Abstract
This paper is dedicated to examine the results of methods determining the one-level and the two-level consensuses fulfilling the 2-optimality criterion with reference to the optimal solution. The 2-optimality criterion requires the sum of the squared distance between a consensus and the profile’s elements to be minimal. This problem is an NP-complete problem, so for solving it heuristic approaches are presented. The researches demonstrate that a better solution is always given by the one-level consensus. In comparison to the optimal solution the two-level algorithm gives results by 5% worse and the one-level method by 1% worse. Additionally, author considers how many units are required to determine the reasonable consensus, which is called a susceptible to a consensus of profiles. Analyses presented in this paper show that the increasing the cardinality of a profile increases the probability of being susceptible to a consensus but for the assumed study cardinality of the profile greater than 384 gives a good result.
This research was partially supported by Grant no. N N519 444939 funded by Polish Ministry of Science and Higher Education (2010-2013).
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Kozierkiewicz-Hetmańska, A. (2012). Comparison of One-Level and Two-Level Consensuses Satisfying the 2-Optimality Criterion. In: Nguyen, NT., Hoang, K., Jȩdrzejowicz, P. (eds) Computational Collective Intelligence. Technologies and Applications. ICCCI 2012. Lecture Notes in Computer Science(), vol 7653. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34630-9_1
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