The phrase "based on their relevance" is correct and usable in written English.
You can use this phrase when you want to explain why something is being done in a certain order or how a person made a decision. For example, "The teacher graded the essays based on their relevance to the assignment."
The selection of relevant people was based on their relevance for the subject matter, their experience and their up-to-date knowledge.
After all, as Google pointed out, search engines are programmed to gather, assess and ultimately rank sites based on their relevance to a given query — that is, they are already making decisions for us.
Interview excerpts have been selected based on their relevance and importance in illustrating emergent themes.
The trends identified as part of the qualitative research are clustered based on their relevance and uncertainty levels.
For Twitter, we have developed two classifiers to classify tweets based on their relevance to a civil unrest event.
In addition, data from overseas surveys has also been considered based on their relevance to the office buildings.
Mandatory criteria are selected first, while the remaining criteria are divided into two groups based on their relevance.
Tinder casts a 50 miles net around its users, taking users within that radius and giving them a rating based on their relevance to you.
The proposed event hierarchy thus groups together events based on their relevance, instead of their semantic meaning as in LooCI's event taxonomy.
The interviewees were selected based on their relevance as key stakeholders with different perspectives of the food industry in Brazil, see Table 1 for details.
Also the models may be ordered based on their relevance to a subject or topic using principles of Bayesian Factor or Bayesian sampling approaches.
