Abstract
This paper continues previous work on additive generators of overlap functions, introducing the construction of grouping functions by means of additive generators, defined as a pair of one-place functions satisfying appropriate properties. Some important results are discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bustince, H., Barrenechea, E., Pagola, M.: Image thresholding using restricted equivalence functions and maximizing the measures of similarity. Fuzzy Sets and Systems 158(5), 496–516 (2007)
Fodor, J., Roubens, M.: Fuzzy preference modelling and multicriteria decision support. Kluwer, New York (1994)
Bustince, H., Pagola, M., Mesiar, R., Hüllermeier, E., Herrera, F.: Grouping, overlaps, and generalized bientropic functions for fuzzy modeling of pairwise comparisons. IEEE Transactions on Fuzzy Systems 20(3), 405–415 (2012)
Bustince, H., Fernandez, J., Mesiar, R., Montero, J., Orduna, R.: Overlap functions. Nonlinear Analysis 72(3-4), 1488–1499 (2010)
Jurio, A., Bustince, H., Pagola, M., Pradera, A., Yager, R.: Some properties of overlap and grouping functions and their application to image thresholding. Fuzzy Sets and Systems 229, 69–90 (2013)
Viceník, P.: Additive generators of associative functions. Fuzzy Sets and Systems 153(2), 137–160 (2005)
Mayor, G., Trillas, E.: On the representation of some aggregation functions. In: Proceedings of the XVI International Symposium on Multiple-Valued Logic (ISMVL 1986), Blacksburg, pp. 110–114 (1986)
Dimuro, G.P., Bedregal, B.C., Santiago, R.H.N., Reiser, R.H.S.: Interval additive generators of interval t-norms and interval t-conorms. Information Sciences 181(18), 3898–3916 (2011)
Dimuro, G.P., Bedregal, B.R.C., Reiser, R.H.S., Santiago, R.H.N.: Interval additive generators of interval t-norms. In: Hodges, W., de Queiroz, R. (eds.) WoLLIC 2008. LNCS (LNAI), vol. 5110, pp. 123–135. Springer, Heidelberg (2008)
Bedregal, B.C., Dimuro, G.P., Santiago, R.H.N., Reiser, R.H.S.: On interval fuzzy S-implications. Information Sciences 180(8), 1373–1389 (2010)
Dimuro, G.: On interval fuzzy numbers. In: 2011 Workshop-School on Theoretical Computer Science, WEIT 2011, pp. 3–8. IEEE, Los Alamitos (2011)
Reiser, R.H.S., Dimuro, G.P., Bedregal, B.C., Santiago, R.H.N.: Interval valued QL-implications. In: Leivant, D., de Queiroz, R. (eds.) WoLLIC 2007. LNCS, vol. 4576, pp. 307–321. Springer, Heidelberg (2007)
Bedregal, B.C., Dimuro, G.P., Reiser, R.H.S.: An approach to interval-valued R-implications and automorphisms. In: Carvalho, J.P., Dubois, D., Kaymak, U., da Costa Sousa, J.M. (eds.) Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, IFSA/EUSFLAT, pp. 1–6 (2009)
Mesiarová-Zemánková, A.: Ranks of additive generators. Fuzzy Sets and Systems 160(14), 2032–2048 (2009)
Dimuro, G.P., Bedregal, B.: Additive generators of overlap functions. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds.) Aggregation Functions in Theory and in Practise. AISC, vol. 228, pp. 167–178. Springer, Heidelberg (2013)
Bedregal, B.C., Dimuro, G.P., Bustince, H., Barrenechea, E.: New results on overlap and grouping functions. Information Sciences 249, 148–170 (2013)
Rao, A.S., Georgeff, M.P.: Modeling rational agents within a BDI-architecture. In: Fikes, R., Sandewall, E. (eds.) Proceedings of the 2nd International Conference on Principles of Knowledge Representation and Reasoning, pp. 473–484. Morgan Kaufmann, San Mateo (1991)
Dimuro, G.P., da Rocha Costa, A.C., Gonçalves, L.V., Hübner, A.: Centralized regulation of social exchanges between personality-based agents. In: Noriega, P., Vázquez-Salceda, J., Boella, G., Boissier, O., Dignum, V., Fornara, N., Matson, E. (eds.) COIN 2006. LNCS (LNAI), vol. 4386, pp. 338–355. Springer, Heidelberg (2007)
Dimuro, G.P., da Rocha Costa, A.C., Gonçalves, L.V., Pereira, D.: Recognizing and learning models of social exchange strategies for the regulation of social interactions in open agent societies. Journal of the Brazilian Computer Society 17, 143–161 (2011)
Pereira, D.R., Gonçalves, L.V., Dimuro, G.P., da Rocha Costa, A.C.: Towards the self-regulation of personality-based social exchange processes in multiagent systems. In: Zaverucha, G., da Costa, A.L. (eds.) SBIA 2008. LNCS (LNAI), vol. 5249, pp. 113–123. Springer, Heidelberg (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Dimuro, G.P., Bedregal, B., Bustince, H., Mesiar, R., Asiain, M.J. (2014). On Additive Generators of Grouping Functions. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 444. Springer, Cham. https://doi.org/10.1007/978-3-319-08852-5_26
Download citation
DOI: https://doi.org/10.1007/978-3-319-08852-5_26
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08851-8
Online ISBN: 978-3-319-08852-5
eBook Packages: Computer ScienceComputer Science (R0)