Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book is dedicated to the memory of Professor Zdzis{l}aw Pawlak who passed away almost six year ago. He is the founder of the Polish school of Artificial Intelligence and one of the pioneers in Computer Engineering and Computer Science with worldwide influence. He was a truly great scientist, researcher, teacher and a human being. This book prepared in two volumes contains more than 50 chapters. This demonstrates that the scientific approaches  discovered by of Professor Zdzis{l}aw Pawlak, especially the rough set approach as a tool for dealing with imperfect knowledge, are vivid and intensively explored by many researchers in many places throughout the world. The submitted papers prove that interest in rough set research is growing and is possible to see many new excellent results both on theoretical foundations and applications of rough sets alone or in combination with other approaches. We are proud to offer the readers this book.

Rough sets. --- Artificial intelligence. --- Rough set theory --- Theory of rough sets --- Engineering. --- Computational intelligence. --- Computational Intelligence. --- Artificial Intelligence (incl. Robotics). --- 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 --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Construction --- Industrial arts --- Technology --- Set theory

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This monograph is devoted to theoretical and experimental study of partial reducts and partial decision rules on the basis of the study of partial covers. The use of partial (approximate) reducts and decision rules instead of exact ones allows us to obtain more compact description of knowledge contained in decision tables, and to design more precise classifiers. Algorithms for construction of partial reducts and partial decision rules, bounds on minimal complexity of partial reducts and decision rules, and algorithms for construction of the set of all partial reducts and the set of all irreducible partial decision rules are considered. The book includes a discussion on the results of numerous experiments with randomly generated and real-life decision tables. These results show that partial reducts and decision rules can be used in data mining and knowledge discovery both for knowledge representation and for prediction. The results obtained in the monograph can be useful for researchers in such areas as machine learning, data mining and knowledge discovery, especially for those who are working in rough set theory, test theory and LAD (Logical Analysis of Data). The monograph can be used under the creation of courses for graduate students and for Ph.D. studies.

Computer science. --- Artificial intelligence. --- Applied mathematics. --- Engineering mathematics. --- Computer Science. --- Artificial Intelligence (incl. Robotics). --- Appl.Mathematics/Computational Methods of Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- 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 --- Informatics --- Science --- Mathematics --- Rough sets. --- Set theory. --- Rough set theory --- Theory of rough sets --- Set theory --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Artificial Intelligence. --- Mathematical and Computational Engineering.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Fuzzy classifiers are important tools in exploratory data analysis, which is a vital set of methods used in various engineering, scientific and business applications. Fuzzy classifiers use fuzzy rules and do not require assumptions common to statistical classification. Rough set theory is useful when data sets are incomplete. It defines a formal approximation of crisp sets by providing the lower and the upper approximation of the original set. Systems based on rough sets have natural ability to work on such data and incomplete vectors do not have to be preprocessed before classification. To achieve better performance than existing machine learning systems, fuzzy classifiers and rough sets can be combined in ensembles. Such ensembles consist of a finite set of learning models, usually weak learners. The present book discusses the three aforementioned fields – fuzzy systems, rough sets and ensemble techniques. As the trained ensemble should represent a single hypothesis, a lot of attention is placed on the possibility to combine fuzzy rules from fuzzy systems being members of classification ensemble. Furthermore, an emphasis is placed on ensembles that can work on incomplete data, thanks to rough set theory.

Fuzzy systems --- Rough sets --- Soft computing --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Computer Science --- Algebra --- Fuzzy systems. --- Rough sets. --- Rough set theory --- Theory of rough sets --- Systems, Fuzzy --- Engineering. --- Computer simulation. --- Pattern recognition. --- Computational intelligence. --- Computational Intelligence. --- Pattern Recognition. --- Simulation and Modeling. --- Intelligence, Computational --- Artificial intelligence --- Design perception --- Pattern recognition --- Form perception --- Perception --- Figure-ground perception --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Construction --- Industrial arts --- Technology --- Set theory --- System analysis --- Fuzzy logic --- Optical pattern recognition. --- Optical data processing --- Pattern perception --- Perceptrons --- Visual discrimination --- Pattern recognition systems. --- Automated Pattern Recognition. --- Computer Modelling. --- Pattern classification systems --- Pattern recognition computers --- Computer vision