computation and reasoning in which the objects of computation are not values of variables but restrictions on values of variables. --

An introduction to decision making under uncertainty from a computational perspective, covering both theory and applications ranging from speech recognition to airborne collision avoidance. Many important problems involve decision making under uncertainty—that is, choosing actions based on often imperfect observations, with unknown outcomes. Designers of automated decision support systems must take into account the various sources of uncertainty while balancing the multiple objectives of the system. This book provides an introduction to the challenges of decision making under uncertainty from a computational perspective. It presents both the theory behind decision making models and algorithms and a collection of example applications that range from speech recognition to aircraft collision avoidance. Focusing on two methods for designing decision agents, planning and reinforcement learning, the book covers probabilistic models, introducing Bayesian networks as a graphical model that captures probabilistic relationships between variables; utility theory as a framework for understanding optimal decision making under uncertainty; Markov decision processes as a method for modeling sequential problems; model uncertainty; state uncertainty; and cooperative decision making involving multiple interacting agents. A series of applications shows how the theoretical concepts can be applied to systems for attribute-based person search, speech applications, collision avoidance, and unmanned aircraft persistent surveillance. Decision Making Under Uncertainty unifies research from different communities using consistent notation, and is accessible to students and researchers across engineering disciplines who have some prior exposure to probability theory and calculus. It can be used as a text for advanced undergraduate and graduate students in fields including computer science, aerospace and electrical engineering, and management science. It will also be a valuable professional reference for researchers in a variety of disciplines.

This book describes the classical axiomatic theories of decision under uncertainty, as well as critiques thereof and alternative theories. It focuses on the meaning of probability, discussing some definitions and surveying their scope of applicability. The behavioral definition of subjective probability serves as a way to present the classical theories, culminating in Savage's theorem. The limitations of this result as a definition of probability lead to two directions - first, similar behavioral definitions of more general theories, such as non-additive probabilities and multiple priors, and second, cognitive derivations based on case-based techniques.

Everyone makes decisions, but not everyone is a decision analyst. A decision analyst uses quantitative models and computational methods to formulate decision algorithms, assess decision performance, identify and evaluate options, determine trade-offs and risks, evaluate strategies for investigation, and so on. Info-Gap Decision Theory is written for decision analysts. The term "decision analyst" covers an extremely broad range of practitioners. Virtually all engineers involved in design (of buildings, machines, processes, etc.) or analysis (of safety, reliability, feasibility, etc.) are decision analysts, usually without calling themselves by this name. In addition to engineers, decision analysts work in planning offices for public agencies, in project management consultancies, they are engaged in manufacturing process planning and control, in financial planning and economic analysis, in decision support for medical or technological diagnosis, and so on and on. Decision analysts provide quantitative support for the decision-making process in all areas where systematic decisions are made. This second edition entails changes of several sorts. First, info-gap theory has found application in several new areas - especially biological conservation, economic policy formulation, preparedness against terrorism, and medical decision-making. Pertinent new examples have been included. Second, the combination of info-gap analysis with probabilistic decision algorithms has found wide application. Consequently "hybrid" models of uncertainty, which were treated exclusively in a separate chapter in the previous edition, now appear throughout the book as well as in a separate chapter. Finally, info-gap explanations of robust-satisficing behavior, and especially the Ellsberg and Allais "paradoxes", are discussed in a new chapter together with a theorem indicating when robust-satisficing will have greater probability of success than direct optimizing with uncertain models. New theory developed systematically Many examples from diverse disciplines Realistic representation of severe uncertainty Multi-faceted approach to risk Quantitative model-based decision theory

Every day decision making and decision making in complex human-centric systems are characterized by imperfect decision-relevant information. Main drawback of the existing decision theories is namely incapability to deal with imperfect information and modeling vague preferences. Actually, a paradigm of non-numerical probabilities in decision making has a long history and arose also in Keynes’s analysis of uncertainty. There is a need for further generalization – a move to decision theories with perception-based imperfect information described in NL. The languages of new decision models for human-centric systems should be not languages based on binary logic but human-centric computational schemes able to operate on NL-described information. Development of new theories is now possible due to an increased computational power of information processing systems which allows for computations with imperfect information, particularly, imprecise and partially true information, which are much more complex than computations over numbers and probabilities. The monograph exposes the foundations of a new decision theory with imperfect decision-relevant information on environment and a decision maker’s behavior. This theory is based on the synthesis of the fuzzy sets theory with perception-based information and the probability theory. The book is self containing and represents in a systematic way the decision theory with imperfect information into the educational systems. The book will be helpful for teachers and students of universities and colleges, for managers and specialists from various fields of business and economics, production and social sphere.

The general scope of the book covers diverse areas of fuzzy systems, soft computing, AI tools such as uncertain computation, decision-making under imperfect information, deep learning, and others. The topics of the papers include theory and application of Soft Computing, Neuro-Fuzzy Technology, Intelligent Control, Deep Learning-Machine Learning, Fuzzy Logic in Data Analytics, Evolutionary Computing, Fuzzy logic and Artificial Intelligence in Engineering, Social Sciences, Business, Economics, Material Sciences, and others.This book presents the proceedings of the 16th International Conference on Applications of Fuzzy Systems, Soft Computing, and Artificial Intelligence Tools, ICAFS-2022, held in Budva, Montenegro, on August 26-27, 2022. This is a useful guide for academics, practitioners, and graduates in fields of fuzzy logic and soft computing. It allows for increasing of interest in development and applying of these paradigms in various real-life fields.