On the Exact Ordering Operators and Their Applications
Ali M. Awin · International Journal of Modeling and Optimization · 2014
Exact and general exact ordering methods are reviewed.Firstly, the exact ordering method is introduced, and few theorems were given to assign the conditions needed to locate the position of a required object among a group of objects to be ordered in a certain manner in three classes .Secondly, the exact ordering method is generalized to any odd number of classes (m).In both cases and if the required object class is put in the middle of other classes then the required object is located exactly as the object in the middle of all objects provided that we arrange the objects orderly in three groups in the first case and in m groups in the second generalized one and where certain defined steps are to be followed; in general m steps are required to determine the required object exactly and where m is the odd number of classes.The possibility of making the subject more interesting, deeper and handled in a sophisticated manner, through the introduction of exact ordering operators, is then discussed; this is by no means complete and this matter will constitute the subject of a future work .Finally few different applications are suggested in physics ,in operational research, in sorting files and in postal mailing.Its use as a practical demonstration with playing cards is also mentioned.