New approach based on fuzzy hypergraphs in granular computing (an application to the urban vulnerability assessment)

[1] C. Berge, Graphs and Hypergraphs, North-Holland Publishing Company, 1973.

[2] A. Bernardini, The vulnerability of buildings-Evaluation on the national scale of the seismic vulnerability of ordinary buildings, CNR-GNDT, Rome, 2000.

[3] P. Bhattacharya, Some remarks on fuzzy graphs, Pattern Recogn. Lett. 6 (1987), no. 5, 297–302.

[4] K.R. Bhutani and A. Battou, On M-strong fuzzy graphs, Inf. Sci. 155 (2003), no. 1–2, 103–109.

[5] R. Bilham, The seismic future of cities, Bull. Earthquake Eng. 7 (2009), no. 4, 839–887.

[6] A. Bretto, Hypergraph Theory, An Introduction Mathematical Engineering, Cham: Springer, 2013.

[7] S.H. Bustince and L.P. Burillo, A theorem for constructing interval-valued intuitionistic fuzzy sets from intuitionistic fuzzy sets, Notes Intuition. Fuzzy Sets 1 (1995), 5–16.

[8] O. Cardona, Indicators of disaster risk and risk management: Summary report, Inter-American Development Bank, 2005.

[9] M.L. Carreno, O.D. Cardona and A.H. Barbat, New methodology for urban seismic risk assessment from a holistic perspective, Bull. Earthquake Eng. 10 (2012), no. 2, 547–565.

[10] G. Chiaselotti, D. Ciucci, T. Gentile and F. Infusino, Rough set theory applied to simple undirected graphs, Int. Conf. Rough Sets Knowledge Technol., Springer, 2015, pp. 423–434.

[11] A. Corsanego and V. Petrini, Evaluation of criteria of seismic vulnerability of the existing building patrimony on the national territory, Seismic Eng. 1 (1994), 76–106.

[12] R. Davidson, EERI annual student paper award a multidisciplinary urban earthquake disaster risk index, Earthquake Spectra 13 (1997), no. 2, 211–223.

[13] L. De Angelis and J.G. Dias, Mining categorical sequences from data using a hybrid clustering method, Eur. Res. 234 (2014), no. 3, 720–730.

[14] L. Duenas-Osorio, J.I. Craig and B.J. Goodno, Seismic response of critical interdependent networks, Earthquake Engin. Struct. Dyn. 36 (2007), no. 2, 285–306.

[15] M.A. Ferreira, F.M. De Sa and C.S. Oliveira, Disruption index, DI: An approach for assessing seismic risk in urban systems (theoretical aspects), Bull. Earthquake Eng. 12 (2014), no. 4, 1431–1458.

[16] R.A. Fisher, The use of multiple measurements in taxonomic problems, Ann. Eugenics 7 (1936), no. 2, 179–188.

[17] J.R.H. Goetschel, Introduction to fuzzy hypergraphs and Hebbian structures, Fuzzy Sets Syst. 76 (1995), no. 1, 113–130.

[18] D.W. Hubbard, The failure of risk management: Why it’s broken and how to fix it, John Wiley & Sons, 2020.

[19] A.K. Jain, Data clustering: 50 years beyond K-means, Pattern Recogn. Lett. 31 (2010), no. 8, 651–666.

[20] G. Karypis and V. Kumar, Multilevel k-way hypergraph partitioning, VLSI Design 11 (2000), no. 3, 285–300.

[21] A. Kauffman, Introduction `a la th´eorie des sous-ensembles flous `a l’usage des ing´enieurs (fuzzy sets theory), Masson 3 (1973).

[22] N. Lantada, L.G. Pujades and A.H. Barbat, Vulnerability index and capacity spectrum based methods for urban seismic risk evaluation. A comparison, Natural Hazards 51 (2009), no. 3, 501.

[23] K.M. Lee and K.J. Cios, Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets, Comput. Inf. Technol.: Explor. Emerg. Technol., World Scientific, 2001, pp. 433–439.

[24] K.H. Lee and K.M. Lee, Fuzzy hypergraph and fuzzy partition, IEEE Trans. Syst. Man Cybernet. 25 (1995), no. 1, 196–201.

[25] P. Masure and C. Lutoff, Urban system exposure to natural disasters: an integrated approach, Assessing and Managing Earthquake Risk, Springer, 2008.

[26] D. Michaud and G.E. Apostolakis, Methodology for ranking the elements of water-supply networks, J. Infrast. Syst. 12 (2006), no. 4, 230–242.

[27] J.N. Mordeson and P.S. Nair, Cycles and cocycles of fuzzy graphs, Inf. Sci. 90 (1996), no. 1–4, 39–49.

[28] J.N. Mordeson and P.S. Nair, Fuzzy graphs and fuzzy hypergraphs, Physica 46 (2012).

[29] S.S. Nazionale, Gruppo Nazionale per la Difesa dai Terremoti, Scheda AeDES di, 2000.

[30] R. Parvathi, S. Thilagavathi and M.G. Karunambigai, Intuitionistic fuzzy hypergraphs, Cybernetics Info. Technol. 9 (2009), no. 2, 46–53.

[31] W. Pedrycz, Fuzzy modelling: paradigms and practice, Springer Science & Business Media, 2012.

[32] W. Pedrycz, Granular computing: Analysis and design of intelligent systems, CRC press, 2018.

[33] A. Rosenfeld, Fuzzy graphs, fuzzy sets and their applications (L.A. Zadeh, K.S. Fu and M. Shimura, Eds.), Academic Press, New York, 1975.

[34] Y. Shvartzshnaider and M. Ott, Design for change: Information-centric architecture to support agile disaster response, IEEE Int. Conf. Commun. (ICC), IEEE, 2013, pp. 4025–4029.

[35] J.G. Stell, Relational granularity for hypergraphs, Int. Conf. Rough Sets Current Trends Comput., Springer, 2010, no. 7, pp. 267–276.

[36] M.S. Sunitha and A. Vijayakumar, A characterization of fuzzy trees, Info. Sci. 113 (1999).

[37] M.S. Sunitha and A. Vijayakumar, Studies on fuzzy graphs, PhD Thesis, Department of Mathematics, Cochin University of Science and Technology, India, 2001.

[38] Q. Wang and Z. Gong, An application of fuzzy hypergraphs and hypergraphs in granular computing, Inf. Sci. 429 (2018), 296–314.

[39] R.V. Whitman, Damage Probability Matrices for Prototype Buildings, Structures Publication, 1973.

[40] Y.Y.Y. Yao, C.J. Liau and N. Zhong, Granular computing based on rough sets, quotient space theory, and belief functions, Int. Symp. Method. Intell. Syst., Springer, 2003, pp. 152–159.

[41] Y.Y. Yao and N. Zhong, Granular computing using information tables, T.Y. Lin, Y.Y. Yao and L.A. Zadeh (eds),

Data Mini. Rough Sets Granular Comput. 95 (2002), 102–124.

[42] L.A. Zadeh, Information and control, Fuzzy Sets Syst. 8 (1965), no. 3, 338–353.

[43] L.A. Zadeh, Similarity relations and fuzzy orderings, Info. Sci. 3 (1971), no. 2, 177–200.

[44] L.A. Zadeh, Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, Fuzzy Sets Syst. 90 (1997), no. 2, 111–127.

[45] L.A. Zadeh, G.J. Klir and B. Yuan, Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers, World Scientific 6(1996).