Abstract
In this paper, a generalization of Yager’s implications is proposed and the resulting new class of implications from f-generated implications with f(0) < + ∞ is studied. The generalization is based on considering a more general internal function than the product into their expression. In this particular case, this more general function has to be, in fact, a binary aggregation function and depending on its properties, the behaviour and additional properties of the generated implication are determined. Finally, we prove that this new class intersects some of the well-known classes, such as (S,N) and (U,N)-implications, among others.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Baczyński, M., Jayaram, B.: Fuzzy Implications. STUDFUZZ, vol. 231. Springer, Heidelberg (2008)
Baczyński, M., Jayaram, B.: (U,N)-implications and their characterizations. Fuzzy Sets and Systems 160, 2049–2062 (2009)
Balasubramaniam, J.: Contrapositive symmetrisation of fuzzy implications–revisited. Fuzzy Sets and Systems 157(17), 2291–2310 (2006)
Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners. STUDFUZZ, vol. 221. Springer (2007)
Carbonell, M., Torrens, J.: Continuous R-implications generated from representable aggregation functions. Fuzzy Sets and Systems 161, 2276–2289 (2010)
De Baets, B., Fodor, J.C.: Residual operators of uninorms. Soft Computing 3, 89–100 (1999)
Durante, F., Klement, E., Mesiar, R., Sempi, C.: Conjunctors and their residual implicators: Characterizations and construction methods. Mediterranean Journal of Mathematics 4, 343–356 (2007)
Fodor, J.C., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)
Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions, 1st edn. Encyclopedia of Mathematics and its Applications. Cambridge University Press, New York (2009)
Maes, K.C., De Baets, B.: On the structure of left-continuous t-norms that have a continuous contour line. Fuzzy Sets and Systems 158, 843–860 (2007)
Mas, M., Monserrat, M., Torrens, J.: Two types of implications derived from uninorms. Fuzzy Sets and Systems 158, 2612–2626 (2007)
Mas, M., Monserrat, M., Torrens, J., Trillas, E.: A survey on fuzzy implication functions. IEEE Transactions on Fuzzy Systems 15(6), 1107–1121 (2007)
Massanet, S., Torrens, J.: The law of importation versus the exchange principle on fuzzy implications. Fuzzy Sets and Systems 168(1), 47–69 (2011)
Massanet, S., Torrens, J.: On a new class of fuzzy implications: h-implications and generalizations. Information Sciences 181(11), 2111–2127 (2011)
Trillas, E., Mas, M., Monserrat, M., Torrens, J.: On the representation of fuzzy rules. Int. J. Approx. Reasoning 48(2), 583–597 (2008)
Yager, R.R.: On some new classes of implication operators and their role in approximate reasoning. Information Sciences 167, 193–216 (2004)
Yager, R.R.: Modeling holistic fuzzy implication using co-copulas. Fuzzy Optimization and Decision Making 5, 207–226 (2006)
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
Massanet, S., Torrens, J. (2012). On a Generalization of Yager’s Implications. 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 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31715-6_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-31715-6_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31714-9
Online ISBN: 978-3-642-31715-6
eBook Packages: Computer ScienceComputer Science (R0)