Did you take a look at:

Hand, D. J., & Till, R. J. (2001). A Simple Generalisation of the Area Under the ROC Curve for Multiple Class Classification Problems. Machine Learning, 45, 171-186.

I think it is fair to say that this is a seminal paper in the field. The method proposed therein is also available in the  R package pROC (see enclosed link).

Given that the above paper was published in 2001, several alternatives/extensions have been proposed for using ROC and the AUC in multi-class settings. I suggest you start with searching for multi-class auc using google. This will directly point you to some of these studies. 

Hope this helps.

http://www.inside-r.org/packages/cran/pROC/docs/multiclass.roc

Did you take a look at:

Hand, D. J., & Till, R. J. (2001). A Simple Generalisation of the Area Under the ROC Curve for Multiple Class Classification Problems. Machine Learning, 45, 171-186.

I think it is fair to say that this is a seminal paper in the field. The method proposed therein is also available in the  R package pROC (see enclosed link).

Given that the above paper was published in 2001, several alternatives/extensions have been proposed for using ROC and the AUC in multi-class settings. I suggest you start with searching for multi-class auc using google. This will directly point you to some of these studies. 

Hope this helps.

http://www.inside-r.org/packages/cran/pROC/docs/multiclass.roc

In the most general case, you should calculate Volume Under ROC Surface (VUS)

(see Mossman, 1999 for VUS in the 1-vs-rest three-class case)

http://mdm.sagepub.com/content/19/1/78.full.pdf+html

Can be approximated by projecting down to set of two-dimensional curves and averaging (see MAUC Hand & Till, 2001: 1-vs-1, unweighted average / Provost & Domingos, 2001: 1-vs-rest) 

Possible alternative metrics in multi-class classification problems could be 

• accuracy, of course
• logarithmic loss https://www.kaggle.com/wiki/LogarithmicLoss
• quadratic weighted kappa (https://www.kaggle.com/c/crowdflower-search-relevance/details/evaluation)
• hamming loss (https://www.kaggle.com/wiki/HammingLoss

(Plug warning) You can also use the Entropy Triangle for multiclass evaluation. It was designed as an information theoretic measure and sheds insights into the performance somehow complementary to those of AUC.

* The papers:

http://www.sciencedirect.com/science/article/pii/S0167865510001662 (original tool)

http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0084217 (more advanced performance measures, etc. And a shameful mistake in one formula! ;))

* The (matlab) tool (it works fine until Matlab R2012b: there seem to be problems with R2015a)

http://www.mathworks.com/matlabcentral/fileexchange/30914-entropy-triangle

* And you can build your own entropy plots in R with packages ggtern and entropy.

Hi...

Please check below link for creating ROC curves. You can download this software package.

https://www.medcalc.org/features/roccurves.php

Please have a look at these two papers: http://homepage.tudelft.nl/a9p19/papers/prasa_06_vuc.pdf

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.14.2427&rep=rep1&type=pdf

Since you already have the computed class-based AUCs for each classifier you can get the average for each classifier for comparison to get a general idea which classifier is the best. But you have to conduct some sort of a statistical test (e.g. students t-test) to check whether the performance of the best classifier is significantly better than others.