Geodesic
Incomparability with respect to the triangular order
Kybernetika, Tome 52 (2016) no. 1, pp. 15-27
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper, we define the set of incomparable elements with respect to the triangular order for any t-norm on a bounded lattice. By means of the triangular order, an equivalence relation on the class of t-norms on a bounded lattice is defined and this equivalence is deeply investigated. Finally, we discuss some properties of this equivalence.
In this paper, we define the set of incomparable elements with respect to the triangular order for any t-norm on a bounded lattice. By means of the triangular order, an equivalence relation on the class of t-norms on a bounded lattice is defined and this equivalence is deeply investigated. Finally, we discuss some properties of this equivalence.
DOI : 10.14736/kyb-2016-1-0015
Classification : 03B52, 03E72
Keywords: triangular norm; $T$-partial order; bounded lattice 
@article{10_14736_kyb_2016_1_0015,
     author = {A\c{s}{\i}c{\i}, Emel and Kara\c{c}al, Funda},
     title = {Incomparability with respect to the triangular order},
     journal = {Kybernetika},
     pages = {15--27},
     year = {2016},
     volume = {52},
     number = {1},
     doi = {10.14736/kyb-2016-1-0015},
     mrnumber = {3482608},
     zbl = {06562210},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-1-0015/}
}
TY  - JOUR
AU  - Aşıcı, Emel
AU  - Karaçal, Funda
TI  - Incomparability with respect to the triangular order
JO  - Kybernetika
PY  - 2016
SP  - 15
EP  - 27
VL  - 52
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-1-0015/
DO  - 10.14736/kyb-2016-1-0015
LA  - en
ID  - 10_14736_kyb_2016_1_0015
ER  - 
%0 Journal Article
%A Aşıcı, Emel
%A Karaçal, Funda
%T Incomparability with respect to the triangular order
%J Kybernetika
%D 2016
%P 15-27
%V 52
%N 1
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-1-0015/
%R 10.14736/kyb-2016-1-0015
%G en
%F 10_14736_kyb_2016_1_0015
Aşıcı, Emel; Karaçal, Funda. Incomparability with respect to the triangular order. Kybernetika, Tome 52 (2016) no. 1, pp. 15-27. doi: 10.14736/kyb-2016-1-0015

[1] Aşıcı, E., Karaçal, F.: On the T-partial order and properties. Inf. Sci. 267 (2014), 323-333. | DOI | MR

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

[3] Baets, B. De, Mesiar, R.: Triangular norms on product lattices. Fuzzy Sets Syst. 104 (1999), 61-75. | DOI | MR | Zbl

[4] Baets, B. De, Mesiar, R.: Triangular norms on the real unit square. In: Proc. 1999 EUSFLAT-ESTYLF Joint Conference, Palma de Mallorca 1999, pp. 351-354.

[5] Casasnovas, J., Mayor, G.: Discrete t-norms and operations on extended multisets. Fuzzy Sets Syst. 159 (2008), 1165-1177. | DOI | MR | Zbl

[6] Gottwald, S.: A Treatise on Many-valued Logic. Studies in Logic and Computation, Research Studies Press, Baldock 2001. | MR

[7] Karaçal, F., Aşıcı, E.: Some notes on T-partial order. J. Inequal. Appl. 2013 (2013), 219. | DOI | MR

[8] Karaçal, F., Kesicioğlu, M. N.: A T-partial order obtained from t-norms. Kybernetika 47 (2011), 300-314. | MR | Zbl

[9] Karaçal, F., Sağıroğlu, Y.: Infinetely $\bigvee$- distributive t-norm on complete lattices and pseudo-complements. Fuzzy Sets Syst. 160 (2009), 32-43. | MR

[10] Karaçal, F., Khadjiev, Dj.: $\bigvee$-distributive and infinitely $\bigvee$-distributive t-norms on complete lattice. Fuzzy Sets Syst. 151 (2005), 341-352. | DOI | MR

[11] Karaçal, F.: On the direct decomposability of strong negations and S-implication operators on product lattices. Inf. Sci. 176 (2006), 3011-3025. | DOI | MR | Zbl

[12] Kesicioğlu, M. N., Karaçal, F., Mesiar, R.: Order-equivalent triangular norms. Fuzzy Sets Syst. 268 (2015), 59-71. | MR

[13] Khadjiev, D., Karaçal, F.: Pairwise comaximal elements and the classification of all $\vee$-distributive triangular norms of length 3. Inf. Sci. 204 (2012), 36-43. | DOI | MR | Zbl

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

[15] Liang, X., Pedrycz, W.: Logic-based fuzzy networks: A study in system modeling with triangular norms and uninorms. Fuzzy Sets Syst. 160 (2009), 3475-3502. | DOI | MR | Zbl

[16] Maes, K. C., Mesiarova-Zemankova, A.: Cancellativity properties for t-norms and t-subnorms. Inf. Sci. 179 (2009), 135-150. | DOI | MR | Zbl

[17] Martin, J., Mayor, G., Torrens, J.: On locally internal monotonic operations. Fuzzy Sets Syst. 137 (2003), 27-42. | DOI | MR | Zbl

[18] Mitsch, H.: A natural partial order for semigroups. Proc. Am. Math. Soc. 97 (1986), 384-388. | DOI | MR | Zbl

[19] Saminger, S.: On ordinal sums of triangular norms on bounded lattices. Fuzzy Sets Syst. 157 (2006), 1403-1413. | DOI | MR | Zbl

[20] Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. Elsevier, Amsterdam 1983. | MR | Zbl

[21] Schweizer, B., Sklar, A.: Espaces métriques aléatoires. C. R. Acad. Sci. Paris Sér. A 247 (1958), 2092-2094. | MR | Zbl

[22] Schweizer, B., Sklar, A.: Statistical metric spaces. Pacific J. Math. 10 (1960), 313-334. | DOI | MR | Zbl

[23] Schweizer, B., Sklar, A.: Associative functions and abstract semigroups. Publ. Math. Debrecen 10 (1963), 69-81. | MR

Cité par Sources :