Geodesic
Smooth implications on a finite chain
Kybernetika, Tome 55 (2019) no. 4, pp. 668-674
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Mas et al. adapted the notion of smoothness, introduced by Godo and Sierra, and discussed two kinds of smooth implications (a discrete counterpart of continuous fuzzy implications) on a finite chain. This work is devoted to exploring the formal relations between smoothness and other six properties of implications on a finite chain. As a byproduct, several classes of smooth implications on a finite chain are characterized.
Mas et al. adapted the notion of smoothness, introduced by Godo and Sierra, and discussed two kinds of smooth implications (a discrete counterpart of continuous fuzzy implications) on a finite chain. This work is devoted to exploring the formal relations between smoothness and other six properties of implications on a finite chain. As a byproduct, several classes of smooth implications on a finite chain are characterized.
DOI : 10.14736/kyb-2019-4-0668
Classification : 03B52, 03E72
Keywords: implications; finite chain; smoothness 
@article{10_14736_kyb_2019_4_0668,
     author = {Su, Yong},
     title = {Smooth implications on a finite chain},
     journal = {Kybernetika},
     pages = {668--674},
     year = {2019},
     volume = {55},
     number = {4},
     doi = {10.14736/kyb-2019-4-0668},
     mrnumber = {4043541},
     zbl = {07177909},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2019-4-0668/}
}
TY  - JOUR
AU  - Su, Yong
TI  - Smooth implications on a finite chain
JO  - Kybernetika
PY  - 2019
SP  - 668
EP  - 674
VL  - 55
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2019-4-0668/
DO  - 10.14736/kyb-2019-4-0668
LA  - en
ID  - 10_14736_kyb_2019_4_0668
ER  - 
%0 Journal Article
%A Su, Yong
%T Smooth implications on a finite chain
%J Kybernetika
%D 2019
%P 668-674
%V 55
%N 4
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2019-4-0668/
%R 10.14736/kyb-2019-4-0668
%G en
%F 10_14736_kyb_2019_4_0668
Su, Yong. Smooth implications on a finite chain. Kybernetika, Tome 55 (2019) no. 4, pp. 668-674. doi: 10.14736/kyb-2019-4-0668

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

[2] Fodor, J.: Smooth associative operations on finite ordinal scales. IEEE Trans. Fuzzy Systems 8 (2000), 6, 791-795. | DOI

[3] Mas, M., Monserrat, M., Torrens, J.: S-implications and R-implications on a finite chain. Kybernetika 40 (2004), 1, 3-20. | MR

[4] Mas, M., Monserrat, M., Torrens, J.: On two types of discrete implications. Int. J. Approx. Reason. 40 (2005), 262-279. | DOI | MR

[5] Mayor, G., Torrens, J.: On a class of operators for expert systems. Int. J. Intell. Systems 8 (1993), 771-778. | DOI | Zbl

[6] Shi, Y., Gasse, B. Van, Ruan, D., Kerre, E. E.: On dependencies and independencies of fuzzy implication axioms. Fuzzy Sets and Systems 161 (2010), 1388-1405. | DOI | MR

[7] Yager, R. R.: Non-numeric multi-criteria multi-person decision making. Group Decisions Negotiation 2 (1993), 81-93. | DOI

Cité par Sources :