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Find the best student using multifactorial evaluation, if the weight factors for the subjects are given as the vector W = [0.3, 0.2, 0.1, 0.4].

12. Search the Web to find the basic characteristics of publicly available or commercial software tools that are based on fuzzy sets and fuzzy logic. Make a report of your search.

14.9 REFERENCES FOR FURTHER STUDY

Chen, Y., T. Wang, B. Wang, Z. Li, A Survey of Fuzzy Decision Tree Classifier, Fuzzy Information and Engineering, Vol. 1, No. 2, 2009, pp. 149–159.

Decision-tree algorithm provides one of the most popular methodologies for symbolic knowledge acquisition. The resulting knowledge, a symbolic decision tree along with a simple inference mechanism, has been praised for comprehensibility. The most comprehensible decision trees have been designed for perfect symbolic data. Over the years, additional methodologies have been investigated and proposed to deal with continuous or multi-valued data, and with missing or noisy features. Recently, with the growing popularity of fuzzy representation, some researchers have proposed to utilize fuzzy representation in decision trees to deal with similar situations. This paper presents a survey of current methods for Fuzzy Decision Tree (FDT) designment and the various existing issues. After considering potential advantages of FDT classifiers over traditional decision-tree classifiers, we discuss the subjects of FDT including attribute selection criteria, inference for decision assignment, and stopping criteria.

Cox, E., Fuzzy Modeling and Genetic Algorithms for Data Mining and Exploration, Morgan Kaufmann, San Francisco, CA, 2005.

Fuzzy Modeling and Genetic Algorithms for Data Mining and Exploration is a handbook for analysts, engineers, and managers involved in developing data-mining models in business and government. As you will discover, fuzzy systems are extraordinarily valuable tools for representing and manipulating all kinds of data, and genetic algorithms and evolutionary programming techniques drawn from biology provide the most effective means for designing and tuning these systems. You do not need a background in fuzzy modeling or genetic algorithms to benefit, for this book provides it, along with detailed instruction in methods that you can immediately put to work in your own projects. The author provides many diverse examples and also an extended example in which evolutionary strategies are used to create a complex scheduling system.

Laurent, A., M. Lesot, eds., Scalable Fuzzy Algorithms for Data Management and Analysis, Methods and Design, IGI Global, Hershey, PA, 2010.

The book presents innovative, cutting-edge fuzzy techniques that highlight the relevance of fuzziness for huge data sets in the perspective of scalability issues, from both a theoretical and experimental point of view. It covers a wide scope of research areas including data representation, structuring and querying, as well as information retrieval and data mining. It encompasses different forms of databases, including data warehouses, data cubes, tabular or relational data, and many applications, among which are music warehouses, video mining, bioinformatics, semantic Web and data streams.

Li, H. X., V. C. Yen, Fuzzy Sets and Fuzzy Decision-Making, CRC Press, Inc., Boca Raton, 1995.

The book emphasizes the applications of fuzzy-set theory in the field of management science and decision science, introducing and formalizing the concept of fuzzy decision making. Many interesting methods of fuzzy decision making are developed and illustrated with examples.

Pal, S. K., S. Mitra, Neuro-Fuzzy Pattern Recognition: Methods in Soft Computing, John Wiley & Sons, Inc., New York, 1999.

The authors consolidate a wealth of information previously scattered in disparate articles, journals, and edited volumes, explaining both the theory of neuro-fuzzy computing and the latest methodologies for performing different pattern-recognition tasks using neuro-fuzzy networksβ€”classification, feature evaluation, rule generation, and knowledge extraction. Special emphasis is given to the integration of neuro-fuzzy methods with rough sets and genetic algorithms to ensure a more efficient recognition system.

Pedrycz, W., F. Gomide, An Introduction to Fuzzy Sets: Analysis and Design, The MIT Press, Cambridge, 1998.

The book provides a highly readable, comprehensive, self-contained, updated, and well-organized presentation of the fuzzy-set technology. Both theoretical and practical aspects of the subject are given a coherent and balanced treatment. The reader is introduced to the main computational models, such as fuzzy modeling and rule-based computation, and to the frontiers of the field at the confluence of fuzzy-set technology with other major methodologies of soft computing.

15

VISUALIZATION METHODS

Chapter Objectives

Recognize the importance of a visual-perception analysis in humans to discover appropriate data-visualization techniques.

Distinguish between scientific-visualization and information-visualization techniques (IVT).

Understand the basic characteristics of geometric, icon-based, pixel-oriented, and hierarchical techniques in visualization of large data sets

Explain the methods of parallel coordinates and radial visualization for n-dimensional data sets.

Analyze the requirements for advanced visualization systems in data mining.

How are humans capable of recognizing hundreds of faces? What is our β€œchannel capacity” when dealing with the visual or any other of our senses? How many distinct visual icons and orientations can humans accurately perceive? It is important to factor all these cognitive limitations when designing a visualization technique that avoids delivering ambiguous or misleading information. Categorization lays the foundation for a well-known cognitive technique: the β€œchunking” phenomena. How many chunks can you hang onto? That varies among people, but the typical range forms β€œthe magical number seven, plus or minus two.” The process of reorganizing large amounts of data into fewer chunks with more bits of information per chunk is known in cognitive science as β€œrecoding.” We expand our comprehension abilities by reformatting problems into multiple dimensions or sequences of chunks, or by redefining the problem in a way that invokes relative judgment, followed by a second focus of attention.

15.1 PERCEPTION AND VISUALIZATION

Perception is our chief means of knowing and understanding the world; images are the mental pictures produced by this understanding. In perception as well as art, a meaningful whole is created by the relationship of the parts to each other. Our ability to see patterns in things and pull together parts into a meaningful whole is the key to perception and thought. As we view our environment, we are actually performing the enormously complex task of deriving meaning out of essentially separate and disparate sensory elements. The eye, unlike the camera, is not a mechanism for capturing images so much as it is a

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