Authors
Popov V.
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Degree
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PhD in Physics & Mathematics, Associate Professor, Lobachevsky state university of Nizhni Novgorod |
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E-mail
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victor972993@rambler.ru |
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Location
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Nizhni Novgorod |
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Articles
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An interval approach to optimization of solving of multi-objective task about appointmentsWe consider the method of conditional optimization of solving of multi-objective task about appointments
on the assumption that the number of candidates is equal or more than the number of vacant
positions. Whereas eligibility assessments of task is unclear and is based on the judgment of experts we
must use elements of fuzzy sets theory and the fuzzy mathematical programming. In our problem the
optimization with interval parameter is supposed the solving of two tasks of mathematical programming
with upper and lower value boundaries. In both tasks, as the objective functions are used the total score
penalty for non-compliance of subjects (candidates) and objects (appointments) for each criterion.
The meet of two solving is general solving of optimization problem. In this paper we use interval
analysis and interval discrete optimization with Boolean variables, which determine appointment matrix.
The Hungarian Method for the assignment problem was used for solving of optimization problems.
An appointment matrix must provide the minimum of value of difference between requirements
to candidates for appointments and requirements to appointments. It should be noted that it is not
always the intersection of the sets of solutions to both problems, and then the task has no decision.
In this case the problem should be solved on the basis of indistinct intervals, but the solving will be
received in the form of an indistinct appointment matrix.
The results of solving of optimization problems are compared with results, which are received on
base of fuzzy binary relations ( (max-min) — composition and (max-prod) — composition).
This comparison is necessary for more reliable conclusions about the selection of candidates
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