Witold Pedrycz

Bio: Witold Pedrycz is an academic researcher from University of Alberta. The author has contributed to research in topics: Fuzzy logic & Fuzzy set. The author has an hindex of 101, co-authored 1766 publications receiving 58203 citations. Previous affiliations of Witold Pedrycz include University of Winnipeg & King Abdulaziz University.

An introduction to fuzzy sets : analysis and design

Abstract: Part 1 Fundamentals of fuzzy sets: basic notions and concepts of fuzzy sets - set membership and fuzzy sets, basic definitions of a fuzzy set, types of membership functions, characteristics of a fuzzy set, basic relationships between fuzzy sets - equality and inclusion, fuzzy sets and sets - the representation theorem, the extension principles, membership function determination, generalizations of fuzzy sets, chapter summary, problems, references fuzzy set operations - set theory operations and their properties, triangular norms, aggregation operations on fuzzy sets, sensitivity of fuzzy sets operators, negations, comparison operations on fuzzy sets, chapter summary, problems, references information-based characterization of fuzzy sets -entropy measures of fuzziness, energy measures of fuzziness, specificity of a fuzzy set, frames of cognition, information encoding and decoding using linguistic landmarks, decoding mechanisms for pointwise data, decoding using membership functions of the linguistic terms of the codebook, general possibility-necessity decoding, distance between fuzzy sets based on their internal, linguistic representation, chapter summary, problems, references fuzzy relations and their calculus -relations and fuzzy relations, operations on fuzzy relations, compositions of fuzzy relations, projections and cylindric extensions of fuzzy relations, binary fuzzy relations, some classes of fuzzy relations, fuzzy-relational equations, estimation and inverse problem in fuzzy relational equations, solving fuzzy-relational equations with the sup-t composition, solutions to dual fuzzy-relational equations, adjoint fuzzy-relational equations, generaliations of fuzzy relational equations, approximate solutions to fuzzy-relational equations, chapter summary, problems, references fuzzy numbers - defining fuzzy numbers, interval analysis and fuzzy numbers, computing with fuzzy numbers, triangular fuzzy numbers and basic operations, general formulas for LR fuzzy numbers, accumulation of fuzziness in computing with fuzzy numbers, inverse problem in computation with fuzzy numbers, fuzzy numbers and approximate operations, chapter summary, problems, references fuzzy modelling - fuzzy models - beyond numerical computations, main phases of system modelling, fundamental design objectives in system modelling, general topology of fuzzy models, compatibility of encoding and decoding modules, classes of fuzzy models, verification and validation of fuzzy models, chapter summary, problems, references. Part 3 Problem solving with fuzzy sets: methodology -analysis and design, fuzzy controllers and fuzzy control, mathematical programming and fuzzy optimization, chapter summary, problems, references case studies - traffic intersection control, distributed traffic control, elevator group control, induction motor control, communication network planning, neurocomputation in fault diagnosis of dynamic systems, multicommodity transportation planning in railways.

Fuzzy control and fuzzy systems

Abstract: From the Publisher: Presents extensive and updated material concerned with the methodology and algorithms of fuzzy sets considered mainly in the context of control engineering and system modeling and analysis. Offers information on fuzzy sets and the concept of fuzzy control, reviewing selected applications and their origin. Discusses design aspects and theoretical developments in the design of fuzzy controllers. Includes comprehensive coverage of the paradigms and algorithms of fuzzy modeling.

Granular computing: an introduction

Abstract: The study is concerned with the fundamentals of granular computing. Granular computing, as the name itself stipulates, deals with representing information in the form of some aggregates (that embrace a number of individual entities) and their ensuing processing. We elaborate on the rationale behind granular computing. Next, a number of formal frameworks of information granulation are discussed including several alternatives such as fuzzy sets, interval analysis, rough sets, and probability. The notion of granularity itself is defined and quantified. A design agenda of granular computing is formulated and the key design problems are raised. A number of granular architectures are also discussed with an objective of delineating the fundamental algorithmic, and conceptual challenges. It is shown that the use of information granules of different size (granularity) lends itself to general pyramid architectures of information processing. The role of encoding and decoding mechanisms visible in this setting is also discussed in detail, along with some particular solutions. We raise an issue of interoperability of granular environments. The intent of the paper is to elaborate on the fundamentals and put the entire area in a certain perspective while not moving into specific algorithmic details.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Data Mining: Concepts and Techniques

Abstract: The increasing volume of data in modern business and science calls for more complex and sophisticated tools. Although advances in data mining technology have made extensive data collection much easier, it's still always evolving and there is a constant need for new techniques and tools that can help us transform this data into useful information and knowledge. Since the previous edition's publication, great advances have been made in the field of data mining. Not only does the third of edition of Data Mining: Concepts and Techniques continue the tradition of equipping you with an understanding and application of the theory and practice of discovering patterns hidden in large data sets, it also focuses on new, important topics in the field: data warehouses and data cube technology, mining stream, mining social networks, and mining spatial, multimedia and other complex data. Each chapter is a stand-alone guide to a critical topic, presenting proven algorithms and sound implementations ready to be used directly or with strategic modification against live data. This is the resource you need if you want to apply today's most powerful data mining techniques to meet real business challenges. * Presents dozens of algorithms and implementation examples, all in pseudo-code and suitable for use in real-world, large-scale data mining projects. * Addresses advanced topics such as mining object-relational databases, spatial databases, multimedia databases, time-series databases, text databases, the World Wide Web, and applications in several fields. *Provides a comprehensive, practical look at the concepts and techniques you need to get the most out of real business data

ANFIS: adaptive-network-based fuzzy inference system

Abstract: The architecture and learning procedure underlying ANFIS (adaptive-network-based fuzzy inference system) is presented, which is a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an input-output mapping based on both human knowledge (in the form of fuzzy if-then rules) and stipulated input-output data pairs. In the simulation, the ANFIS architecture is employed to model nonlinear functions, identify nonlinear components on-line in a control system, and predict a chaotic time series, all yielding remarkable results. Comparisons with artificial neural networks and earlier work on fuzzy modeling are listed and discussed. Other extensions of the proposed ANFIS and promising applications to automatic control and signal processing are also suggested. >