The evolution of skyline and ranking queries has created new archetypes like flexible skylines, which have proven to be an efficient method to select relevant data from large datasets using multi objective optimization. This paper aims to study the possible applications of Poisson distribution mass function as a monotonic scoring function in flexible skyline processes, especially those featuring schemas whose attributes can be translated to constant mean rates. Moreover, a method to express users's requirement by means of the F-dominant set of tuples will be proposed using parametrical variations in F[1], simultaneously, algorithm construction and potential applications will be studied.