Abstract
The purpose of this paper is to compare two methods for computing the greatest solutions of two-mode systems of FREIs. The first one is the direct method developed recently in [26], and the second one consists in converting the two-mode case into the one-mode case, and computing the greatest solutions of related one-mode systems of FREIs, using algorithms provided in [13, 15]. The conversion is made by means of the well-known method used in social network analysis for transforming two-mode networks into one-mode networks. We prove theoretically interesting result according to which solutions of any two-mode system of FREIs can be derived from solutions of the related one-mode system, and vice versa. However, from the computational point of view, the conversion based method is more memory and time demanding, what favors the direct method.
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References
Barber, M.J.: Modularity and community detection in bipartite networks. Phys. Rev. E 76, 066102 (2007)
Batagelj, V.: Social network analysis, large-scale. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and Systems Science, pp. 8245–8265. Springer, New York (2009)
Borgatti, S.P.: Two-mode concepts in social network analysis. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and Systems Science, pp. 8279–8291. Springer, New York (2009)
Brynielsson, J., Kaati, L., Svenson, P.: Social positions and simulation relations. Soc. Netw. Anal. Min. 2, 39–52 (2012)
Ćirić, M., Ignjatović, J.: The existence of generalized inverses of fuzzy matrices. In: Kóczy, L., Kacprzyk, J., Medina, J. (Eds.), ESCIM (2016). Studies in Computational Intelligence, to appear
Ćirić, M., Ignjatović, J., Damljanović, N., Bašić, M.: Bisimulations for fuzzy automata. Fuzzy Sets Syst. 186, 100–139 (2012)
Ćirić, M., Ignjatović, J., Jančić, Damljanović, N.: Computation of the greatest simulations and bisimulations between fuzzy automata. Fuzzy Sets Syst. 208, 22–42 (2012)
Ćirić, M., Stamenković, A., Ignjatović, J., Petković, T.: Fuzzy relation equations and reduction of fuzzy automata. J. Comput. Syst. Sci. 76, 609–633 (2010)
Doreian, P.: Positional analysis and blockmodeling. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and Systems Science, pp. 6913–6927. Springer, New York (2009)
Everett, M.G., Borgatti, S.P.: The dual-projection approach for two-mode networks. Soc. Netw. 35, 204–210 (2013)
Fararo, T., Doreian, P.: Tripartite structural analysis: generalizing the Breiger-Wilson formalism. Soc. Netw. 6, 141–175 (1984)
Hanneman, R.A., Riddle, M.: Introduction to Social Network Methods. University of California, Riverside, Riverside CA (2005)
Ignjatović, J., Ćirić, M.: Weakly linear systems of fuzzy relation inequalities and their applications: abrief survey. Filomat 26(2), 207–241 (2012)
Ignjatović, J., Ćirić, M.: Moore-Penrose equations in involutive residuated semigroups and involutive quantales. Filomat 31(2), 183–196 (2017)
Ignjatović, J., Ćirić, M., Bogdanović, S.: On the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations. Fuzzy Sets Syst. 161, 3081–3113 (2010)
Ignjatović, J., Ćirić, M., Damljanović, N., Jančić, I.: Weakly linear systems of fuzzy relation inequalities: the heterogeneous case. Fuzzy Sets Syst. 199, 64–91 (2012)
Latapy, M., Magnien, C., Del Vecchio, N.: Basic notions for the analysis of large twomode networks. Soc. Netw. 30, 31–48 (2008)
Lerner, J.: Role assignments. In: Brandes, U., Erlebach, T. (Eds.), Network Analysis: Methodological Foundations, Lecture Notes in Computer Science, vol. 3418, pp. 216–252. Springer (2005)
Melamed, D.: Community structures in bipartite networks: a dual-projection approach. PLoS ONE 9(5), e97823 (2014)
Melamed, D., Breiger, R.L., West, A.J.: Community structure in multi-mode networks: Applying an eigenspectrum approach. Connections 33, 18–23 (2013)
Sanchez, E.: Equations de relations Floues. Thèse de Doctorat, Faculté de Médecine de Marseille (1974)
Sanchez, E.: Resolution of composite fuzzy relation equations. Inf. Control 30, 38–48 (1976)
Sanchez, E.: Solutions in composite fuzzy relation equations: application to medical diagnosis in Brouwerian logic. In: Gupta, M.M., Saridis, G.N., Gaines, B.R. (Eds.), Fuzzy Automata and Decision Processes, North-Holland, Amsterdam, pp. 221–234 (1977)
Scott, J.: Social network analysis, overview of. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and Systems Science, pp. 8265–8279. Springer, New York (2009)
Stamenković, A., Ćirić, M., Ignjatović, J.: Reduction of fuzzy automata by means of fuzzy quasi-orders. Inf. Sci. 275, 168–198 (2014)
Stanković, I., Ćirić, M., Ignjatović, J.: Fuzzy relation equations and inequalities with two unknowns and their applications. Fuzzy Sets Syst. 322, 86–105 (2017)
Zhou, T., Ren, J., Medo, M., Zhang, Y.-C.: Bipartite network projection and personal recommendation, Phys. Rev. E 76(4) (2007). Article number 046115
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Ćirić, M., Ignjatović, J., Stanković, I. (2019). Direct and Indirect Methods for Solving Two-Mode Systems of Fuzzy Relation Equations and Inequalities. In: Cornejo, M., Kóczy, L., Medina, J., De Barros Ruano, A. (eds) Trends in Mathematics and Computational Intelligence. Studies in Computational Intelligence, vol 796. Springer, Cham. https://doi.org/10.1007/978-3-030-00485-9_18
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