Approximate reasoning is a key motivation in fuzzy sets and possibility theory. This volume provides a coherent view of this field, and its impact on database research and information retrieval. First, the semantic foundations of approximate reasoning are presented. Special emphasis is given to the representation of fuzzy rules and specialized types of approximate reasoning. Then syntactic aspects of approximate reasoning are surveyed and the algebraic underpinnings of fuzzy consequence relations are presented and explained. The second part of the book is devoted to inductive and neuro-fuzzy methods for learning fuzzy rules. It also contains new material on the application of possibility theory to data fusion. The last part of the book surveys the growing literature on fuzzy information systems. Each chapter contains extensive bibliographical material. Fuzzy Sets in Approximate Reasoning and Information Systems is a major source of information for research scholars and graduate students in computer science and artificial intelligence, interested in human information processing.

Fuzzy Sets, Logics and Reasoning about Knowledge reports recent results concerning the genuinely logical aspects of fuzzy sets in relation to algebraic considerations, knowledge representation and commonsense reasoning. It takes a state-of-the-art look at multiple-valued and fuzzy set-based logics, in an artificial intelligence perspective. The papers, all of which are written by leading contributors in their respective fields, are grouped into four sections. The first section presents a panorama of many-valued logics in connection with fuzzy sets. The second explores algebraic foundations, with an emphasis on MV algebras. The third is devoted to approximate reasoning methods and similarity-based reasoning. The fourth explores connections between fuzzy knowledge representation, especially possibilistic logic and prioritized knowledge bases. Readership: Scholars and graduate students in logic, algebra, knowledge representation, and formal aspects of artificial intelligence.

Analogical reasoning is known as a powerful mode for drawing plausible conclusions and solving problems. It has been the topic of a huge number of works by philosophers, anthropologists, linguists, psychologists and computer scientists. As such, it has been early studied in artificial intelligence, with a particular renewal of interest in the last decade.

The present volume provides a structured view of current research trends on computational approaches to analogical reasoning. It starts with an overview of analogical reasoning with an extensive bibliography.

The 14 collected contributions cover a large scope of issues. First, the use of analogical proportions and analogies is explained and discussed in various natural language processing problems, as well as in automated deduction. Then, different formal frameworks for handling analogies are presented, dealing with case-based reasoning, heuristic-driven theory projection, commonsense reasoning about incomplete rule bases, logical proportions induced by similarity and dissimilarity indicators and analogical proportions in lattice structures. Lastly, the volume reports case studies and discussions about the use of similarity judgments and the process of analogy making, at work in IQ tests, creativity or other cognitive tasks.

This volume gathers fully revised and expanded versions of papers presented at an international workshop as well as invited contributions. All chapters have benefited of a thorough peer review process."

Fundamentals of Fuzzy Sets covers the basic elements of fuzzy set theory. Its four-part organization provides easy referencing of recent as well as older results in the field. The first part discusses the historical emergence of fuzzy sets, and delves into fuzzy set connectives, and the representation and measurement of membership functions. The second part covers fuzzy relations, including orderings, similarity, and relational equations. The third part, devoted to uncertainty modelling, introduces possibility theory, contrasting and relating it with probabilities, and reviews information measures of specificity and fuzziness. The last part concerns fuzzy sets on the real line - computation with fuzzy intervals, metric topology of fuzzy numbers, and the calculus of fuzzy-valued functions. Each chapter is written by one or more recognized specialists and offers a tutorial introduction to the topics, together with an extensive bibliography.

Analogical reasoning is known as a powerful mode for drawing plausible conclusions and solving problems. It has been the topic of a huge number of works by philosophers, anthropologists, linguists, psychologists, and computer scientists. As such, it has been early studied in artificial intelligence, with a particular renewal of interest in the last decade. The present volume provides a structured view of current research trends on computational approaches to analogical reasoning. It starts with an overview of the field, with an extensive bibliography. The 14 collected contributions cover a large scope of issues. First, the use of analogical proportions and analogies is explained and discussed in various natural language processing problems, as well as in automated deduction. Then, different formal frameworks for handling analogies are presented, dealing with case-based reasoning, heuristic-driven theory projection, commonsense reasoning about incomplete rule bases, logical proportions induced by similarity and dissimilarity indicators, and analogical proportions in lattice structures. Lastly, the volume reports case studies and discussions about the use of similarity judgments and the process of analogy making, at work in IQ tests, creativity or other cognitive tasks. This volume gathers fully revised and expanded versions of papers presented at an international workshop‚ as well as invited contributions. All chapters have benefited of a thorough peer review process.

Spatial information is pervaded by uncertainty. Indeed, geographical data is often obtained by an imperfect interpretation of remote sensing images, while people attach ill-defined or ambiguous labels to places and their properties. As another example, medical images are often the result of measurements by imprecise sensors (e.g. MRI scans). Moreover, by processing spatial information in real-world applications, additional uncertainty is introduced, e.g. due to the use of interpolation/extrapolation techniques or to conflicts that are detected in an information fusion step. To the best of our knowledge, this book presents the first overview of spatial uncertainty which goes beyond the setting of geographical information systems. Uncertainty issues are especially addressed from a representation and reasoning point of view. In particular, the book consists of 14 chapters, which are clustered around three central topics. The first of these topics is about the uncertainty in meaning of linguistic descriptions of spatial scenes. Second, the issue of reasoning about spatial relations and dealing with inconsistency in information merging is studied. Finally, interpolation and prediction of spatial phenomena are investigated, both at the methodological level and from an application-oriented perspective. The concept of uncertainty by itself is understood in a broad sense, including both quantitative and more qualitative approaches, dealing with variability, epistemic uncertainty, as well as with vagueness of terms.

