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The second reason for the unreliability of inference in AI systems, apart from imperfection of knowledge, is imperfection of the system of notions which is used for a description of the real (physical) world.
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This results from the more complex subject of research in these branches.
Formal definitions of fuzzy set and rough set theories are contained in Appendix J.
A membership function for a set determines this set.
Fuzzy logic is an example of multi-valued logic with an infinite number of values, which has been introduced by Polish logician and mathematician Jan Łukasiewicz.
A formal definition of the function T for logical operators is contained in Appendix J.
If the reader has omitted Chap. 9, the rest of this section may be difficult to understand.
Ebrahim Mamdani—a professor of electrical engineering and computer science at Imperial College, London. A designer of the first fuzzy controller. His work mainly concerns fuzzy logic.
A fuzzy rule is not applicable at a reasoning cycle if its degree of fulfillment equals 0.
Rough set theory is discussed in this book only from the AI point of view. However, this theory is applied much more broadly and it is interpreted in a more general way in computer science.
Passenger cars are objects.
A set of attributes means a set of attributes together with their domains.
In fact, in rough set theory these two cars are not distinguishable. In order to distinguish between them one should introduce an additional attribute, e.g., the registration number. However, in the context of our problem this is not necessary.
- Defining Vague Notions in Knowledge-Based Systems
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