The pair were vital for Martin Jol's side last season, with American playmaker Dempsey finishing as the club's top scorer with 17 Premier League goals, while Dembele was a creative force in the side with several assists as Fulham finished in the top half of the table.
Ruiz, on the other hand, struggled to adapt in his first season in England after a £10.5 million move from Eredivisie outift FC Twente, with a lack of form and several injuries ensuring his debut campaign ended with frustration.
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He told the club's official magazine Fultime: "I don't think Fulham fans have seen the best of me yet. Last season I found it hard at times, and there were a couple of injuries too that didn't help.
"Of course, it could have gone better, but I did a few things to show people what I have, and for sure, this season I'll do my best for the fans.
"Mousa and Clint have both left. They were two players that could do many things on the football pitch. But now we don't have them, and as a result, I do feel a bit more responsibility on my shoulders.
"But I've had pressure before when I was at Twente and it's the same for the national team – so I don't mind that kind of pressure. I know that I can make a difference."
Ruiz stated that while there were teams from La Liga looking to sign him, the club's level of interest in him was a major factor in his decision to join the west London outfit, and has thanked the fans for supporting him while adapting to the physical nature of the Premier League.
He added: "There were teams from both leagues [Premier League and La Liga] that wanted me, but Fulham was the club that showed the most interest.
"I admit that I didn't know a lot about the club but I watched some videos and talked to people and then I was convinced that Fulham was the best option. It just seemed like a good club and a good place to be."
"I really want to do well for Fulham. My first season was a bit hit and miss, but sometimes it takes a while for a new signing to find their feet.
"I showed what I could do at times and now I am used to the physical demands of the Premier League, I want to repay Fulham for bringing me to England.
"The fans have been very supportive as well. They appreciate good football at Fulham, which is how I like to play and hopefully we will see a lot of that over the rest of the season."