Just one more thing to Mr. Ayman answer. The membership of each element to every cluster is restricted between 0 and 1 and the total sum of membership values of one element to all cluster must be equal to 1.

You can also say that K-means is a hard clustering while C-means is soft one but both are still unsupervised.

I have a bit different opinion on the above answers. We have families of c-means algorithms, not only fuzzy c-means. These are intuitionistic fuzzy c-means, rough c-means, rough fuzzy c-means, rough intuitionistic fuzzy c-means; all their kernelised versions, possibilistic versions, possibilistic kernelised versions and so on.

So, how can we explain all these?

Dear Mr. Tripathy,

       All these are modified versions of the mother FCM algorithm. 

Generally, you can modify FCM algorithm in different ways e.g. the membership function or distance metric used or even the initialization.

As you mentioned above kernalized versions are a modification to replace the Euclidean distance. Possibilitic versions allow the sum of membership values not to be restricted to 1 and so on. But the main idea is optimizing the quadratic objective function with respect to some constraints are still dominant and consequently the update of the membership function and cluster centers.

Regards

Actually, there is no strict distinction between k-means and c-means recently. We can look at Google Scholar and use search for “fuzzy k-means” and "fuzzy c-means", there are 57900 and 74700 results respectively.

Join this discussion for more information:

http://stackoverflow.com/questions/2345903/whats-is-the-difference-between-k-means-and-fuzzy-c-means-objective-function

Can I apply the C-means in "soft set theory"?

There are some clustering algorithms using soft sets and variants available in the literature. You can find out.

k-means clustering and c-means clustering  both is same, here k,c means number of clusters.