By Alexander Gegov
This e-book offers a scientific learn at the inherent complexity in fuzzy platforms, caused by the massive quantity and the negative transparency of the bushy principles. The examine makes use of a unique method for complexity administration, geared toward compressing the bushy rule base via removal 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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Extra info for Complexity Management in Fuzzy Systems: A Rule Base Compression Approach
With all possible permutations of linguistic values of inputs available, although that may not always be the case. As far as the permutations of linguistic values of the outputs are concerned, it is fairly common for some of them to be missing and therefore a fuzzy rule base is likely to be non-exhaustive. e. with each available permutation of linguistic values of inputs yielding only one permutation of linguistic values of outputs. And finally, it is quite common for some permutations of linguistic values of outputs to be yielded by more than one permutation of linguistic values of inputs and therefore a fuzzy rule base is likely to be non-monotonic.
E. with each available permutation of linguistic values of inputs yielding only one permutation of linguistic values of outputs. And finally, it is quite common for some permutations of linguistic values of outputs to be yielded by more than one permutation of linguistic values of inputs and therefore a fuzzy rule base is likely to be non-monotonic. Theoretically speaking, there are 16 possible permutations of Boolean values of properties for a fuzzy rule bases but not all of these permutations are equally desirable.
14 An element in a Boolean square matrix is on-diagonal if and only if its row and column index are the same. 15 An element in a Boolean square matrix is off-diagonal if and only if its row and column index are different. 16 An identity Boolean matrix is a square homogenous Boolean matrix all of whose on-diagonal elements are equal to 1 and all of whose off-diagonal elements are equal 0. The basic operations that can be applied to elements of Boolean matrices are ‘addition’ and ‘multiplication’.