Neuro-fuzzy hybridization is the oldest and most popular methodology in soft computing (Mitra & Hayashi, 2000). Neuro-fuzzy hybridization is known as Fuzzy Neural Networks, or Neuro-Fuzzy Systems (NFS) in the literature (Lin & Lee, 1996; Mitra & Hayashi, 2000). NFS is capable of abstracting a fuzzy model from given numerical examples using neural learning techniques to formulate accurate predictions on unseen samples. The fuzzy model incorporates the human-like style of fuzzy reasoning through a linguistic model that comprises of if-then fuzzy rules and linguistic terms described by membership functions. Hence, the main strength of NFS in modeling data is universal approximation (Tikk, Kóczy, & Gedeon, 2003) with the ability to solicit interpretable if-then fuzzy rules (Guillaume, 2001). However, modeling data using NFS involves the contradictory requirements of interpretability versus accuracy. Prevailingly, NFS that focused on accuracy employed optimization which resulted in membership functions that derailed from human-interpretable linguistic terms, or employed large number of if-then fuzzy rules on high-dimensional data that exceeded human level interpretation. This article presents a novel hybrid intelligent Rough set-based Neuro-Fuzzy System (RNFS). RNFS synergizes the sound concept of knowledge reduction from rough set theory with NFS. RNFS reinforces the strength of NFS by employing rough set-based techniques to perform attribute and rule reductions, thereby improving the interpretability without compromising the accuracy of the abstracted fuzzy model.
The core problem in soft computing is about bridging the gap between subjective knowledge and objective data (Dubois & Prade, 1998). There are two approaches of addressing this problem; namely, modeling data in which a function is built to accurately mimic the data, and abstracting data in which a system is built to produce articulated knowledge preferably in natural language form (Dubois & Prade, 1998). The emphasis of the former is on the ability to reproduce what has been observed. Neural networks with their prominent learning capabilities inspired from biological systems are highly suitable in this approach. On the other hand, the emphasis of the latter is on the ability to explain the data in a human interpretable way. Fuzzy systems with the ability of modeling linguistic terms that are expressions of human language are likewise highly effective in this approach. In fuzzy systems, linguistic expressions are formulated from explicit knowledge in the form of if-then fuzzy rules where the linguistic terms of the antecedents and consequents are fuzzy sets. However, the parameters of these linguistic expressions are sometimes difficult to specify and have to be manually tuned. In contrast, although neural networks are capable of learning from data, they are black box models and thus soliciting knowledge from neural networks is not a straightforward task. Hence, a neural network is capable of modeling data, but a user cannot learn from it. On the other hand, a user can learn from a fuzzy system, but it is not capable of learning from data.
Neuro-fuzzy hybridization synergizes these two techniques by combining the human-like reasoning style of fuzzy systems with the learning and connectionist structure of neural networks. Thus, Neuro-Fuzzy Systems (NFS) are gray-box models that are capable of abstracting a fuzzy model from given numerical examples using neural learning techniques. Hence, a Neuro-Fuzzy System learns and at the same time, a user can learn from it as well. However, the use of NFS in abstracting data involves two contradictory requirements in fuzzy modeling: interpretability versus accuracy (Casillas, Cordón, Herrera, & Magdalena, 2003). In practice, only one of the two properties prevails. Hence, they can be classified as linguistic NFS that are focused on interpretability, mainly using the Mamdani model (Mamdani & Assilian, 1975); and precise NFS that are focused on accuracy, mainly using the Takagi-Sugeno-Kang model (Takagi & Sugeno, 1985).
Key Terms in this Chapter
Knowledge Reduction: Knowledge reduction in rough set theory comprises of attribute reduction and partial attribute reduction.
Rough Set-Based Neuro Fuzzy System: A hybrid intelligent system that synergizes the sound concept of knowledge reduction in rough set theory with neuro-fuzzy systems.
Rough Set: A rough set is a formal approximation of a crisp set in terms of a pair of sets that give the lower and upper approximation of the original set
Attribute Reduction: The process whereby dispensable attributes are removed from the knowledge while maintaining knowledge consistency.
Rule Reduction: The process of partial attribute reduction whereby dispensable attributes from certain rules of the knowledge is removed while maintaining knowledge consistency.
Fuzzy System: A system whose variables range over states that are fuzzy sets. A fuzzy system is capable of modelling the linguistic terms that are expressions of human language.
Neuro-Fuzzy System: A hybrid intelligent system that synergizes the human-like reasoning style of fuzzy systems with the learning and connectionist structure of neural networks.
Neural Network: A network of many simple processors called units or neurons. A neural network is capable of learning the nonlinear relationships in data.