But I think that "complaints on the part of customers" might imply that there were other complaints as well, from other people.
"There were many complaints about the event. Complaints on the part of customers tended to blame lazy employees for the problems, while complaints on the part of employees blamed unreasonable customer demands."
"complaints of customers" = when customers complain personally and directly. They show up at the store to complain. "complaints on the part of customers" = where a spokesman or representative complains, acting on behalf of the customers. The customers are not present, but the spokesman is representing them.
@MetRon@Ariana_H @bucklemaker Thanks a lot！I see. But I still have some questions when using the phase "on the part of" as follows： Dose it have the function of emphasis on the noun appearing after it, like the "customers" in the examples？ Is this usage "on the part of" commonly used? Can I use it like "The complaints on the part of customers are that ..." or like "We should protect the rights on the part of customers." in my writing？Do these sound nature？😄