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Since the emergence of the formal concept of probability theory in the seventeenth century, uncertainty has been perceived solely in terms of probability theory. However, this apparently unique link between uncertainty and probability theory has come under investigation a few decades back. Uncertainties are nowadays accepted to be of various kinds. Uncertainty in general could refer to different sense like not certainly known, questionable, problematic, vague, not definite or determined, ambiguous, liable to change, not reliable. In Indian languages, particularly in Sanskrit-based languages, there are other higher levels of uncertainties. It has been shown that several mathematical concepts such as the theory of fuzzy sets, theory of rough sets, evidence theory, possibility theory, theory of complex systems and complex network, theory of fuzzy measures and uncertainty theory can also successfully model uncertainty.

This book is a collection of selected papers presented at the SIGEF conference, held at the Faculty of Economics and Business of the University of Girona (Spain), 06-08 July, 2015.This edition of the conference has been presented with the slogan “Scientific methods for the treatment of uncertainty in social sciences”. There are different ways for dealing with uncertainty in management. The book focuses on soft computing theories and their role in assessing uncertainty in a complex world.It gives a comprehensive overview of quantitative management topics and discusses some of the most recent developments in all the areas of business and management in soft computing including Decision Making, Expert Systems and Forgotten Effects Theory, Forecasting Models, Fuzzy Logic and Fuzzy Sets, Modelling and Simulation Techniques, Neural Networks and Genetic Algorithms and Optimization and Control. The book might be of great interest for anyone working in the area of management and business economics and might be especially useful for scientists and graduate students doing research in these fields.

This book contains revised and significantly extended versions of selected papers from three workshops on Uncertainty Reasoning for the Semantic Web (URSW), held at the International Semantic Web Conferences (ISWC) in 2011, 2012, and 2013. The 16 papers presented were carefully reviewed and selected from numerous submissions. The papers included in this volume are organized in topical sections on probabilistic and Dempster-Shafer models, fuzzy and possibilistic models, inductive reasoning and machine learning, and hybrid approaches.

This book constitutes the refereed proceedings of the International Symposium on Integrated Uncertainty in Knowledge Modeling and Decision Making, IUKM 2013, held in Beijing China, in July 2013. The 19 revised full papers were carefully reviewed and selected from 49 submissions and are presented together with keynote and invited talks. The papers provide a wealth of new ideas and report both theoretical and applied research on integrated uncertainty modeling and management.

This book contains revised and significantly extended versions of selected papers from three workshops on Uncertainty Reasoning for the Semantic Web (URSW), held at the International Semantic Web Conferences (ISWC) in 2008, 2009, and 2010 or presented at the first international Workshop on Uncertainty in Description Logics (UniDL), held at the Federated Logic Conference (FLoC) in 2010. The 17 papers presented were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on probabilistic and Dempster-Shafer models, fuzzy and possibilistic models, inductive reasoning and machine learning, and hybrid approaches.

This book constitutes the refereed proceedings of the 12th EuropeanConference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2013, held in Utrecht, The Netherlands, in July 2013. The 44 revised full papers presented were carefully reviewed andselected from 89 submissions. Papers come from researchers interested in advancing the technology and from practitioners using uncertainty techniques in real-world applications. The scope of the ECSQARU conferences encompasses fundamental issues, representation, inference, learning, and decision making in qualitative and numeric uncertainty paradigms.

