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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.


Papers
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Journal ArticleDOI
01 Mar 2005
TL;DR: A novel contribution of a gradient-based learning of the prototypes developed in the l∞-based FCM is offered, which discusses a deformation effect of the hyperbox-shape of granules due to an interaction between the granules.
Abstract: In this study, we propose a model of granular data emerging through a summarization and processing of numeric data. This model supports data analysis and contributes to further interpretation activities. The structure of data is revealed through the FCM equipped with the Tchebyschev (l∞) metric. The paper offers a novel contribution of a gradient-based learning of the prototypes developed in the l∞-based FCM. The l∞ metric promotes development of easily interpretable information granules, namely hyperboxes. A detailed discussion of their geometry is provided. In particular, we discuss a deformation effect of the hyperbox-shape of granules due to an interaction between the granules. It is shown how the deformation effect can be quantified. Subsequently, we show how the clustering gives rise to a two-level topology of information granules: the core part of the topology comes in the form of hyperbox information granules. A residual structure is expressed through detailed, yet difficult to interpret, membership grades. Illustrative examples including synthetic data are studied.

447 citations

BookDOI
01 Jun 2007
TL;DR: A comprehensive, coherent, and in depth presentation of the state of the art in fuzzy clustering, addressing timely and relevant concepts and methods whilst identifying major challenges and recent developments in the area.
Abstract: DESCRIPTION A comprehensive, coherent, and in depth presentation of the state of the art in fuzzy clustering. Fuzzy clustering is now a mature and vibrant area of research with highly innovative advanced applications. Encapsulating this through presenting a careful selection of research contributions, this book addresses timely and relevant concepts and methods, whilst identifying major challenges and recent developments in the area. Split into five clear sections, Fundamentals, Visualization, Algorithms and Computational Aspects, Real-Time and Dynamic Clustering, and Applications and Case Studies, the book covers a wealth of novel, original and fully updated material, and in particular offers:

441 citations

Journal ArticleDOI
TL;DR: A logic-driven clustering in which prototypes are formed and evaluated in a sequential manner that considers an inverse similarity problem and shows how the relevance of the prototypes translates into their granularity.
Abstract: We introduce a logic-driven clustering in which prototypes are formed and evaluated in a sequential manner. The way of revealing a structure in data is realized by maximizing a certain performance index (objective function) that takes into consideration an overall level of matching (to be maximized) and a similarity level between the prototypes (the component to be minimized). The prototypes identified in the process come with the optimal weight vector that serves to indicate the significance of the individual features (coordinates) in the data grouping represented by the prototype. Since the topologies of these groupings are in general quite diverse the optimal weight vectors are reflecting the anisotropy of the feature space, i.e., they show some local ranking of features in the data space. Having found the prototypes we consider an inverse similarity problem and show how the relevance of the prototypes translates into their granularity.

433 citations

Journal ArticleDOI
TL;DR: The aim of this paper is to review foundations and schools of research and to elaborate on current developments in granular computing research.
Abstract: Granular computing, as a new and rapidly growing paradigm of information processing, has attracted many researchers and practitioners. Granular computing is an umbrella term to cover any theories, methodologies, techniques, and tools that make use of information granules in complex problem solving. The aim of this paper is to review foundations and schools of research and to elaborate on current developments in granular computing research. We first review some basic notions of granular computing. Classification and descriptions of various schools of research in granular computing are given. We also present and identify some research directions in granular computing.

405 citations

Journal ArticleDOI
TL;DR: Proposed is an idea of conditional clustering whose main objective is to develop clusters preserving homogeneity of the clustered patterns with regard to their similarity in the input space as well as their respective values assumed in the output space.
Abstract: This paper is concerned with the use of radial basis function (RBF) neural networks aimed at an approximation of nonlinear mappings from R/sup n/ to R. The study is devoted to the design of these networks, especially their layer composed of RBF, using the techniques of fuzzy clustering. Proposed is an idea of conditional clustering whose main objective is to develop clusters (receptive fields) preserving homogeneity of the clustered patterns with regard to their similarity in the input space as well as their respective values assumed in the output space. The detailed clustering algorithm is accompanied by extensive simulation studies.

389 citations


Cited by
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Journal ArticleDOI

[...]

08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
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 …

33,785 citations

Book
08 Sep 2000
TL;DR: This book presents dozens of algorithms and implementation examples, all in pseudo-code and suitable for use in real-world, large-scale data mining projects, and provides a comprehensive, practical look at the concepts and techniques you need to get the most out of real business data.
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

23,600 citations

Journal ArticleDOI
01 May 1993
TL;DR: 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.
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. >

15,085 citations