# Download Complexity Management in Fuzzy Systems: A Rule Base by Alexander Gegov PDF

By Alexander Gegov

This ebook offers a scientific research at the inherent complexity in fuzzy platforms, caused by the big quantity and the negative transparency of the bushy ideas. The learn makes use of a unique method for complexity administration, aimed toward compressing the bushy rule base via removal the redundancy whereas maintaining the answer. The compression relies on formal equipment for presentation, manipulation, transformation and simplification of fuzzy rule bases.

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Extra resources for Complexity Management in Fuzzy Systems: A Rule Base Compression Approach

Example text

In this case, the row index of an element in A*B is the same as the index of the corresponding row from the matrix A, whereas the column index of an element in A*B is the same as the index of the corresponding column from the matrix B. e. the number of columns in the first matrix must be equal to the number of rows in the second matrix. The only difference is that instead of applying the arithmetic ‘addition’ and ‘multiplication’ operations on elements of the matrices, we apply the ‘maximum’ and ‘minimum’ operations, respectively.

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.

3 Presentation of Rule Bases by Boolean Matrices 43 4. Label the columns of the Boolean matrix with the sorted permutations of linguistic values of outputs. 5. Go through all the elements of the Boolean matrix and set each element equal to 1 or 0 using steps 6 and 7. 6. If an element of the Boolean matrix reflects an existing mapping from an input onto an output permutation, set it equal to 1. 7. If an element of the Boolean matrix reflects a non-existing mapping from an input onto an output permutation, set it equal to 0.