ANFIS stands for Adaptive Neuro-Fuzzy Inference System. There is a Toolbox in Matlab with lots of help sand demos.
For example start running a demo program called gasdemo.m This demo teaches how fuel consumption (MPG) for automobiles, using data from previously recorded observations, can be predicted using ANFIS.
A nice tutorial is provided by Heikki Koivo (2000): ANFIS (Adaptive Neuro-Fuzzy Inference System).
The best method for learning in presence of missing values reminds me of Hop Field Neural networks[HNN] which is unsupervised recurrent machine learning algorithm using Hebbian theory. It works on the concept of auto associative memory just like human brain where a significant part of the input data is enough to recall the input pattern.
For example :
If you train a HNN with human faces and during testing if you provide a face with goggles(missing or replaced values for eyes), still the HNN recalls the training pattern.
I recommend distance-based methods like k nearest neighbors method. They cope well with missing features. When some features are missing you simple calculate distance omitting them. And you construct local classifier/aproximator based on the nearest points.
Neural networks, neuro-fuzzy systems, linear regression, Partial Least Squares regression, LASSO and elastic net need complete input information (all features) in my opinion.