What is a monotone dataset and monotone classification? Classification algorithms, such as k-Nearest Neighbors, are well known in machine learning area, but I faced this new expression Monotone classification and I wonder what does it stand for.

I guess that it has something to do with some peculiar characteristic of the dataset, e.g. if all the objects have growing attributes and, plotted in a 2D plane, they look as if they were gathered around the line of the function f(x) = x or something like this, but as english is not my native language, I couldn't understand the raw meaning of Monotone and Monotone classifiers, the things I read were so confusing that I don't think it is worth it to mention.

I read this:


  The evaluation of teaching courses based on surveys gathered from
  students’ opinions can be categorized as a monotonic classification
  problem if it intends to predict a final qualification that summarizes
  the general quality of the course. The students are asked to evaluate
  each course according to several aspects related to interest,
  achieving appropriate class participation, teaching resources,
  capabilities of the teacher, etc.


I would like to be able to say why these surveys behave as a monotone dataset, but no explanation fits what I have in mind about the monotone definition.
A monotone classifier is a classifier that is a monotonic function.

One reasonable definition of monotone data set is that it is a data set that is consistent with some monotone model (i.e., where there exists a monotone classifier that gets 100% accuracy).  I don't know if this is a standard definition so hopefully any text that uses that phrase would provide a definition.

Why use a monotone classifier in the setting you mention? Perhaps we have some a priori reason for believing that, all else being equal, the higher the students rate their satisfaction, the higher the quality of the course.  That amounts to a monotonicity assumption about the underlying model that relates quality to satisfaction.  If we assume that the data was generated from a monotone model, it is reasonable to try to learn a monotone classifier.  Whether this is appropriate in any particular setting depends on whether you have a reason to think that the data does come from a monotone process/model or not.