As desired, the infonnation demand correspondence is single valued at equilibrium prices. Hence no planner is needed to assign infonnation allocations to individuals. Proposition 4. For any given infonnation price system p E. P (F •), almost every a E A demands a unique combined infonnation structure (although traders may be indifferent among partial infonnation sales from different information allocations, etc.). In particular, the aggregate excess demand correspondence for net combined infonnation trades is a continuous function. Proof Uniqueness fails only if an agent can obtain the same expected utility from two or more net combined infonnation allocations. If this happens, appropriate slight perturbations of personal probability vectors destroy the equality unless the utility functions and wealth allocations were independent across states. Yet, when utilities and wealths don't depend on states in S, no infonnation to distinguish the states is desired, so that the demand for such infonnation structures must equal zero. To show the second claim, recall that if the correspondence is single valued for almost every agent, then its integral is also single valued. Finally, note that an upper hemicontinuous (by Proposition 2) correspondence which is single valued everywhere is, in fact, a continuous function. [] REFERENCES Allen, Beth (1986a).'The Demand for (Differentiated) Infonnation'; Review of Economic Studies. 53. (311-323). Allen, Beth (1986b).'General Equilibrium with Infonnation Sales'; Theory and Decision. 21. (1-33). Allen, Beth (1990).'Infonnation as an Economic Commodity'; American Economic Review. 80. (268-273).

This book constitutes the refereed proceedings of the 6th International Conference on Scalable Uncertainty Management, SUM 2012, held in Marburg, Germany, in September 2012. The 41 revised full papers and 13 revised short papers were carefully reviewed and selected from 75 submissions. The papers cover topics in all areas of managing and reasoning with substantial and complex kinds of uncertain, incomplete or inconsistent information including applications in decision support systems, machine learning, negotiation technologies, semantic web applications, search engines, ontology systems, information retrieval, natural language processing, information extraction, image recognition, vision systems, data and text mining, and the consideration of issues such as provenance, trust, heterogeneity, and complexity of data and knowledge.

Managing uncertainty and inconsistency has been extensively explored in - ti?cial Intelligence over a number of years. Now with the advent of massive amounts of data and knowledge from distributed heterogeneous,and potentially con?icting, sources, there is interest in developing and applying formalisms for uncertainty andinconsistency widelyin systems that need to better managethis data and knowledge. The annual International Conference on Scalable Uncertainty Management (SUM) has grown out of this wide-ranging interest in managing uncertainty and inconsistency in databases, the Web, the Semantic Web, and AI. It aims at bringing together all those interested in the management of large volumes of uncertainty and inconsistency, irrespective of whether they are in databases,the Web, the Semantic Web, or in AI, as well as in other areas such as information retrieval, risk analysis, and computer vision, where signi?cant computational - forts are needed. After a promising First International Conference on Scalable Uncertainty Management was held in Washington DC, USA in 2007, the c- ference series has been successfully held in Napoli, Italy, in 2008, and again in Washington DC, USA, in 2009.

This book constitutes the refereed proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2009, held in Verona, Italy, July 1-3, 2009. There are 76 revised full papers presented together with 3 invited lectures by three outstanding researchers in the area. All papers were carefully reviewed and selected from 118 submissions for inclusion in the book. The papers are organized in topical sections on algorithms for uncertain inference, argumentation systems, Bayesian networks, Belief functions, Belief revision and inconsistency handling, classification and clustering, conditioning, independence, inference, default reasoning, foundations of reasoning, decision making under uncertainty, Fuzzy sets and Fuzzy logic, implementation and application of uncertain systems, logics for reasoning under uncertainty, Markov decision process, and Mathematical Fuzzy Logic.

It is commonly assumed that computers process information. But what is inf- mation? In a technical, important, but nevertheless rather narrow sense, Sh- non'sinformationtheorygivesa?rstanswertothisquestion.Thistheoryfocuses on measuring the information content of a message. Essentially this measure is the reduction of the uncertainty obtained by receiving a message. The unc- tainty of a situation of ignorance in turn is measured by entropy. This theory hashad an immense impact on the technologyof information storage,data c- pression, information transmission and coding and still is a very active domain of research. Shannon's theory has also attractedmuch interest in a more philosophic look at information, although it was readily remarked that it is only a “syntactic” theory of information and neglects “semantic” issues. Several attempts have been made in philosophy to give information theory a semantic?avor, but still mostly based on or at least linked to Shannon's theory. Approaches to semantic informationtheoryalsoveryoftenmakeuseofformallogic.Thereby,information is linked to reasoning, deduction and inference, as well as to decision making. Further, entropy and related measure were soon found to have important connotations with regard to statistical inference. Surely, statistical data and observation represent information, information about unknown, hidden para- ters. Thus a whole branch of statistics developed around concepts of Shannon's information theory or derived from them. Also some proper measurements - propriate for statistics, like Fisher's information, were proposed.

