Geodesic
Construction methods for implications on bounded lattices
Kybernetika, Tome 55 (2019) no. 4, pp. 641-667
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In this paper, the ordinal sum construction methods of implications on bounded lattices are studied. Necessary and sufficient conditions of an ordinal sum for obtaining an implication are presented. New ordinal sum construction methods on bounded lattices which generate implications are discussed. Some basic properties of ordinal sum implications are studied.
In this paper, the ordinal sum construction methods of implications on bounded lattices are studied. Necessary and sufficient conditions of an ordinal sum for obtaining an implication are presented. New ordinal sum construction methods on bounded lattices which generate implications are discussed. Some basic properties of ordinal sum implications are studied.
DOI : 10.14736/kyb-2019-4-0641
Classification : 03B52, 03E72
Keywords: ordinal sum; implication; bounded lattice 
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Kesicioğlu, M. Nesibe. Construction methods for implications on bounded lattices. Kybernetika, Tome 55 (2019) no. 4, pp. 641-667. doi: 10.14736/kyb-2019-4-0641

[1] Baczyński, M., Drygaś, P., Król, A., Mesiar, R.: New types of ordinal sum of fuzzy implications. In: Fuzzy systems (FUZZ-IEEE), 2017 IEEE International Conference, 2017. | DOI

[2] Baczyński, M., Jayaram, B.: Fuzzy Implications. Studies in Fuzziness and Soft Computing 231, Springer, Berlin, Heidelberg, 2008. | MR | Zbl

[3] Birkhoff, G.: Lattice Theory. Third edition. Providence, 1967. | DOI | MR

[4] Çaylı, G. D.: On a new class of t-norms and t-conorms on bounded lattices. Fuzzy Sets and Systems 132 (2018), 129-143. | DOI | MR

[5] Drygaś, P., Król, A.: Various kinds of fuzzy implications. In: Novel Developments in Uncertainty Represent, and Processing (K. T. Atanassov et al., eds.), Advences in Intelligent Systems and Computing 401, Springer Internat. Publ. AG, 2016, pp. 37-49. | DOI

[6] Drygaś, P., Król, A.: Generating fuzzy implications by ordinal sums. Tatra Mt. Math. Publ. 66 (2016), 39-50. | DOI | MR

[7] Dubois, D., Prade, H.: A review of fuzzy set aggregation connectives. Inform. Sci. 36 (1985), 85-121. | DOI | MR | Zbl

[8] Dubois, D., Prade, H.: Fuzzy sets in approximate reasoning, Part 1: inference with possibility distributions. Fuzzy Sets and Systems 40 (1991), 143-202. | DOI | MR

[9] Ertuğrul, Ü., Kesicioğlu, M. N., Karaçal, F.: Ordering based on uninorms. Inform. Sci. 330 (2016), 315-327. | DOI

[10] Ertuğrul, Ü., Karaçal, F., Mesiar, R.: Modified ordinal sums of triangular norms and triangular conorms on bounded lattices. Int. J. Intell. Systems 30 (2015), 807-817. | DOI

[11] Fodor, J., Rudas, I. J.: Migrative t-norms with respect to continuous ordinal sums. Inform. Sci. 181 (2011), 4860-4866. | DOI | MR

[12] Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, 2009. | DOI | MR | Zbl

[13] Kesicioğlu, M. N., Mesiar, R.: Ordering based on implications. Inform. Sci. 276 (2014), 377-386. | DOI | MR

[14] Klement, E. P., (eds.), R. Mesiar: Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular Norms. Elsevier, Amsterdam 2005. | MR

[15] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht 2000. | MR | Zbl

[16] Klement, E. P., Mesiar, R., Pap, E.: Triangular norms as ordinal sums of semigroups in the sense of A. H. Clifford. Semigroup Forum 65 (2002), 71-82. | DOI | MR

[17] Ma, Z., Wu, W. M.: Logical operators on complete lattices. Inform. Sci. 55 (1991), 77-97. | DOI | MR | Zbl

[18] Mas, M., Monserrat, M., Torrens, J.: The law of importation for discrete implications. Inform. Sci. 179 (2009), 4208-4218. | DOI | MR

[19] Mas, M., Monserrat, M., Torrens, J., Trillas, E.: A survey on fuzzy implication functions. IEEE Trans. Fuzzy Syst. 15 (2007), 1107-1121. | DOI

[20] Medina, J.: Characterizing when an ordinal sum of t-norms is a t-norm on bounded lattices. Fuzzy Sets and Systems 202 (2012), 75-88. | DOI | MR

[21] Mesiar, R., Mesiarová, A.: Residual implications and left-continuous t-norms which are ordinal sum of semigroups. Fuzzy Sets and Systems 143 (2004), 47-57. | DOI | MR

[22] Mesiarová-Zemánková, A.: Ordinal sum construction for uninorms and generalized uninorms. Int. J. Approx. Reason. 76 (2016), 1-17. | DOI | MR

[23] Mesiarová-Zemánková, A.: Ordinal sums of representable uninorms. Fuzzy Sets and Systems 308 (2017), 42-53. | DOI | MR

[24] Riera, J. V., Torrens, J.: Residual implications on the set of discrete fuzzy numbers. Inform. Sci. 247 (2013), 131-143. | DOI | MR

[25] Saminger, S.: On ordinal sum of triangular norms on bounded lattices. Fuzzy Sets and Systems 157 (2006), 1403-1416. | DOI | MR

[26] Su, Y., Xie, A., Liu, H.: On ordinal sum implications. Inform. Sci. 293 (2015), 251-262. | DOI | MR

[27] Xie, A., Liu, H., Zhang, F., Li, C.: On the distributivity of fuzzy implications over continuous Archimedean t-conorms and continuous t-conorms given as ordinal sums. Fuzzy Sets and Systems 205 (2012), 76-100. | DOI | MR

[28] Yager, R. R.: Aggregation operators and fuzzy systems modelling. Fuzzy Sets and Systems 67 (1994), 129-145. | DOI | MR

[29] Yager, R. R., Rybalov, A.: Uninorm aggregation operators. Fuzzy Sets and Systems 80 (1996), 111-120. | DOI | MR | Zbl

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