Rough sets. Theoretical aspects of reasoning about data.

*(English)*Zbl 0758.68054
Theory and Decision Library. Series D: System Theory, Knowledge Engineering and Problem Solving. 9. Dordrecht: Kluwer Academic Publishers Group. VIII, 229 p. (1991).

A formal framework for the automatical transformation of data into knowledge is proposed. In this context knowledge is understood as summarized and organized data.

The approach is based on the concept of rough sets, which allows to go from refined universes of discourse to coarser ones, to describe a coarser granularity of knowledge. In rough sets some objects are indiscernible. In contrast fuzzy sets try to formalize the vagueness of many common concepts. Vagueness and indiscernibility are different aspects of imperfect knowledge, therefore rough sets and fuzzy sets each have their own domain of application.

Mathematically, the theory of rough sets is very simple: only finite sets and equivalence relations are required. But as the book shown, the theory can be applied in many fields.

The book consists of two parts: the seven chapters of the first part contain theoretical foundations, the second part presents applications in five chapters. The chapters are: Part I: 1. Knowledge (its relation to classification, knowledge bases, equivalence, generalization and specialization of knowledge), 2. Imprecise categories, approximations and rough sets, 3. Reduction of knowledge, 4. Dependencies in knowledge base, 5. Knowledge representation, 6. Decision tables, 7. Reasoning about knowledge. Part II (Applications) contains the chapters 8. Decision making, 9. Data analysis, 10. Dissimilarity analysis, 11. Switching circuits, 12. Machine learning.

Each chapter contains many examples, a summary, exercises and a list of references. Therefore, the book is easy to understand. It should be useful to researchers, practitioners and students in many areas.

The approach is based on the concept of rough sets, which allows to go from refined universes of discourse to coarser ones, to describe a coarser granularity of knowledge. In rough sets some objects are indiscernible. In contrast fuzzy sets try to formalize the vagueness of many common concepts. Vagueness and indiscernibility are different aspects of imperfect knowledge, therefore rough sets and fuzzy sets each have their own domain of application.

Mathematically, the theory of rough sets is very simple: only finite sets and equivalence relations are required. But as the book shown, the theory can be applied in many fields.

The book consists of two parts: the seven chapters of the first part contain theoretical foundations, the second part presents applications in five chapters. The chapters are: Part I: 1. Knowledge (its relation to classification, knowledge bases, equivalence, generalization and specialization of knowledge), 2. Imprecise categories, approximations and rough sets, 3. Reduction of knowledge, 4. Dependencies in knowledge base, 5. Knowledge representation, 6. Decision tables, 7. Reasoning about knowledge. Part II (Applications) contains the chapters 8. Decision making, 9. Data analysis, 10. Dissimilarity analysis, 11. Switching circuits, 12. Machine learning.

Each chapter contains many examples, a summary, exercises and a list of references. Therefore, the book is easy to understand. It should be useful to researchers, practitioners and students in many areas.

Reviewer: F.Lehmann (Neubiberg)