This volume gives a state of the art of triangular norms which can be used for the generalization of several mathematical concepts, such as conjunction, metric, measure, etc. 16 chapters written by leading experts provide a state of the art overview of theory and applications of triangular norms and related operators in fuzzy logic, measure theory, probability theory, and probabilistic metric spaces.Key Features:- Complete state of the art of the importance of triangular norms in various m...

A broad spectrum of modern Information Technology (IT) tools, techniques, main developments and still open challenges is presented. Emphasis is on new research directions in various fields of science and technology that are related to data analysis, data mining, knowledge discovery, information retrieval, clustering and classification, decision making and decision support, control, computational mathematics and physics, to name a few. Applications in many relevant fields are presented, not...

This book collects the abstracts of the contributions presented at AGOP 2017, the 9th International Summer School on Aggregation Operators. The conference took place in Skövde (Sweden) in June 2017. Contributions include works from theory and fundamentals of aggregation functions to their use in applications. Aggregation functions are usually defined as those functions that are monotonic and that satisfy the unanimity condition. In particular settings these conditions are relaxed.A...

Aggregation is the process of combining several numerical values into a single representative value, and an aggregation function performs this operation. These functions arise wherever aggregating information is important: applied and pure mathematics (probability, statistics, decision theory, functional equations), operations research, computer science, and many applied fields (economics and finance, pattern recognition and image processing, data fusion, etc.). This is a comprehensive, ri...

The book is a collection of contributions by leading experts, developed around traditional themes discussed at the annual Linz Seminars on Fuzzy Set Theory. The different chapters have been written by former PhD students, colleagues, co-authors and friends of Peter Klement, a leading researcher and the organizer of the Linz Seminars on Fuzzy Set Theory. The book also includes advanced findings on topics inspired by Klement’s research activities, concerning copulas, measures and integrals, ...

This book collects the contributions presented at AGOP 2019, the 10th International Summer School on Aggregation Operators, which took place in Olomouc (Czech Republic) in July 2019. It includes contributions on topics ranging from the theory and foundations of aggregation functions to their various applications.Aggregation functions have numerous applications, including, but not limited to, data fusion, statistics, image processing, and decision-making. They are usually defined as...

This book highlights a broad range of modern information technology tools, techniques, investigations and open challenges, mainly with applications in systems research and computational physics. Divided into three major sections, it begins by presenting specialized calculation methods in the framework of data analysis and intelligent computing. In turn, the second section focuses on application aspects, mainly for systems research, while the final section investigates how various tasks in ...

The book provides the first full length exploration of fuzzy computability. It describes the notion of fuzziness and present the foundation of computability theory. It then presents the various approaches to fuzzy computability. This text provides a glimpse into the different approaches in this area, which is important for researchers in order to have a clear view of the field. It contains a detailed literature review and the author includes all proofs to make the presentation accessible. ...

This two volume set LNCS 9234 and 9235 constitutes the refereed conference proceedings of the 40th International Symposium on Mathematical Foundations of Computer Science, MFCS 2015, held in Milan, Italy, in August 2015. The 82 revised full papers presented together with 5 invited talks were carefully selected from 201 submissions. The papers feature high-quality research in all branches of theoretical computer science. They have been organized in the following topical main sections: logic...

This fundamental monograph introduces both the probabilistic and algebraic aspects of information theory and coding. It has evolved from the authors' years of experience teaching at the undergraduate level, including several Cambridge Maths Tripos courses. The book provides relevant background material, a wide range of worked examples and clear solutions to problems from real exam papers. It is a valuable teaching aid for undergraduate and graduate students, or for researchers and engineer...

Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate thos...

Csiszár and Körner's book is widely regarded as a classic in the field of information theory, providing deep insights and expert treatment of the key theoretical issues. It includes in-depth coverage of the mathematics of reliable information transmission, both in two-terminal and multi-terminal network scenarios. Updated and considerably expanded, this new edition presents unique discussions of information theoretic secrecy and of zero-error information theory, including the deep connecti...