Approximate reasoning is a key motivation in fuzzy sets and possibility theory. This volume provides a coherent view of this field, and its impact on database research and information retrieval. First, the semantic foundations of approximate reasoning are presented. Special emphasis is given to the representation of fuzzy rules and specialized types of approximate reasoning. Then syntactic aspects of approximate reasoning are surveyed and the algebraic underpinnings of fuzzy consequence relations are presented and explained. The second part of the book is devoted to inductive and neuro-fuzzy methods for learning fuzzy rules. It also contains new material on the application of possibility theory to data fusion. The last part of the book surveys the growing literature on fuzzy information systems. Each chapter contains extensive bibliographical material. Fuzzy Sets in Approximate Reasoning and Information Systems is a major source of information for research scholars and graduate students in computer science and artificial intelligence, interested in human information processing.

Fundamentals of Fuzzy Sets covers the basic elements of fuzzy set theory. Its four-part organization provides easy referencing of recent as well as older results in the field. The first part discusses the historical emergence of fuzzy sets, and delves into fuzzy set connectives, and the representation and measurement of membership functions. The second part covers fuzzy relations, including orderings, similarity, and relational equations. The third part, devoted to uncertainty modelling, introduces possibility theory, contrasting and relating it with probabilities, and reviews information measures of specificity and fuzziness. The last part concerns fuzzy sets on the real line - computation with fuzzy intervals, metric topology of fuzzy numbers, and the calculus of fuzzy-valued functions. Each chapter is written by one or more recognized specialists and offers a tutorial introduction to the topics, together with an extensive bibliography.

Fuzzy Sets, Logics and Reasoning about Knowledge reports recent results concerning the genuinely logical aspects of fuzzy sets in relation to algebraic considerations, knowledge representation and commonsense reasoning. It takes a state-of-the-art look at multiple-valued and fuzzy set-based logics, in an artificial intelligence perspective. The papers, all of which are written by leading contributors in their respective fields, are grouped into four sections. The first section presents a panorama of many-valued logics in connection with fuzzy sets. The second explores algebraic foundations, with an emphasis on MV algebras. The third is devoted to approximate reasoning methods and similarity-based reasoning. The fourth explores connections between fuzzy knowledge representation, especially possibilistic logic and prioritized knowledge bases. Readership: Scholars and graduate students in logic, algebra, knowledge representation, and formal aspects of artificial intelligence.

This volume contains the articles presented at the 6th International Symposium on Foundationsof Informationand KnowledgeSystems (FoIKS 2010)which was held in So?a, Bulgaria during February 15-19, 2010. The FoIKS symposia provide a biennial forum for presenting and discussing theoreticalandappliedresearchoninformationandknowledgesystems.Thegoal is to bring together researchers with an interest in this subject, share research experiences, promote collaboration and identify new issues and directions for future research. FoIKS 2010 solicited original contributions dealing with any foundational aspects of information and knowledge systems. This included submissions that apply ideas, theories or methods from speci?c disciplines to information and knowledge systems. Examples of such disciplines are discrete mathematics, logic and algebra, model theory, information theory, complexity theory, algorithmics and computation, statistics, and optimization. Previous FoIKS symposia were held in Pisa (Italy) in 2008, Budapest (Hungary) in 2006, Vienna (Austria) in 2004, Schloss Salzau near Kiel (Germany) in 2002,and Burg/Spreewaldnear Berlin (Germany) in 2000.FoIKS took up the tradition of the conference series Mathematical Fundamentals of Database Systems (MFDBS), which initiated East-West collaboration in the ? eld of database theory. Former MFDBS conferences were held in Rostock (Germany) in 1991, Visegrad (Hungary) in 1989, and Dresden (Germany) in 1987. The FoIKS symposia are a forum for intense discussions. Speakers are given su?cient time to present their ideas and results within the larger context of their research. Furthermore, participants are asked in advance to prepare a ?rst response to a contribution of another author.

This book constitutes the refereed proceedings of the First International Conference on Scalable Uncertainty Management, SUM 2007, held in Washington, DC, USA, in Oktober 2007.

The 20 revised full papers presented were carefully reviewed and selected from numerous submissions for inclusion in the book. 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. The papers deal with the following topics: uncertainty models, probabilistic logics, fuzzy logics, and annotated logics, inconsistency logics, database algebras and calculi, scalable database systems, spatial, temporal, mobile and multimedia databases, as well as implementations, and applications.

Probability theory has been the only well-founded theory of uncertainty for a long time. It was viewed either as a powerful tool for modelling random phenomena, or as a rational approach to the notion of degree of belief. During the last thirty years, in areas centered around decision theory, artificial intelligence and information processing, numerous approaches extending or orthogonal to the existing theory of probability and mathematical statistics have come to the front. The common feature of those attempts is to allow for softer or wider frameworks for taking into account the incompleteness or imprecision of information. Many of these approaches come down to blending interval or fuzzy interval analysis with probabilistic methods.

This book gathers contributions to the 4th International Conference on Soft methods in Probability and Statistics. Its aim is to present recent results illustrating such new trends that enlarge the statistical and uncertainty modeling traditions, towards the handling of incomplete or subjective information. It covers a broad scope ranging from philosophical and mathematical underpinnings of new uncertainty theories, with a stress on their impact in the area of statistics and data analysis, to numerical methods and applications to environmental risk analysis and mechanical engineering. A unique feature of this collection is to establish a dialogue between fuzzy random variables and imprecise probability theories.