Abstract—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.
Index Terms—Class, exact, ordering, required object.
Ali M. Awin is with the Department of Mathematics, University of
Tripoli , Tripoli, Libya ( e-mail: awinsus@yahoo.com)
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Cite: Ali M. Awin, "On the Exact Ordering Operators and Their Applications," International Journal of Modeling and Optimization vol. 4, no. 5, pp. 358-361, 2014.
