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While most of the rough-fuzzy hybridization efforts are focused on classi cation, such hybridization is nding increasing popularity in neurocomputing. Use of rough set theory in neurocomputing is relatively recent, when in 1996 Lingras [203,204] showed how upper and lower bounds of ranges of numbers may be able to reduce training time and improve prediction performance. Lingras [205] also showed how rough neurons can be combined with neo-fuzzy neurons. A slightly different knowledge-based approach can be found in a book by Pal and Mitra [257], where they report the usefulness of rough and fuzzy hybridization in knowledge-based networks. Han et al. [122] used a combination of rough-fuzzy neural computing for classifying faults in high voltage power systems. They also showed how the combination of rough and fuzzy sets compares
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favorably with fuzzy neural computing. Pal et al. [259] used an innovative combination of multiple technologies including rough sets, fuzzy sets, neurocomputing, and genetic algorithms that provided accelerated training and a compact network suitable for generating a minimum number of rules with high certainty values. Zhang [413] combined the logical view of rough set theory with fuzzy neurocomputing. Rough set theory was used to reduce the rule set in the initial fuzzy system by eliminating inconsistent and redundant rules. The resulting rule set is used to create and train a simple fuzzy neural network. A similar hybridization can also be found in [142], where particle swarm optimization is used to re ne network parameters. The traditional rough set strength of rule set management was combined with neuro-fuzzy systems by [6] for time series prediction based on actual stock market data. The proposed model creates rules with reasonable interpretability and leads to higher yields. The use of upper and lower bounds of numeric ranges is also shown to be effective in classi cation of multi-spectral images in [226], where a rough-fuzzy Hop eld net (RFHN) is proposed. The approach used upper and lower bounds of gray levels captured from a training vector in multi-spectral images instead of all the information in the image. The resulting RFHN reduces training time because of the use of 2/N pixels for an N -dimensional multi-spectral image. The resulting classi cation is also shown to be an improvement over the conventional approach. A similar improvement in performance with the use of rough-fuzzy neural networks over fuzzy neural networks was reported in [98] for prediction of short-term electricity load forecasting. They also used genetic algorithms for the selection of the best set of inputs for the prediction. The application of rough-fuzzy neurocomputing continues to diversify as indicated by the rough-fuzzy neural network controller used by [52] for wastewater management.
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There is a 15-year history of hybridization of fuzzy and genetic algorithms (GAs). The rst 10-year history of such hybridization is reported in [61]. Hybridization of GAs with rough set theory was rst based on lower and upper bounds of numeric ranges in the form of rough genetic algorithms in 1998 [206]. Another hybridization between GAs and rough set theory used rough sets representation in the genetic encoding [210] for creating rough set representations of clusters. Mitra and Mitra [233] proposed a hybrid decision support system for detecting the different stages of cervical cancer. Hybridization included the evolution of knowledge-based subnetwork modules with GAs using rough set theory and the ID3 algorithm. Genetic algorithms have been used with hybridized rough and fuzzy neural research by a number of authors. For example, [98] used GAs for selecting the best set of inputs for rough-fuzzy neurocomputing. Similarly [259] used GAs in rough and fuzzy set based rule generation. These genetic algorithms were not speci cally extended based on either rough or fuzzy set theory. One example of
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