Large-scale data processing is important. Most successful applications of m- ern science and engineering, from discovering the human genome to predicting weather to controlling space missions, involve processing large amounts of data and large knowledge bases. The corresponding large-scale data and knowledge processing requires intensive use of computers. Computers are based on processing exact data values and truth values from the traditional 2-value logic. The ability of computers to perform fast data and knowledgeprocessingisbasedonthehardwaresupportforsuper-fastelementary computer operations, such as performing arithmetic operations with (exactly known) numbers and performing logical operations with binary (“true”-“false”) logical values. In practice, we need to go beyond exact data values and truth values from the traditional 2-value logic. In practical applications, we need to go beyond such operations. Input is only known with uncertainty. Let us?rst illustrate this need on the example of operations with numbers. Hardware-supported computer operations (implicitly) assume that we know the exact values of the input quantities. In reality, the input data usually comes from measurements. Measurements are never 100% accurate. Due to such factors as imperfection of measurement - struments and impossibility to reduce noise level to 0, the measured value x of each input quantity is, in general, di?erent from the (unknown) actual value x of this quantity. It is therefore necessary to?nd out how this input uncertainty def?x = x?x = 0 a?ects the results of data processing.

Intelligent systems are necessary to handle modern computer-based technologies managing information and knowledge. This book discusses the theories required to help provide solutions to difficult problems in the construction of intelligent systems. Particular attention is paid to situations in which the available information and data may be imprecise, uncertain, incomplete or of a linguistic nature. The main aspects of clustering, classification, summarization, decision making and systems modeling are also addressed. Topics covered in the book include fundamental issues in uncertainty, the rapidly emerging discipline of information aggregation, neural networks, Bayesian networks and other network methods, as well as logic-based systems.

This book constitutes the refereed proceedings of the Second International Conference on Scalable Uncertainty Management, SUM 2008, held in Naples, Italy, in Oktober 2008. The 27 revised full papers presented together with the extended abstracts of 3 invited talks/tutorials were carefully reviewed and selected from 42 submissions. The papers address artificial intelligence researchers, database researchers, and practitioners to demonstrate theoretical techniques required to manage the uncertainty that arises in large scale real world applications and to cope with large volumes of uncertainty and inconsistency in databases, the Web, the semantic Web, and artificial intelligence in general.

The chapters in Thinking With Data are based on presentations given at the 33rd Carnegie Symposium on Cognition. The Symposium was motivated by the confluence of three emerging trends: (1) the increasing need for people to think effectively with data at work, at school, and in everyday life, (2) the expanding technologies available to support peopl

The volume'Modern Information Processing: From Theory to Applications,'edited by Bernadette Bouchon-Meunier, Giulianella Coletti and Ronald Yager, is a collection of carefully selected papers drawn from the program of IPMU'04, which was held in Perugia, Italy. The book represents the cultural policy of IPMU conference which is not focused on narrow range of methodologies, but on the contrary welcomes all the theories for the management of uncertainty and aggregation of information in intelligent systems, providing a medium for the exchange of ideas between theoreticians and practitioners in these and related areas.The book is composed by 7 sections: UNCERTAINTYPREFERENCESCLASSIFICATION AND DATA MININGAGGREGATION AND MULTI-CRITERIA DECISION MAKINGKNOWLEDGE REPRESENTATION•The book contributes to enhancement of our ability to deal effectively with uncertainty in all of its manifestations. •The book can help to build brigs among theories and methods methods for the management of uncertainty. •The book addresses issues which have a position of centrality in our information-centric world. •The book presents interesting results devoted to representing knowledge: the goal is to capture the subtlety of human knowledge (richness) and to allow computer manipulation (formalization). •The book contributes to the goal: an efficient use of the information for a good decision strategy.APPLIED DOMAINS· The book contributes to enhancement of our ability to deal effectively with uncertainty in all of its manifestations.· The book can help to build brigs among theories and methods methods for the management of uncertainty.· The book addresses issues which have a position of centrality in our information-centric world.· The book presents interesting results devoted to representing knowledge: the goal is to capture the subtlety of human knowledge (richness) and to allow computer manipulation (formalization).· The book contributes to the goal: an efficient use of the information for a good decision strategy.

