By Alexander Gegov
This ebook offers a scientific research at the inherent complexity in fuzzy platforms, as a result of the big quantity and the terrible transparency of the bushy ideas. The examine makes use of a unique method for complexity administration, geared toward compressing the bushy rule base via elimination the redundancy whereas conserving the answer. The compression is predicated on formal equipment for presentation, manipulation, transformation and simplification of fuzzy rule bases.
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Additional info for Complexity Management in Fuzzy Systems: A Rule Base Compression Approach
17 A fuzzy rule base is complete if and only if each row in its Boolean matrix contains at least one non-zero element. 18 A fuzzy rule base is incomplete if and only if at least one row in its Boolean matrix contains only zero elements. 19 A fuzzy rule base is exhaustive if and only if each column in its Boolean matrix contains at least one non-zero element. 20 A fuzzy rule base is non-exhaustive if and only if at least one column in its Boolean matrix contains only zero elements. 21 A fuzzy rule base is consistent if and only if each row in its Boolean matrix contains not more than one non-zero element.
The first group of equations is based on a set theoretic approach to operations on elements in Boolean matrices while the second group of equations is based on a Boolean logic approach. This specific type of duality is a reflection of the general type of duality that is known to exist between set theory and Boolean logic. The above duality facilitates the manipulation and the interpretation of fuzzy rule bases, which are presented formally. For example, a set theoretic based presentation of a fuzzy rule base can be easily converted into an equivalent Boolean logic based presentation if this conversion is expected to improve the transparency of the fuzzy rules.
G. due to time constraints on the additional observations, then we should be able to achieve at least a ‘medium’ status by means of additional observations on the outputs. Obviously, if a fuzzy rule base is initially in a ‘medium’ property status, then we should be able to achieve a ‘high’ status by means of additional observations on the inputs. 7. In this case, a transition is desirable only if it is from a lower to a higher property status although such a transition may not always be possible due to inability to make sufficient additional observations.