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Rough sets. --- Rough set theory --- Theory of rough sets --- Set theory

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This unique collection of research papers offers a comprehensive and up-to-date guide to algebraic approaches to rough sets and reasoning with vagueness. It bridges important gaps, outlines intriguing future research directions, and connects algebraic approaches to rough sets with those for other forms of approximate reasoning. In addition, the book reworks algebraic approaches to axiomatic granularity. Given its scope, the book offers a valuable resource for researchers and teachers in the areas of rough sets and algebras of rough sets, algebraic logic, non classical logic, fuzzy sets, possibility theory, formal concept analysis, computational learning theory, category theory, and other formal approaches to vagueness and approximate reasoning. Consultants in AI and allied fields will also find the book to be of great practical value.

Algebra. --- Computer science. --- Mathematics. --- General Algebraic Systems. --- Mathematical Logic and Formal Languages. --- Information and Communication, Circuits. --- Rough sets. --- Rough set theory --- Theory of rough sets --- Set theory --- Math --- Science --- Informatics --- Mathematics --- Mathematical analysis --- Mathematical logic. --- Information theory. --- Communication theory --- Communication --- Cybernetics --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Syllogism

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This special book is dedicated to the memory of Professor Zdzisław Pawlak, the father of rough set theory, in order to commemorate both the 10th anniversary of his passing and 35 years of rough set theory. The book consists of 20 chapters distributed into four sections, which focus in turn on a historical review of Professor Zdzisław Pawlak and rough set theory; a review of the theory of rough sets; the state of the art of rough set theory; and major developments in rough set based data mining approaches. Apart from Professor Pawlak’s contributions to rough set theory, other areas he was interested in are also included. Moreover, recent theoretical studies and advances in applications are also presented. The book will offer a useful guide for researchers in Knowledge Engineering and Data Mining by suggesting new approaches to solving the problems they encounter.

Engineering. --- Artificial intelligence. --- Computational intelligence. --- Computational Intelligence. --- Artificial Intelligence (incl. Robotics). --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Construction --- Industrial arts --- Technology --- Artificial Intelligence. --- Rough sets. --- Pawlak, Zdzisław. --- Rough set theory --- Theory of rough sets --- Set theory

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This book explores reasoning with rough sets by developing a granularity-based framework. It begins with a brief description of rough set theory. Next, we examine some relations between rough set theory and non-classical logics including modal logic. We also develop a granularity-based framework for reasoning in which various types of reasoning can be formalized. This book will be of interest to researchers working on the areas in Artificial Intelligence, database and logic.

Rough sets. --- Granular computing. --- GC (Computer science) --- Rough set theory --- Theory of rough sets --- Engineering. --- Artificial intelligence. --- Computational intelligence. --- Computational Intelligence. --- Artificial Intelligence (incl. Robotics). --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Construction --- Industrial arts --- Technology --- Set theory --- Artificial Intelligence.

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This book presents a study in knowledge discovery in data with knowledge understood as a set of relations among objects and their properties. Relations in this case are implicative decision rules and the paradigm in which they are induced is that of computing with granules defined by rough inclusions, the latter introduced and studied  within rough mereology, the fuzzified version of mereology. In this book basic classes of rough inclusions are defined and based on them methods for inducing granular structures from data are highlighted. The resulting granular structures are subjected to classifying algorithms, notably k—nearest  neighbors and bayesian classifiers. Experimental results are given in detail both in tabular and visualized form for fourteen data sets from UCI data repository. A striking feature of granular classifiers obtained by this approach is that preserving the accuracy of them on original data, they reduce  substantially the size of the granulated data set as well as the set of granular decision rules. This feature makes the presented approach attractive in cases where a small number of  rules providing a high classification accuracy is desirable. As basic algorithms used throughout the text are explained and illustrated with  hand examples, the book may also serve as a textbook.

Engineering. --- Computational Intelligence. --- Artificial Intelligence (incl. Robotics). --- Artificial intelligence. --- Ingénierie --- Intelligence artificielle --- Engineering & Applied Sciences --- Computer Science --- Rough sets. --- Whole and parts (Philosophy) --- Approximation theory. --- Theory of approximation --- Ganzheit (Philosophy) --- Mereology --- Totality (Philosophy) --- Unity (Philosophy) --- Wholeness --- Rough set theory --- Theory of rough sets --- Computational intelligence. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Construction --- Industrial arts --- Technology --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Categories (Philosophy) --- Set theory --- Artificial Intelligence.