Neural networks are a set of algorithms inspired by the structure of the human brain’s neural network; they attempt to mimic how our brains function. Neural networks have the potential to learn any complex relationship between input and output, as they are universal function approximators.
Thanks to their exceptional performance in solving complex problems (e.g. pattern recognition, image classification, video processing, speech recognition, and natural language processing), such networks are revolutionizing AI.
Next, we have fuzzy logic. This is an AI technique that simulates human reasoning. “Fuzzy” in this context refers to a human-like ‘fuzziness’ in decision-making, i.e. including all the intermediate states between 100% true and 100% false (like mostly true, partially true, partially false, and mostly false).
Building a high-performing fuzzy system is challenging: identifying membership function and inferential rules are dependent on domain experts (human intervention). Thus, the idea arose that neural networks can be used as alternative learning algorithms for the automation and development of fuzzy systems. These systems, where neural network and fuzzy logic are used together, are known as neuro-fuzzy systems or fuzzy neural networks.
There are several ways to integrate neural networks and fuzzy logic. They are divided into three main categories:
Cooperative Neuro-Fuzzy System
In a cooperative system, the neural network and the fuzzy system work independently, as separate blocks. The neural network is used as a preprocessor, using training data to deduce membership functions and/or inferential rules. After deducing the fuzzy inferential parameters, the neural network block is taken away and only the fuzzy system block is executed. One of the major drawbacks of cooperative systems is that they lack interpretability. This is due to the black-box nature of neural networks.
Figure 1. Cooperative System 
Concurrent Neuro-Fuzzy System
In concurrent systems, the neural network and the fuzzy system work together to continuously deduce the required set of parameters. Here the objective is to improve the performance of the entire system rather than optimizing the fuzzy system. In some cases, the neural network acts as an assistant to the fuzzy system by preprocessing the inputs. In other cases, it post-processes the fuzzy system’s output. Like co-operative systems, concurrent systems are not fully interpretable due to the presence of the neural network.
Figure 2. Concurrent System 
Hybrid Neuro-Fuzzy System
In hybrid systems, the fuzzy system is a special kind of neural network. In this system, the neural network and fuzzy system no longer work as separate blocks but are one fused entity: the neural network learning algorithm is used to ascertain the parameter of the fuzzy inferential system (fuzzy rules and fuzzy sets) from input data in an iterative way.
The hybrid system can be used to generate parameters in two ways – either by entirely using input-output data or by initializing with à priori knowledge (human experts). This fusion of neural networks and fuzzy systems has the advantage of learning in a supervised way. Also, their functionality can be easily interpreted.
Hybrid neuro-fuzzy systems can be created in several ways. Popular architectures include Fuzzy Adaptive Learning Control Network (FALCON), Adaptive Network-based Fuzzy Inference System (ANFIS), Generalized Approximate Reasoning-based Intelligence Control (GARIC), Neuronal Fuzzy Controller (NEFCON), and Self-Constructing Neural Fuzzy Inference Network (SONFIN).
In this section, we discussed different ways to learn fuzzy parameters using neural networks. Data acquisition and the preprocessing of input data is essential to the improved performance of neuro-fuzzy systems. For high-performing neuro-fuzzy systems, the major requirements include fast learning, on-the-go adaptability, reduced computational expense, and achieving a global minimum for error.
Image adapted from Neuro-Fuzzy Systems: A Survey
Technical articles are published from the Absolutdata Labs group, and hail from The Absolutdata Data Science Center of Excellence. These articles also appear in BrainWave, Absolutdata’s quarterly data science digest.
Subscribe to BrainWave