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

By Alexander Gegov

This publication provides a scientific examine at the inherent complexity in fuzzy structures, due to the massive quantity and the bad transparency of the bushy ideas. The learn makes use of a unique method for complexity administration, geared toward compressing the bushy rule base by way of removal the redundancy whereas maintaining the answer. The compression is predicated on formal equipment for presentation, manipulation, transformation and simplification of fuzzy rule bases.

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Sample text

41 A fuzzy rule base is consistent if and only if its binary relation does not contain any one-to-many mappings. 42 A fuzzy rule base is inconsistent if and only if its binary relation contains at least one one-to-many mapping. 43 A fuzzy rule base is monotonic if and only if its binary relation does not contain any many-to-one mappings. 44 A fuzzy rule base is non-monotonic if and only if its binary relation contains at least one many-to-one mapping. 9 and Eqs. 32). 9 can be derived more easily from the properties of the binary relations in Eqs.

G. the inputs i2 and i3 can be fused into a new hybrid input i4 (velocity/acceleration). In this case, the RFS will be illustrated in Fig. 6. From the two methods presented above, the one based on removal of inputs is more straightforward but it involves a higher risk as a result of the removal of the corresponding variable. On the other hand, the method based i1 (S, B) i4 (S, B) RFS Fig. 6. 6. 3 Singular Value Decomposition of Output Matrix 21 on fusion of inputs is more difficult to apply due to the necessity to justify the fusion of particular variables but it is less risky.

6. From the two methods presented above, the one based on removal of inputs is more straightforward but it involves a higher risk as a result of the removal of the corresponding variable. On the other hand, the method based i1 (S, B) i4 (S, B) RFS Fig. 6. 6. 3 Singular Value Decomposition of Output Matrix 21 on fusion of inputs is more difficult to apply due to the necessity to justify the fusion of particular variables but it is less risky. As in the case of removal and merging of linguistic values, removal and fusion of inputs is usually associated with loss or aggregation of information.

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