Comparison of One-Level and Two-Level Consensuses Satisfying the 2-Optimality Criterion
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.
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- 1.Arrow, K.J.: Social Choice and Individual Values. Wiley, New York (1963)Google Scholar
- 2.Badache, N., Hurfin, M., Madeco, R.: Solving the consensus problem in a mobile environment. In: Proc. of IEEE International Performance, Computing and Communications Conference, pp. 29–35. IEEE, Piscatawy (1999)Google Scholar
- 7.Day, W.H.E.: Consensus Methods as Tools for Data Analysis. In: Bock, H.H. (ed.) Classification and Related Methods for Data Analysis, pp. 312–324. North-Holland (1988)Google Scholar
- 8.Kamel, M.: Identifying, classifying, and resolving semantic conflicts in distributed heteroge-neous databases. Journal of Database Management 6, 20–32 (1994)Google Scholar
- 9.Katarzyniak, R., Nguyen, N.T.: Reconciling inconsistent profiles of agents’ knowledge states in distributed multiagent systems using consensus methods. System Science 26(4), 93–119 (2001)Google Scholar
- 10.Kozierkiewicz-Hetmańska, A., Nguyen, N.T.: A Comparison Analysis of Consensus Deter-mining Using One and Two-level Methods. In: Proc. of KES 2012 (to be appeared, 2012)Google Scholar
- 12.Mirkin, B.G.: Problems of group choice. Nauka Moscow (1974)Google Scholar
- 16.Nguyen, N.T.: Consensus Choice Methods and their Application to Solving Conflicts in Distributed Systems. Wroclaw University of Technology Press (2002) (in Polish)Google Scholar