an Introduction to Nave Set Theory And Its Applications

Since its inception 20 years ago the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of this theory can be found in artificial intelligence, computer science, control engineering, decision theory, expert systems, logic, management science, operations research, pattern recognition, robotics and others. Theoretical advances have been made in many directions. In fact it seems extremely difficult for a newcomer to the field or for somebody who wants to apply fuzzy set theory to his problems to recognize properly the present "state of the art." Therefore, many applications use fuzzy set theory on a much more elementary level than appropriate and necessary. On the other hand, theoretical publications are already so specialized and assume such a background in fuzzy set theory that they are hard to understand.

Fuzzy Set Theory and Advanced Mathematical Applications contains contributions by many of the leading experts in the field, including coverage of the mathematical foundations of the theory, decision making and systems science, and recent developments in fuzzy neural control. The book supplies a readable, practical toolkit with a clear introduction to fuzzy set theory and its evolution in mathematics and new results on foundations of fuzzy set theory, decision making and systems science, and fuzzy control and neural systems. Each chapter is self-contained, providing up-to-date coverage of its subject.

The book compares neoclassical and Marxian economics and points out that both the schools of thought seek to analyze how a capitalist society functions. The authors show that the neoclassical economics vindicates capitalism and prescribes policies that further the interest of the rich (giant capitalists), who own most of the non-human productive resources of the economy, whereas Marxian analysis yields the result that a capitalist society is exploitative and crisis-prone. Marxian economics also suggests that the class struggle inherent in a capitalist society will eventually transform it into an equal, just and humane socialist society.