Evangelos Triantaphyllou - Böcker

2. Some Background Information 49 3. Definitions and Terminology 52 4. The One Clause at a Time (OCAT) Approach 54 4. 1 Data Binarization 54 4. 2 The One Clause at a Time (OCAT) Concept 58 4. 3 A Branch-and-Bound Approach for Inferring Clauses 59 4. 4 Inference of the Clauses for the Illustrative Example 62 4. 5 A Polynomial Time Heuristic for Inferring Clauses 65 5. A Guided Learning Approach 70 6. The Rejectability Graph of Two Collections of Examples 72 6. 1 The Definition of the Rej ectability Graph 72 6. 2 Properties of the Rejectability Graph 74 6. 3 On the Minimum Clique Cover of the Rej ectability Graph 76 7. Problem Decomposition 77 7. 1 Connected Components 77 7. 2 Clique Cover 78 8. An Example of Using the Rejectability Graph 79 9. Conclusions 82 References 83 Author's Biographical Statement 87 Chapter 3 AN INCREMENTAL LEARNING ALGORITHM FOR INFERRING LOGICAL RULES FROM EXAMPLES IN THE FRAMEWORK OF THE COMMON REASONING PROCESS, by X. Naidenova 89 1. Introduction 90 2. A Model of Rule-Based Logical Inference 96 2. 1 Rules Acquired from Experts or Rules of the First Type 97 2. 2 Structure of the Knowledge Base 98 2. 3 Reasoning Operations for Using Logical Rules of the First Type 100 2. 4 An Example of the Reasoning Process 102 3. Inductive Inference of Implicative Rules From Examples 103 3.

Multi-Criteria Decision Making (MCDM) has been one of the fastest growing problem areas in many disciplines. The central problem is how to evaluate a set of alternatives in terms of a number of criteria. Although this problem is very relevant in practice, there are few methods available and their quality is hard to determine. Thus, the question "Which is the best method for a given problem?" has become one of the most important and challenging ones. This is exactly what this book has as its focus and why it is important. The author extensively compares, both theoretically and empirically, real-life MCDM issues and makes the reader aware of quite a number of surprising abnormalities with some of these methods. What makes this book so different is that even though the analyses are rigorous, the results can be understood even by the non-specialist.

The importance of having ef cient and effective methods for data mining and kn- ledge discovery (DM&KD), to which the present book is devoted, grows every day and numerous such methods have been developed in recent decades. There exists a great variety of different settings for the main problem studied by data mining and knowledge discovery, and it seems that a very popular one is formulated in terms of binary attributes. In this setting, states of nature of the application area under consideration are described by Boolean vectors de ned on some attributes. That is, by data points de ned in the Boolean space of the attributes. It is postulated that there exists a partition of this space into two classes, which should be inferred as patterns on the attributes when only several data points are known, the so-called positive and negative training examples. The main problem in DM&KD is de ned as nding rules for recognizing (cl- sifying) new data points of unknown class, i. e. , deciding which of them are positive and which are negative. In other words, to infer the binary value of one more attribute, called the goal or class attribute. To solve this problem, some methods have been suggested which construct a Boolean function separating the two given sets of positive and negative training data points.

2. Some Background Information 49 3. Definitions and Terminology 52 4. The One Clause at a Time (OCAT) Approach 54 4. 1 Data Binarization 54 4. 2 The One Clause at a Time (OCAT) Concept 58 4. 3 A Branch-and-Bound Approach for Inferring Clauses 59 4. 4 Inference of the Clauses for the Illustrative Example 62 4. 5 A Polynomial Time Heuristic for Inferring Clauses 65 5. A Guided Learning Approach 70 6. The Rejectability Graph of Two Collections of Examples 72 6. 1 The Definition of the Rej ectability Graph 72 6. 2 Properties of the Rejectability Graph 74 6. 3 On the Minimum Clique Cover of the Rej ectability Graph 76 7. Problem Decomposition 77 7. 1 Connected Components 77 7. 2 Clique Cover 78 8. An Example of Using the Rejectability Graph 79 9. Conclusions 82 References 83 Author's Biographical Statement 87 Chapter 3 AN INCREMENTAL LEARNING ALGORITHM FOR INFERRING LOGICAL RULES FROM EXAMPLES IN THE FRAMEWORK OF THE COMMON REASONING PROCESS, by X. Naidenova 89 1. Introduction 90 2. A Model of Rule-Based Logical Inference 96 2. 1 Rules Acquired from Experts or Rules of the First Type 97 2. 2 Structure of the Knowledge Base 98 2. 3 Reasoning Operations for Using Logical Rules of the First Type 100 2. 4 An Example of the Reasoning Process 102 3. Inductive Inference of Implicative Rules From Examples 103 3.

Multi-Criteria Decision Making (MCDM) has been one of the fastest growing problem areas in many disciplines. The central problem is how to evaluate a set of alternatives in terms of a number of criteria. Although this problem is very relevant in practice, there are few methods available and their quality is hard to determine. Thus, the question 'Which is the best method for a given problem?' has become one of the most important and challenging ones. This is exactly what this book has as its focus and why it is important. The author extensively compares, both theoretically and empirically, real-life MCDM issues and makes the reader aware of quite a number of surprising 'abnormalities' with some of these methods. What makes this book so valuable and different is that even though the analyses are rigorous, the results can be understood even by the non-specialist. Audience: Researchers, practitioners, and students; it can be used as a textbook for senior undergraduate or graduate courses in business and engineering.

The importance of having ef cient and effective methods for data mining and kn- ledge discovery (DM&KD), to which the present book is devoted, grows every day and numerous such methods have been developed in recent decades. There exists a great variety of different settings for the main problem studied by data mining and knowledge discovery, and it seems that a very popular one is formulated in terms of binary attributes. In this setting, states of nature of the application area under consideration are described by Boolean vectors de ned on some attributes. That is, by data points de ned in the Boolean space of the attributes. It is postulated that there exists a partition of this space into two classes, which should be inferred as patterns on the attributes when only several data points are known, the so-called positive and negative training examples. The main problem in DM&KD is de ned as nding rules for recognizing (cl- sifying) new data points of unknown class, i. e. , deciding which of them are positive and which are negative. In other words, to infer the binary value of one more attribute, called the goal or class attribute. To solve this problem, some methods have been suggested which construct a Boolean function separating the two given sets of positive and negative training data points.