Primarily, the book draws together a series of important case studies to provide a comprehensive review and synthesis of the most recent concepts, theories and methods in scaling and uncertainty analysis. It compares current definitions and ideas concerning scale within a coherent framework, and examines two key scaling approaches: similarity-based scaling, which is rooted in the idea of similitude or self-similarity; and dynamic model-based scaling, which emphasizes processes and mechanisms. With case studies focusing on issues ranging from population to ecosystem processes; from biodiversity to landscape patterns; and from basic research to multidisciplinary management and policy-making, the book will appeal to both researchers and practitioners working on landscape issues. It will also provide a valuable resource for graduate students and professional trainees in ecology, environmental policy, resource management and global change science.

Conditionals are fascinating and versatile objects of knowledge representation. On the one hand, they may express rules in a very general sense, representing, for example, plausible relationships, physical laws, and social norms. On the other hand, as default rules or general implications, they constitute a basic tool for reasoning, even in the presence of uncertainty. In this sense, conditionals are intimately connected both to information and inference. Due to their non-Boolean nature, however, conditionals are not easily dealt with. They are not simply true or false — rather, a conditional “if A then B” provides a context, A, for B to be plausible (or true) and must not be confused with “A entails B” or with the material implication “not A or B.” This ill- trates how conditionals represent information, understood in its strict sense as reduction of uncertainty. To learn that, in the context A, the proposition B is plausible, may reduce uncertainty about B and hence is information. The ab- ity to predict such conditioned propositions is knowledge and as such (earlier) acquired information. The?rst work on conditional objects dates back to Boole in the 19th c- tury, and the interest in conditionals was revived in the second half of the 20th century, when the emerging Arti?cial Intelligence made claims for appropriate formaltoolstohandle“generalizedrules.”Sincethen,conditionalshavebeenthe topic of countless publications, each emphasizing their relevance for knowledge representation, plausible reasoning, nonmonotonic inference, and belief revision.

These are the proceedings of the 8th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2005, held in Barcelona (Spain), July 6–8, 2005. The ECSQARU conferences are biennial and have become a major forum for advances in the theory and practice of r- soning under uncertainty. The?rst ECSQARU conference was held in Marseille (1991), and after in Granada (1993), Fribourg (1995), Bonn (1997), London (1999), Toulouse (2001) and Aalborg (2003). The papers gathered in this volume were selected out of 130 submissions, after a strict review process by the members of the Program Committee, to be presented at ECSQARU 2005. In addition, the conference included invited lectures by three outstanding researchers in the area, Seraf´?n Moral (Imprecise Probabilities), Rudolf Kruse (Graphical Models in Planning) and J´ erˆ ome Lang (Social Choice). Moreover, the application of uncertainty models to real-world problems was addressed at ECSQARU 2005 by a special session devoted to s- cessful industrial applications, organized by Rudolf Kruse. Both invited lectures and papers of the special session contribute to this volume. On the whole, the programme of the conference provided a broad, rich and up-to-date perspective of the current high-level research in the area which is re?ected in the contents of this volume. IwouldliketowarmlythankthemembersoftheProgramCommitteeandthe additional referees for their valuable work, the invited speakers and the invited session organizer.

