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Preference aggregation as a problem of a single consensus ranking determination, using Kemeny rule, for m rankings, including ties, of n alternatives is considered in the paper. The Kemeny Ranking Problem (KRP) may have considerably more than one optimal solutions (strict orders or permutations of the alternatives) and, hence, special efforts to deal with this phenomenon are needed. In the paper, there is proposed an efficient formal rule for convolution of the N multiple optimal permutations, the output profile β(N, n), into an exact single final consensus ranking, which can include ties. The convolution rule is as follows: in the final consensus ranking, alternatives are arranged in ascending order of their rank sums (total ranks) calculated for the output profile β; some two alternatives are considered to be tolerant if they have the same rank sums in β. The equivalent convolution rule can be also applied as follows: in the final consensus ranking, alternatives are arranged in descending order of row sums (total scores) calculated for a tournament table built for β; some two alternatives are deemed to be tolerant if they have the same row sums. It is shown that, for any alternative, its total rank and total score are equal in sum to the output profile dimension N×n. The convolution rules are validated using Borda count.

The purpose of the study is to select the optimal conditions for collecting non-coordinate information about a spacecraft by a space optical-electronic means at the time objects pass the vicinity of the points of the minimum distance between their orbits. The quantitative indicator is proposed that characterize the measure of the possibility of obtaining non-coordinate information about space objects with the required level of quality. The arguments of the function characterizing the indicator are the distance between spacecraft; their relative speed; phase angle of illumination of a spacecraft by the Sun in relation to the optical-electronic means; the length of the time interval during which both objects are in the vicinity of the point of a minimum distance between their orbits. The value of the indicator is computed by solving three particular research problems. The first task is to search for neighborhoods that include the minimum distances between the orbits of the controlled spacecraft and optical-electronic means. To solve it, a fast algorithm for calculating the minimum distance between orbits used. Additionally, the drift of the found neighborhoods is taken into account on the time interval up to 60 hours. The second task is to estimate the characteristics of motion and the conditions of optical visibility of a controlled spacecraft in the vicinity of the minimum points of the distance between the orbits of spacecraft. The solution to this problem is carried out by using the SGP4 library of space objects motion forecast. The third task is justification and calculation of an index characterizing the measure of the possibility of obtaining an optical image of a spacecraft for given conditions of optical visibility. To solve the problem, the developed system of fuzzy inference rules and the Mamdani algorithm is used. The presented method is implemented as a program. In the course of a computational experiment, an assessment was made of the possibility of obtaining non-coordinate information on low-orbit and geostationary space objects. The proposed indicator provides an increase in the efficiency of the procedure for collecting non-coordinate information about space objects by choosing the most informative alternatives for monitoring space objects from the available set of possible observations at a given planning interval for collecting information about space objects.