Abstract
For crisp as well as fuzzy relations, the results concerning transitive closures and openings are well known. For reciprocal relations transitivity is often defined in terms of stochastic transitivity. This paper focuses on stochastic transitive openings of reciprocal relations, presenting theoretical results as well as a practical method to construct such transitive openings.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bandler, W., Kohout, L.J.: Special properties, closures and interiors of crisp and fuzzy relations. Fuzzy Sets and Systems 26, 317–331 (1988)
Basu, K.: Fuzzy revealed preference theory. J. Econom. Theory 32, 212–227 (1984)
Bezdek, J., Spillman, B., Spillman, R.: A fuzzy relational space for group decision theory. Fuzzy Sets and Systems 1, 255–268 (1978)
Boixader, D., Recasens, J.: Transitive openings. In: Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2011) and LFA 2011, pp. 493–497 (2011)
Chiclana, F., Herrera-Viedma, E., Alonso, S., Herrera, F.: Cardinal consistency of reciprocal preference relations: a characterization of multiplicative transitivity. IEEE Transactions on Fuzzy Systems 17, 14–23 (2009)
De Baets, B., De Meyer, H.: On the existence and construction of T-transitive closures. Information Sciences 152, 167–179 (2003)
De Baets, B., De Meyer, H.: Transitivity frameworks for reciprocal relations: cycle-transitivity versus FG-transitivity. Fuzzy Sets and Systems 152, 249–270 (2005)
De Baets, B., De Meyer, H., De Schuymer, B., Jenei, S.: Cyclic evaluation of transitivity of reciprocal relations. Social Choice and Welfare 26, 217–238 (2006)
De Meyer, H., Naessens, H., De Baets, B.: Algorithms for computing the min-transitive closure and associated partition tree of a symmetric fuzzy relation. European Journal of Operational Research 155, 226–238 (2004)
Floyd, R.W.: Algorithm 97: shortest path. Communications of the ACM 5(6), 345 (1962)
Freson, S., De Meyer, H., De Baets, B.: An Algorithm for Generating Consistent and Transitive Approximations of Reciprocal Preference Relations. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS, vol. 6178, pp. 564–573. Springer, Heidelberg (2010)
Freson, S., De Meyer, H., De Baets, B.: On the transitive closure of reciprocal [0,1]-valued relations. In: Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2011) and LFA 2011, pp. 1015–1021 (2011)
Monjardet, B.: A generalisation of probabilistic consistency: linearity conditions for valued preference relations. In: Kacprzyk, J., Roubens, M. (eds.) Non-conventional Preference Relations in Decision Making. LNEMS, vol. 301. Springer (1988)
Montero, F.J., Tejada, J.: Some problems on the definition of fuzzy preference relations. Fuzzy Sets and Systems 20, 45–53 (1986)
Tanino, T.: Fuzzy preference relations in group decision making. LNEMS, vol. 301, pp. 54–71 (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Freson, S., De Meyer, H., De Baets, B. (2012). Opening Reciprocal Relations w.r.t. Stochastic Transitivity. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31724-8_32
Download citation
DOI: https://doi.org/10.1007/978-3-642-31724-8_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31723-1
Online ISBN: 978-3-642-31724-8
eBook Packages: Computer ScienceComputer Science (R0)