Geodesic
$T$-equivalences generated by shape function on the real line
Kybernetika, Tome 39 (2003) no. 3, pp. 281-288 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

This paper is devoted to give a new method of generating T-equivalence using shape function and finding the exact calculation formulas of T-equivalence induced by shape function on the real line. Some illustrative examples are given.
This paper is devoted to give a new method of generating T-equivalence using shape function and finding the exact calculation formulas of T-equivalence induced by shape function on the real line. Some illustrative examples are given.
Classification : 03E02, 03E72, 26A21, 26E50
Keywords: fuzzy number; fuzzy relation; t-norm; T-equivalence; shape function 
@article{KYB_2003_39_3_a2,
     author = {Hong, Dug Hun},
     title = {$T$-equivalences generated by shape function on the real line},
     journal = {Kybernetika},
     pages = {281--288},
     year = {2003},
     volume = {39},
     number = {3},
     mrnumber = {1995731},
     zbl = {1249.26006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2003_39_3_a2/}
}
TY  - JOUR
AU  - Hong, Dug Hun
TI  - $T$-equivalences generated by shape function on the real line
JO  - Kybernetika
PY  - 2003
SP  - 281
EP  - 288
VL  - 39
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/KYB_2003_39_3_a2/
LA  - en
ID  - KYB_2003_39_3_a2
ER  - 
%0 Journal Article
%A Hong, Dug Hun
%T $T$-equivalences generated by shape function on the real line
%J Kybernetika
%D 2003
%P 281-288
%V 39
%N 3
%U http://geodesic.mathdoc.fr/item/KYB_2003_39_3_a2/
%G en
%F KYB_2003_39_3_a2
Hong, Dug Hun. $T$-equivalences generated by shape function on the real line. Kybernetika, Tome 39 (2003) no. 3, pp. 281-288. http://geodesic.mathdoc.fr/item/KYB_2003_39_3_a2/

[1] Baets B. De, Marková A.: Analytical for the addition of fuzzy intervals. Fuzzy Sets and Systems 91 (1997), 203–213 | DOI | MR

[2] Baets B. De, Mareš, M., Mesiar R.: T-partition of the real line generated by impotent shapes. Fuzzy Sets and Systems 91 (1997), 177–184 | MR

[3] Baets B. De, Mesiar R.: Pseudo-metrics and T-equivalence. J. Fuzzy Math. 5 (1997), 471–481 | MR

[4] Harrison M. A.: Introduction to Switching and Automata Theory. McGraw–Hill, New York 1965 | MR | Zbl

[5] Hong D. H., Hwang S. Y.: On the convergence of T-sum of L-R fuzzy numbers. Fuzzy Sets and Systems 63 (1994), 175–180 | DOI | MR | Zbl

[6] Hong D. H., Hwang C.: A T-sum bound of L-R fuzzy numbers. Fuzzy Sets and Systems 91 (1997), 239–252 | DOI | MR

[7] Hong D. H., Ro P.: The law of large numbers for fuzzy numbers with bounded supports. Fuzzy Sets and Systems 116 (2000), 269–274 | MR

[8] Jacas J., Recasens J.: Fuzzy numbers and equality relations. In: Proc. 2nd IEEE International Conference on Fuzzy Systems, San Francisco 1993, pp. 1298–1301

[9] Ling C.: Representation of associative function. Publ. Math. Debrecen 12 (1965), 189–212 | MR

[10] Mareš M., Mesiar R.: Composition of shape generators. Acta Mathematica et Informatica Universitatis Ostravienses 4 (1996), 37–46 | MR | Zbl

[11] Mareš M., Mesiar R.: Fuzzy quantities and their aggregation, in aggregation operations. In: New Trends and Applications. Physica–Verlag, Heidelberg 2002, pp. 291–352 | MR

[12] Marková–Stupňanová A.: Idempotents of T-addition of fuzzy numbers. Tatra Mt. Math. Publ. 12 (1997), 67–72 | MR | Zbl

[13] Mesiar R.: A note to T-sum of L-R fuzzy numbers. Fuzzy Sets and Systems 87 (1996), 259–261 | DOI | MR

[14] Schweizer B., Sklar A.: Probabilistic Metric Spaces. North–Holland, New York 1983 | MR | Zbl