Showing papers by "Zdzisław Pawlak published in 1991"

Rough Sets: Theoretical Aspects of Reasoning about Data

Abstract: I. Theoretical Foundations.- 1. Knowledge.- 1.1. Introduction.- 1.2. Knowledge and Classification.- 1.3. Knowledge Base.- 1.4. Equivalence, Generalization and Specialization of Knowledge.- Summary.- Exercises.- References.- 2. Imprecise Categories, Approximations and Rough Sets.- 2.1. Introduction.- 2.2. Rough Sets.- 2.3. Approximations of Set.- 2.4. Properties of Approximations.- 2.5. Approximations and Membership Relation.- 2.6. Numerical Characterization of Imprecision.- 2.7. Topological Characterization of Imprecision.- 2.8. Approximation of Classifications.- 2.9. Rough Equality of Sets.- 2.10. Rough Inclusion of Sets.- Summary.- Exercises.- References.- 3. Reduction of Knowledge.- 3.1. Introduction.- 3.2. Reduct and Core of Knowledge.- 3.3. Relative Reduct and Relative Core of Knowledge.- 3.4. Reduction of Categories.- 3.5. Relative Reduct and Core of Categories.- Summary.- Exercises.- References.- 4. Dependencies in Knowledge Base.- 4.1. Introduction.- 4.2. Dependency of Knowledge.- 4.3. Partial Dependency of Knowledge.- Summary.- Exercises.- References.- 5. Knowledge Representation.- 5.1. Introduction.- 5.2. Examples.- 5.3. Formal Definition.- 5.4. Significance of Attributes.- 5.5. Discernibility Matrix.- Summary.- Exercises.- References.- 6. Decision Tables.- 6.1. Introduction.- 6.2. Formal Definition and Some Properties.- 6.3. Simplification of Decision Tables.- Summary.- Exercises.- References.- 7. Reasoning about Knowledge.- 7.1. Introduction.- 7.2. Language of Decision Logic.- 7.3. Semantics of Decision Logic Language.- 7.4. Deduction in Decision Logic.- 7.5. Normal Forms.- 7.6. Decision Rules and Decision Algorithms.- 7.7. Truth and Indiscernibility.- 7.8. Dependency of Attributes.- 7.9. Reduction of Consistent Algorithms.- 7.10. Reduction of Inconsistent Algorithms.- 7.11. Reduction of Decision Rules.- 7.12. Minimization of Decision Algorithms.- Summary.- Exercises.- References.- II. Applications.- 8. Decision Making.- 8.1. Introduction.- 8.2. Optician's Decisions Table.- 8.3. Simplification of Decision Table.- 8.4. Decision Algorithm.- 8.5. The Case of Incomplete Information.- Summary.- Exercises.- References.- 9. Data Analysis.- 9.1. Introduction.- 9.2. Decision Table as Protocol of Observations.- 9.3. Derivation of Control Algorithms from Observation.- 9.4. Another Approach.- 9.5. The Case of Inconsistent Data.- Summary.- Exercises.- References.- 10. Dissimilarity Analysis.- 10.1. Introduction.- 10.2. The Middle East Situation.- 10.3. Beauty Contest.- 10.4. Pattern Recognition.- 10.5. Buying a Car.- Summary.- Exercises.- References.- 11. Switching Circuits.- 11.1. Introduction.- 11.2. Minimization of Partially Defined Switching Functions.- 11.3. Multiple-Output Switching Functions.- Summary.- Exercises.- References.- 12. Machine Learning.- 12.1. Introduction.- 12.2. Learning From Examples.- 12.3. The Case of an Imperfect Teacher.- 12.4. Inductive Learning.- Summary.- Exercises.- References.

Reasoning about Knowledge

Abstract: The concept of the rough set has inspired a variety of logical research (cf. Jian-Ming et al. (1991), Konikowska (1987), Nakamura et al. (1988), Orlowska (1983, 1985a,b,c, 1986, 1987a,b, 1988a,b, 1989, 1990), Pawlak (1987), Rasiowa et al. (1985, 1986a,b), Rauszer (1985, 1986), Szczerba (1987a,b), Vakarelov (1981, 1989, 1991a,b,c), Wasilewska (1988a,b,c, 1989a,b,c) and others). Most of the above mentioned logical research has been directed to create deductive logical tools to deal with approximate (deductive) reasoning.

Imprecise Categories, Approximations and Rough Sets

Abstract: Fundamental concepts in the proposed theory of knowledge are classifications and categories. In fact, categories are features (i.e. subsets) of objects which can be worded using knowledge available in a given knowledge base. Certainly some categories can be definable in one knowledge base but undefinable in another one. Thus, if a category is not definable in a given knowledge base, the question arises whether it can be defined “approximately” in the knowledge base. In other words, we want to address here the central point of our approach, the vague categories.

Reduction of Knowledge

Abstract: A fundamental problem we are going to address in this section is whether the whole knowledge is always necessary to define some categories available in the knowledge considered. This problem arises in many practical applications and will be referred to as knowledge reduction. Its significance will be clearly seen in the second part of the book, where various applications are discussed.

Dependencies in Knowledge Base

Abstract: Theorizing, next to classification, is the second most important aspect when drawing inferences about the world. Essentially, developing theories is based on discovering inference rules of the form “if … then … ”. (Sometimes the rules can describe causal relationships). In our philosophy, this aspect can be formulated as how, from a given knowledge, another knowledge can be induced.