I used to play a lot of Bridge, where the Swiss format for tournaments is quite common and popular. A quick, albeit not very thorough, search of the forums suggests that it hasn't been used in fpl before, so I thought it was time to give it a go.
What is the Swiss Format?
The Swiss Format is usually used when you have too many entrants for a Round-Robin League to be practical and you don't want a Knock Out Cup because that would mean sending most of your entrants home after just a few matches. The Swiss is a little bit of both. In the first round, matches are drawn either randomly or by some established ranking. The winners then advance to play other winners in the 2nd round (like in a Knock Out Cup), but the losers also continue to play against other losers. This continues in subsequent rounds with competitors being matched with an opponent with a similar W-D-L record, but you can't play the same opponent more than once. By the end of the rounds you usually finish up with the those at the top of the standings having played most of the opponents around them (like in a Round-Robin). The format is popular because the stronger teams/players tend to get thrown together early on, giving everyone a chance of keeping up, and a bad result or two doesn't necessarily wreck your chances of winning the competition.
Rules for the FISO Swiss Cup
The Swiss Cup shall consist of 9 Rounds followed by a Semi-Final and a Final. In each round you will play against a single opponent for 4 GWs. Each GW the difference in fpl points scored (after transfer cost is deducted) shall be converted into Match Points (MP), according to the following table, which are then awarded to the team with the higher score.

At the end of the 4 GWs the MPs are added up to find the Round Winner and the margin of victory is converted to Victory Points (VP) as follows:

In the first round the fixtures are arranged according to fpl ID (That's random enough and if there is a tendency for the better managers to have earlier IDs then that is in keeping with the philosophy of the Swiss Format). In the subsequent rounds teams are matched with opponents with a similar Victory Point score who they haven't played before.
If there are an odd number of teams then one of the lowest ranked teams will play against an AVERAGE opponent which scores the fpl average every GW.
An example, just in case it's not all clear:
In GW1 Player A scores a disappointing 37 points in fpl. His opponent, Player B, scores 75 points. This is a difference of 38 points, which converts into 12 Match Points awarded to Player B. In the next 3 GWs Player A scores 54, 75 and 62 points, while Player B scores 41, 68 and 42 points. The scores for Round 1 are now complete as follows:

Player A has a total of 18MPs against Player B's 12. This 6 MP margin of victory converts to 13 VP for Player A and 7 VP for Player B.
In Round 2 Player A will go on to play another opponent with 13 VP and Player B one with 7 VP.
MPs and VPs - What's the Point?
Match Points are a way of flattening out the scores a little so that a big result in one GW (say due to a captain pick or playing a chip) is less likely to result in an insurmountable lead, rendering the other 3 GWs almost irrelevant. Good, consistent scoring over several GWs will often score more MPs than getting the same score all in one GW.
Victory Points provide a further flattening of the scores, but they also normalise the field as each Round has a share of 20 VP. It sets an upper limit on how much of an advantage can be gained in a one-sided match.
The Finals
The following Tie-breakers are used to determine the standings of all the teams:
1. Victory Points
2. Rounds won
3. GWs won
4. Total Match Points
5. Match Point Difference (Total MP Scored - Total MP Conceded)
6. Total fpl Points
7. fpl ID (Lowest wins)
At the end of 9 Rounds (GWs 1 to 36) the top 4 Teams in the standings shall qualify for the Semi-Finals, to be played in GW37, with the top ranked team playing the 4th ranked, and the 2nd ranked playing the 3rd ranked. The winners of the Semi-Finals will play in the Final in GW38. Restrictions on not playing the same team more than once do not apply in the Finals.
Both the Semi-Finals and The Final are straight single GW contests. Most fpl points scored (after transfer cost is deducted) wins.
In the case of a tie there shall be a penalty shoot-out.
Penalty Shoot Out
In the Penalty Shoot Out the 3 Forwards in each team, regardless of whether or not they were on the bench, are ranked from highest GW score to lowest and compared with their counterparts in the opponent's team. The highest scores a penalty and is awarded a 'Score' and the lowest a 'Miss'. If they are tied then both score.
This is then repeated for the 5 Midfielders in each team.
Finally the active GW Goalkeeper for each team are compared and the higher of the two will be awarded a 'Save' which converts one of the opponent's 'Score's to 'Saved'. In addition each fpl save bonus point which the Goalkeepers earned in the GW will result in another 'Save'.
The number of 'Score's remaining are then totaled up to determine the winner.
If scores are still level then the process is repeated for the 5 Defenders, but no further GK 'Saves' are awarded.
If scores are still level after all of the Penalties then the higher ranked team during the season's 9 rounds is declared the winner.
Roll of Honour
In order to know who is the best all-time manager in the Swiss Cup all of your team's achievements during the season will be recorded in the Roll of Honour in the form of Honour Points. These shall be totaled up and carried over from season to season. Honour Points shall be awarded for the following:
For each Round won - 2 Points
For each Round tied - 1 Point
Bonus Points for finishing in the top 20% at the end of the season - 1 point for the team at the bottom of the top 20% and 1 additional point for each place above that.
Losing Semi-Finalists - 1 Point
Losing Finalist - 3 Points
Champion - 6 Points
Registration
Playing in the Swiss Cup will not require you to enter any fpl mini-leagues, so it will not cost you any of your slots.
If you are registered for the H2H Leagues then you are also automatically entered into the Swiss Cup. If you have entered the H2H but don't want to play in the Swiss Cup then let me know here, over on the H2H thread or by PM to me.
If you want to play in The Swiss Cup but not the H2H then you can sign up below with either your fpl link, fpl ID or an up to date fpl button.
(The FPL Team Link should be of the form https://fantasy.premierleague.com/a/entry/xxxx/history, where 'xxxx' is your Team ID. This link, with Team ID, can be found in the URL on your FPL team page by pressing 'View Gameweek History'.
The closing date for registration is Wednesday 8th August.