A basic EPS is calculated using the weighted average number of shares in issue during the period. A diluted EPS is calculated using all shares in issue and those due to be issued (e.g. under share option schemes).
A fully diluted EPS is calculated using all shares issued, due to be issued and which could be issued if all existing warrants are exercised, convertible bonds are converted to equity etc. This tends to be less commonly used because of the complexity and uncertainties involved, and the difference it makes is usually small.
If there is a lot of potential dilution through warrants and convertible exercise, then it is necessary, as a minimum to calculate the dilution that would result.
If there is uncertainty about whether the warrants (or embedded options in the convertibles) will be exercised, then it may be necessary to calculate the value market cap without dilution and deduct the option value of these securities. Doing this is likely to make most equity investors wish that companies avoided issuing such securities, so it if fortunate that it is unlikely that you will need to do this in practice — but you should be aware of the possibility so that you can spot such situations (high potential dilution, plus uncertainty about exercise) when they do arise.