In the field of

artificial intelligence Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech re ...

, neuro-fuzzy refers to combinations of

artificial neural network Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains. An ANN is based on a collection of connected unit ...

s and

fuzzy logic Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely ...

Overview

Neuro-fuzzy hybridization results in a

hybrid intelligent system Hybrid intelligent system denotes a software system which employs, in parallel, a combination of methods and techniques from artificial intelligence subfields, such as: * Neuro-symbolic systems * Neuro-fuzzy systems * Hybrid connectionist-symbolic ...

that these two techniques by combining the human-like reasoning style of fuzzy systems with the learning and

connectionist Connectionism refers to both an approach in the field of cognitive science that hopes to explain mind, mental phenomena using artificial neural networks (ANN) and to a wide range of techniques and algorithms using ANNs in the context of artificial ...

structure of neural networks. Neuro-fuzzy hybridization is widely termed as fuzzy neural network (FNN) or neuro-fuzzy system (NFS) in the literature. Neuro-fuzzy system (the more popular term is used henceforth) incorporates the human-like reasoning style of fuzzy systems through the use of

fuzzy set In mathematics, fuzzy sets (a.k.a. uncertain sets) are sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh in 1965 as an extension of the classical notion of set. At the same time, defined a ...

s and a linguistic model consisting of a set of IF-THEN fuzzy rules. The main strength of neuro-fuzzy systems is that they are

universal approximator In the mathematical theory of artificial neural networks, universal approximation theorems are results that establish the density of an algorithmically generated class of functions within a given function space of interest. Typically, these result ...

s with the ability to solicit interpretable IF-THEN rules. The strength of neuro-fuzzy systems involves two contradictory requirements in fuzzy modeling: interpretability versus accuracy. In practice, one of the two properties prevails. The neuro-fuzzy 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 Takagi-Sugeno-Kang (TSK) model. Although generally assumed to be the realization of a

fuzzy system A fuzzy control system is a control system based on fuzzy logic—a mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in contrast to classical or digital logic, w ...

through

networks, this term is also used to describe some other configurations including: *Deriving

fuzzy rule Fuzzy rules are used within fuzzy logic systems to infer an output based on input variables. Modus ponens and modus tollens are the most important rules of inference. A modus ponens rule is in the form :Premise: ''x is A'' :Implication: ''IF x is ...

s from trained RBF networks. *

Fuzzy logic Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely ...

based tuning of

neural network A neural network is a network or circuit of biological neurons, or, in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus, a neural network is either a biological neural network, made up of biological ...

training parameters. *Fuzzy logic criteria for increasing a network size. *Realising fuzzy

membership function In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all other elements to zero. That is, if is a subset of some set , one has \mathbf_(x)=1 if x ...

through clustering algorithms in

unsupervised learning Unsupervised learning is a type of algorithm that learns patterns from untagged data. The hope is that through mimicry, which is an important mode of learning in people, the machine is forced to build a concise representation of its world and t ...

in SOMs and

neural networks A neural network is a network or circuit of biological neurons, or, in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus, a neural network is either a biological neural network, made up of biological ...

. *Representing

fuzzification In mathematics, fuzzy sets (a.k.a. uncertain sets) are sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh in 1965 as an extension of the classical notion of set. At the same time, defined ...

, fuzzy inference and

defuzzification Defuzzification is the process of producing a quantifiable result in crisp logic, given fuzzy sets and corresponding membership degrees. It is the process that maps a fuzzy set to a crisp set. It is typically needed in fuzzy control systems. The ...

through multi-layers feed-forward

networks. It must be pointed out that interpretability of the Mamdani-type neuro-fuzzy systems can be lost. To improve the interpretability of neuro-fuzzy systems, certain measures must be taken, wherein important aspects of interpretability of neuro-fuzzy systems are also discussed. A recent research line addresses the

data stream mining Data Stream Mining (also known as stream learning) is the process of extracting knowledge structures from continuous, rapid data records. A data stream is an ordered sequence of instances that in many applications of data stream mining can be read o ...

case, where neuro-fuzzy systems are sequentially updated with new incoming samples on demand and on-the-fly. Thereby, system updates not only include a recursive adaptation of model parameters, but also a dynamic evolution and pruning of model components (neurons, rules), in order to handle

concept drift In predictive analytics and machine learning, concept drift means that the statistical properties of the target variable, which the model is trying to predict, change over time in unforeseen ways. This causes problems because the predictions become ...

and dynamically changing system behavior adequately and to keep the systems/models "up-to-date" anytime. Comprehensive surveys of various evolving neuro-fuzzy systems approaches can be found in and.

Pseudo outer-product based fuzzy neural networks

Pseudo outer product-based fuzzy neural networks (POPFNN) are a family of neuro-fuzzy systems that are based on the linguistic fuzzy model. Three members of POPFNN exist in the literature: *POPFNN-AARS(S), which is based on the Approximate Analogical Reasoning Scheme *POPFNN-CRI(S), which is based on commonly accepted fuzzy Compositional Rule of InferenceAng, K. K., Quek, C., & Pasquier, M. (2003). "POPFNN-CRI(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), 838-849. *POPFNN-TVR, which is based on Truth Value Restriction The "POPFNN" architecture is a five-layer

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 fine-tuning Various fuzzy membership generation

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...

s 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.

Notes

References

*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, , Chapter 3, pp. 53–83, 2005
information on publisher's site
*Ang, K. K., & Quek, C. (2005). "RSPOP: Rough Set-Based Pseudo Outer-Product Fuzzy Rule Identification Algorithm". ''Neural Computation'', 17(1), 205-243. *Kosko, Bart (1992). ''Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence''. Englewood Cliffs, NJ: Prentice Hall. {{ISBN, 0-13-611435-0. *Lin, C.-T., & Lee, C. S. G. (1996). ''Neural Fuzzy Systems: A Neuro-Fuzzy Synergism to Intelligent Systems''. Upper Saddle River, NJ: Prentice Hall. *A. Bastian, J. Gasós (1996): "Selection of input variables for model identification of static nonlinear systems", Journal of Intelligent and Robotic Systems, Vol. 16, pp. 185–207. *Quek, C., & Zhou, R. W. (2001). "The POP learning algorithms: reducing work in identifying fuzzy rules." ''Neural Networks'', 14(10), 1431-1445.

External links

Fuzzy logic Neural networks