Abstract
In this paper we investigate about lattice-valued restricted equivalence functions and its characterization by means a particular class of lattice-valued implication operators.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Baczyński, M., Jayaram, B.: Fuzzy Implications. Studies in Fuzziness and Soft Computing. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-69082-5
Bedregal, B.C., Santos, H.S., Callejas-Bedregal, R.: T-norms on bounded lattices: T-norm morphisms and operators. In: IEEE International Conference on Fuzzy Systems, pp. 22–28 (2006)
Bedregal, B.C.: On interval fuzzy negations. Fuzzy Sets Syst. 161, 2290–2313 (2010)
Bedregal, B.C.: Xor-Implications and E-Implications: classes of fuzzy implications based on fuzzy Xor. Electron. Notes Theor. Comput. Sci. 274, 5–18 (2009)
Bedregal, B., Beliakov, G., Bustince, H., Fernandez, J., Pradera, A., Reiser, R.: (S, N)-implications on bounded lattices. In: Baczyński, M., Beliakov, G., Bustince Sola, H., Pradera, A. (eds.) Advances in Fuzzy Implication Functions. Studies in Fuzziness and Soft Computing, vol. 300. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-35677-3_5
Birkhoff, G.: Lattice Theory. American Mathematical Society, Providence (1973)
Bustince, H., Burillo, P., Soria, F.: Automorphisms, negations and implication operators. Fuzzy Sets Syst. 134(2), 209–229 (2003)
Bustince, H., Barrenechea, E., Pagola, M.: Restricted equivalence functions. Fuzzy Sets Syst. 157(17), 2333–2346 (2006)
Bustince, H., Barrenechea, E., Pagola, M.: Relationship between restricted dissimilarity functions, restricted equivalence functions and normal \({E}_N\)-functions: image thresholding invariant. Pattern Recogn. Lett. 29, 525–536 (2008)
Calvo, T.: On mixed De Morgan triplets. Fuzzy Sets Syst. 50, 47–50 (1992)
Chen, G., Pham, T.T.: Fuzzy Sets, Fuzzy Logic and Fuzzy Control Systems. CRC Press, Boca Raton (2001)
De Cooman, G., Kerre, E.E.: Order norms on bounded partially ordered sets. J. Fuzzy Math. 2, 281–310 (1994)
Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, Cambridge (2002)
Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publisher, Dordrecht (1994)
Hajek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998)
Hungerford, T.W.: Algebra. Graduate Texts in Mathematics. Springer, New York (2000)
Julio, A., Pagola, M., Paternain, D., Lopez-Molina, C., Melo-Pinto, P.: Interval-valued restricted equivalence functions applied on clustering techniques. In: IFSA-EUSFLAT, pp. 831–836 (2009)
Klement, E.P., Mesiar, R.: Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms. Elsevier B.V., Amsterdam (2005)
Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht (2000)
Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic, Theory and Applications. Prentice Hall PTR, Upper Saddle River (1995)
Mas, M., Monserrat, M., Torrens, J., Trillas, E.: A survey on fuzzy implications functions. IEEE Trans. Fuzzy Syst. 15(6), 1107–1121 (2007)
Palmeira, E.S., Bedregal, B.C., Mesiar, R., Fernandez, J.: A new way to extend T-norms, T-conorms and negations. Fuzzy Sets Syst. 240, 1–21 (2014)
Palmeira, E.S., Bedregal, B.C.: Extension of fuzzy logic operators defined on bounded lattices via retractions. Comput. Math. Appl. 63, 1026–1038 (2012)
Palmeira, E.S., Bedregal, B.: Restricted equivalence function on L([0, 1]). In: Melin, P., Castillo, O., Kacprzyk, J., Reformat, M., Melek, W. (eds.) NAFIPS 2017. AISC, vol. 648, pp. 410–420. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-67137-6_45
Palmeira, E.S., Bedregal, B.C., dos Santos, J.A.: Some results on extension of lattice-valued QL-implications. J. Braz. Comput. Soc. 22(1), 41–49 (2016)
Palmeira, E.S., Bedregal, B.C., Bustince, H., Paternain, D., De Miguel, L.: Application of two different methods for extending lattice-valued restricted equivalence functions used for constructing similarity measures on L-fuzzy sets. Inf. Sci. 441, 95–112 (2018)
Saminger-Platz, S., Klement, E.P., Mesiar, R.: On extensions of triangular norms on bounded lattices. Indag. Math. 19(1), 135–150 (2008)
Takano, M.: Strong completeness of lattice-valued logic. Arch. Math. Logic 41, 497–505 (2002)
Yager, R.R.: On the implication operator in fuzzy logic. Inf. Sci. 31(2), 141–164 (1983)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Palmeira, E., Bedregal, B., Vargas, R.R. (2018). Characterization of Lattice-Valued Restricted Equivalence Functions. In: Barreto, G., Coelho, R. (eds) Fuzzy Information Processing. NAFIPS 2018. Communications in Computer and Information Science, vol 831. Springer, Cham. https://doi.org/10.1007/978-3-319-95312-0_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-95312-0_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-95311-3
Online ISBN: 978-3-319-95312-0
eBook Packages: Computer ScienceComputer Science (R0)