Intelligent systems are required to enhance the capacities being made available to us by the internet and other computer based technologies. The theory necessary to help providing solutions to difficult problems in the construction of intelligent systems are discussed. In particular, attention is paid to situations in which the available information and data may be imprecise, uncertain, incomplete or of a linguistic nature. Various methodologies to manage such information are discussed. Among these are the probabilistic, possibilistic, fuzzy, logical, evidential and network-based frameworks.One purpose of the book is not to consider these methodologies separately, but rather to consider how they can be used cooperatively to better represent the multiplicity of modes of information. Topics in the book include representation of imperfect knowledge, fundamental issues in uncertainty, reasoning, information retrieval, learning and mining, as well as various applications.Key Features:• Tools for construction of intelligent systems • Contributions by world leading experts • Fundamental issues and applications • New technologies for web searching • Methods for modeling uncertain information • Future directions in web technologies • Transversal to methods and domains

Risk, Reliability, Uncertainty, and Robustness of Water Resource Systems is based on the Third George Kovacs Colloquium organized by the International Hydrological Programme (UNESCO) and the International Association of Hydrological Sciences. Thirty-five leading scientists with international reputations provide reviews of topical areas of research on water resource systems, including aspects of extreme hydrological events: floods and droughts; water quantity and quality dams; reservoirs and hydraulic structures; evaluating sustainability and climate change impacts. As well as discussing essential challenges and research directions, the book will assist in applying theoretical methods to the solution of practical problems in water resources. The authors are multi-disciplinary, stemming from such areas as: hydrology, geography, civil, environmental and agricultural engineering, forestry, systems sciences, operations research, mathematics, physics and geophysics, ecology and atmospheric sciences. This review volume will be valuable for graduate students, scientists, consultants, administrators, and practising hydrologists and water managers.

Uncertainty in Artificial Intelligence: Proceedings of the Eighth Conference (1992) covers the papers presented at the Eighth Conference on Uncertainty in Artificial Intelligence, held at Stanford University on July 17-19, 1992. The book focuses on the processes, methodologies, technologies, and approaches involved in artificial intelligence. The selection first offers information on Relative Evidential Support (RES), modal logics for qualitative possibility and beliefs, and optimizing causal orderings for generating DAGs from data. Discussions focus on reversal, swap, and unclique operators, modal representation of possibility, and beliefs and conditionals. The text then examines structural controllability and observability in influence diagrams, lattice-based graded logic, and dynamic network models for forecasting. The manuscript takes a look at reformulating inference problems through selective conditioning, entropy and belief networks, parallelizing probabilistic inference, and a symbolic approach to reasoning with linguistic quantifiers. The text also ponders on sidestepping the triangulation problem in Bayesian net computations; exploring localization in Bayesian networks for large expert systems; and expressing relational and temporal knowledge in visual probabilistic networks. The selection is a valuable reference for researchers interested in artificial intelligence.

Uncertainty in Artificial Intelligence contains the proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence held at the Catholic University of America in Washington, DC, on July 9-11, 1993. The papers focus on methods of reasoning and decision making under uncertainty as applied to problems in artificial intelligence (AI) and cover topics ranging from knowledge acquisition and automated model construction to learning, planning, temporal reasoning, and machine vision. Comprised of 66 chapters, this book begins with a discussion on causality in Bayesian belief networks before turning to a decision theoretic account of conditional ought statements that rectifies glaring deficiencies in classical deontic logic and forms a sound basis for qualitative decision theory. Subsequent chapters explore trade-offs in constructing and evaluating temporal influence diagrams; normative engineering risk management systems; additive belief-network models; and sensitivity analysis for probability assessments in Bayesian networks. Automated model construction and learning as well as algorithms for inference and decision making are also considered. This monograph will be of interest to both students and practitioners in the fields of AI and computer science.

Uncertainty Proceedings 1991

Uncertainty Proceedings 1994