Data Mining - Mehmed Kantardzic [235]
This book represents one of the first comprehensive texts on GAs. It introduces in a very systematic way most of the techniques that are, with small modifications and improvements, part of today’s approximate-optimization solutions.
Hruschka, E., R. Campello, A. Freitas, A. Carvalho, A Survey of Evolutionary Algorithms for Clustering, IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, Vol. 39, No. 2, 2009, pp. 133–155.
This paper presents a survey of evolutionary algorithms designed for clustering tasks. It tries to reflect the profile of this area by focusing more on those subjects that have been given more importance in the literature. In this context, most of the paper is devoted to partitional algorithms that look for hard clustering of data, although overlapping (i.e., soft and fuzzy) approaches are also covered in the paper. The paper ends by addressing some important issues and open questions that can be the subjects of future research.
Michalewicz, Z., Genetic Algorithms + Data Structures = Evolution Programs, Springer, Berlin, Germany, 1999.
This textbook explains the field of GAs in simple terms, and discusses the efficiency of its methods in many interesting test cases. The importance of these techniques is their applicability to many hard-optimization problems specified with large amounts of discrete data, such as the TSP, scheduling, partitioning, and control.
14
FUZZY SETS AND FUZZY LOGIC
Chapter Objectives
Explain the concept of fuzzy sets with formal interpretation in continuous and discrete domains.
Analyze the characteristics of fuzzy sets and fuzzy-set operations.
Describe the extension principle as a basic mechanism for fuzzy inferences.
Discuss the importance of linguistic imprecision and computing with them in decision-making processes.
Construct methods for multifactorial evaluation and extraction of a fuzzy rule-based model from large, numeric data sets.
Understand why fuzzy computing and fuzzy systems are an important part of data-mining technology.
In the previous chapters, a number of different methodologies for the analysis of large data sets have been discussed. Most of the approaches presented, however, assume that the data are precise, that is, they assume that we deal with exact measurements for further analysis. Historically, as reflected in classical mathematics, we commonly seek a precise and crisp description of things or events. This precision is accomplished by expressing phenomena in numeric or categorical values. But in most, if not all, real-world scenarios, we will never have totally precise values. There is always going to be a degree of uncertainty. However, classical mathematics can encounter substantial difficulties because of this fuzziness. In many real-world situations, we may say that fuzziness is reality, whereas crispness or precision is simplification and idealization. The polarity between fuzziness and precision is quite a striking contradiction in the development of modern information-processing systems. One effective means of resolving the contradiction is the fuzzy-set theory, a bridge between high precision and the high complexity of fuzziness.
14.1 FUZZY SETS
Fuzzy concepts derive from fuzzy phenomena that commonly occur in the real world. For example, rain is a common natural phenomenon that is difficult to describe precisely since it can rain with varying intensity, anywhere from a light shower to a torrential downpour. Since the word rain does not adequately or precisely describe the wide variations in the amount and intensity of any rain event, “rain” is considered a fuzzy phenomenon.
Often, the concepts formed in the human brain for perceiving, recognizing, and categorizing natural phenomena are also fuzzy. The boundaries of these concepts are vague. Therefore, the judging and reasoning that emerges from them are also fuzzy. For instance, “rain” might be classified as “light rain,” “moderate rain,” and “heavy rain” in order to describe the degree