Data Mining - Mehmed Kantardzic [248]
what will be corresponding relation matrix of R (for all discrete X and Y values)?
8. Apply the extension principle to the fuzzy set
where the mapping function f(x) = x2 − 3.
(a) What is the resulting image B where B = f(A)?
(b) Sketch this transformation graphically.
9. Assume that the proposition “if x is A then y is B” is given where A and B are fuzzy sets:
Given a fact expressed by the proposition “x is A*,” where
derive the conclusion in the form “y is B*” using the generalized modus ponens inference rule.
10. Solve Problem number 9 by using
11. The test scores for the three students are given in the following table:
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