 Neurofuzzy

In the field of artificial intelligence, neurofuzzy refers to combinations of artificial neural networks and fuzzy logic. Neurofuzzy was proposed by J. S. R. Jang. Neurofuzzy hybridization results in a hybrid intelligent system that synergizes these two techniques by combining the humanlike reasoning style of fuzzy systems with the learning and connectionist structure of neural networks. Neurofuzzy hybridization is widely termed as Fuzzy Neural Network (FNN) or NeuroFuzzy System (NFS) in the literature. Neurofuzzy system (the more popular term is used henceforth) incorporates the humanlike reasoning style of fuzzy systems through the use of fuzzy sets and a linguistic model consisting of a set of IFTHEN fuzzy rules. The main strength of neurofuzzy systems is that they are universal approximators with the ability to solicit interpretable IFTHEN rules.
The strength of neurofuzzy systems involves two contradictory requirements in fuzzy modeling: interpretability versus accuracy. In practice, one of the two properties prevails. The neurofuzzy in fuzzy modeling research field is divided into two areas: linguistic fuzzy modeling that is focused on interpretability, mainly the Mamdani model; and precise fuzzy modeling that is focused on accuracy, mainly the TakagiSugenoKang (TSK) model.
Although generally assumed to be the realization of a fuzzy system through connectionist networks, this term is also used to describe some other configurations including:
 Deriving fuzzy rules from trained RBF networks.
 Fuzzy logic based tuning of neural network training parameters.
 Fuzzy logic criteria for increasing a network size.
 Realising fuzzy membership function through clustering algorithms in unsupervised learning in SOMs and neural networks.
 Representing fuzzification, fuzzy inference and defuzzification through multilayers feedforward connectionist networks.
It must be pointed out that interpretability of the Mamdanitype neurofuzzy systems can be lost. To improve the interpretability of neurofuzzy systems, certain measures must be taken, wherein important aspects of interpretability of neurofuzzy systems are also discussed.^{[1]}
Pseudo outerproductbased fuzzy neural networks
Pseudo outerproductbased fuzzy neural networks ("POPFNN") are a family of neurofuzzy systems that are based on the linguistic fuzzy model.^{[2]}
Three members of POPFNN exist in the literature:
 POPFNNAARS(S), which is based on the Approximate Analogical Reasoning Scheme^{[3]}
 POPFNNCRI(S), which is based on commonly accepted fuzzy Compositional Rule of Inference^{[4]}
 POPFNNTVR, which is based on Truth Value Restriction
The "POPFNN" architecture is a fivelayer neural network where the layers from 1 to 5 are called: input linguistic layer, condition layer, rule layer, consequent layer, output linguistic layer. The fuzzification of the inputs and the defuzzification of the outputs are respectively performed by the input linguistic and output linguistic layers while the fuzzy inference is collectively performed by the rule, condition and consequence layers.
The learning process of POPFNN consists of three phases:
 Fuzzy membership generation
 Fuzzy rule identification
 Supervised finetuning
Various fuzzy membership generation algorithms can be used: Learning Vector Quantization (LVQ), Fuzzy Kohonen Partitioning (FKP) or Discrete Incremental Clustering (DIC). Generally, the POP algorithm and its variant LazyPOP are used to identify the fuzzy rules.
References
 ^ Y. Jin (2000). Fuzzy modeling of highdimensional systems: Complexity reduction and interpretability improvement. IEEE Transactions on Fuzzy Systems, 8(2), 212221, 2000
 ^ Zhou, R. W., & Quek, C. (1996). "POPFNN: A Pseudo Outerproduct Based Fuzzy Neural Network". Neural Networks, 9(9), 15691581.
 ^ Quek, C., & Zhou, R. W. (1999). "POPFNNAAR(S): a pseudo outerproduct based fuzzy neural network." IEEE Transactions on Systems, Man and Cybernetics, Part B, 29(6), 859870.
 ^ Ang, K. K., Quek, C., & Pasquier, M. (2003). "POPFNNCRI(S): pseudo outer product based fuzzy neural network using the compositional rule of inference and singleton fuzzifier." IEEE Transactions on Systems, Man and Cybernetics, Part B, 33(6), 838849.
 Abraham A., "Adaptation of Fuzzy Inference System Using Neural Learning, Fuzzy System Engineering: Theory and Practice", Nadia Nedjah et al. (Eds.), Studies in Fuzziness and Soft Computing, Springer Verlag Germany, ISBN 354025322X, Chapter 3, pp. 53–83, 2005. information on publisher's site.
 Ang, K. K., & Quek, C. (2005). "RSPOP: Rough SetBased Pseudo OuterProduct Fuzzy Rule Identification Algorithm". Neural Computation, 17(1), 205243.
 Kosko, Bart (1992). Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence. Englewood Cliffs, NJ: Prentice Hall. ISBN 0136114350.
 Lin, C.T., & Lee, C. S. G. (1996). Neural Fuzzy Systems: A NeuroFuzzy Synergism to Intelligent Systems. Upper Saddle River, NJ: Prentice Hall.
 Quek, C., & Zhou, R. W. (2001). "The POP learning algorithms: reducing work in identifying fuzzy rules." Neural Networks, 14(10), 14311445.
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