anfis-pytorch:使用pyTorch框架实现ANFIS

# ANFIS in pyTorch # This is an implementation of the ANFIS system using pyTorch. ### ANFIS ANFIS is a way of presenting a fuzzy inference system (FIS) as a series of numeric layers so that it can be trained like a neural net. The canonical reference is the original paper by [Jyh-Shing Roger Jang](http://mirlab.org/jang/): * Jang, J.-S.R. (1993). "ANFIS: adaptive-network-based fuzzy inference system". IEEE Transactions on Systems, Man and Cybernetics. 23 (3): 665–685. doi:10.1109/21.256541 Note that it assumes a Takagi Sugeno Kang (TSK) style of defuzzification rather than the more usual Mamdani style. ### Background: other implementations The original C code from Jang that implements the ANFIS system, along with is test cases, is available from [a repository at CMU](https://www.cs.cmu.edu/Groups/AI/areas/fuzzy/systems/anfis/). The version most people seem to use is the [ANFIS library for Matlab](https://www.mathworks.com/help/fuzzy/anfis.html). Their [documentation](https://www.mathworks.com/help/fuzzy/neuro-adaptive-learning-and-anfis.html) is quite helpful for understanding how ANFIS works, even if you don't use Matlab. There's an implementation for the R language by Cristobal Fresno and Elmer A. Fernandez of the [BioScience Data Mining Group](http://www.bdmg.com.ar/?page_id=176) in Argentina (that URL seems a bit unstable). Again, their documentation is very helpful, particularly the "ANFIS vignette" report that comes with the distribution (I've put a [local copy](./Anfis-vignette.pdf) here). It shows how to run the system using examples from Jang's paper, and gives some of the results. I also found a re-implementation of this R code in Python [anfis](https://github.com/twmeggs/anfis) by Tim Meggs that was helpful in understanding the original R code. ### Navigation The ANFIS framework is mainly in three files: * [anfis.py](./anfis.py) This is where the layers of the ANFIS system are defined as Torch modules. * [membership.py](./membership.py) At the moment I only have Bell and Gaussian membership functions, but any others will go in here too. * [experimental.py](./experimental.py) The experimental infrastructure to train and test the FIS, and to plot some graphs etc. There are then some runnable examples: * [jang_examples.py](./jang_examples.py) these are four examples from Jang's paper (based partly on the details in the paper, and particle on the example folders in his source code distribution). * [vignette_examples.py](./vignette_examples.py) these are three examples from the Vignette paper. Two of these use Gaussians rather than Bell MFs. ### Installation You need to install Python and PyTorch, nothing special. I'm using [Python 3.6.5](https://www.python.org/downloads/), the [Anaconda 4.6.11](https://www.anaconda.com/distribution/) distribution and [PyTorch](https://pytorch.org) version 1.0.1. ### Author ### * [James Power](http://www.cs.nuim.ie/~jpower/), Maynooth University.