A note about operations like T W (the weakest t -norm) based addition on fuzzy intervals

Dug Hun Hong

Kybernetika (2009)

  • Volume: 45, Issue: 3, page 541-547
  • ISSN: 0023-5954

Abstract

top
We investigate a relation about subadditivity of functions. Based on subadditivity of functions, we consider some conditions for continuous t -norms to act as the weakest t -norm T W -based addition. This work extends some results of Marková-Stupňanová [15], Mesiar [18].

How to cite

top

Hong, Dug Hun. "A note about operations like $T_W$ (the weakest $t$-norm) based addition on fuzzy intervals." Kybernetika 45.3 (2009): 541-547. <http://eudml.org/doc/37670>.

@article{Hong2009,
abstract = {We investigate a relation about subadditivity of functions. Based on subadditivity of functions, we consider some conditions for continuous $t$-norms to act as the weakest $t$-norm $T_W$-based addition. This work extends some results of Marková-Stupňanová [15], Mesiar [18].},
author = {Hong, Dug Hun},
journal = {Kybernetika},
keywords = {fuzzy arithmetics; fuzzy intervals; triangular norms; fuzzy arithmetics; fuzzy intervals; triangular norms},
language = {eng},
number = {3},
pages = {541-547},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A note about operations like $T_W$ (the weakest $t$-norm) based addition on fuzzy intervals},
url = {http://eudml.org/doc/37670},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Hong, Dug Hun
TI - A note about operations like $T_W$ (the weakest $t$-norm) based addition on fuzzy intervals
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 3
SP - 541
EP - 547
AB - We investigate a relation about subadditivity of functions. Based on subadditivity of functions, we consider some conditions for continuous $t$-norms to act as the weakest $t$-norm $T_W$-based addition. This work extends some results of Marková-Stupňanová [15], Mesiar [18].
LA - eng
KW - fuzzy arithmetics; fuzzy intervals; triangular norms; fuzzy arithmetics; fuzzy intervals; triangular norms
UR - http://eudml.org/doc/37670
ER -

References

top
  1. Additions of interactive fuzzy numbers, IEEE Trans. Automat. Control 26 (1981), 926–936. MR0635852
  2. t -norm-based addition of fuzzy intervals, Fuzzy Sets and Systems 51 (1992), 155–159. MR1188307
  3. The convergence of T -product of fuzzy numbers, Fuzzy Sets and Systems 85 (1997), 373–378. MR1428313
  4. A note on t -norm-based addition of fuzzy intervals, Fuzzy Sets and Systems 75 (1995), 73–76. Zbl0947.26024MR1351592
  5. A T -sum bound of L R -fuzzy numbers, Fuzzy Sets and Systems 91 (1997), 239–252. MR1480049
  6. A note to the sum of fuzzy variables, Fuzzy Sets and Systems 93 (1998), 121–124. MR1601517
  7. On the compositional rule of inference under triangular norms, Fuzzy Sets and Systems 66 (1994), 25–38. MR1294689
  8. Shape preserving multiplications of fuzzy intervals, Fuzzy Sets and Systems 123 (2001), 93–96. MR1848797
  9. Some results on the addition of fuzzy intervals, Fuzzy Sets and Systems 122 (2001), 349–352. Zbl1010.03524MR1854823
  10. On shape-preserving additions of fuzzy intervals, J. Math. Anal. Appl. 267 (2002), 369–376. Zbl0993.03070MR1886835
  11. g , p -fuzzification of arithmetic operations, Tatra Mountains Math. Publ. 1 (1992), 65–71. MR1230464
  12. Triangular norm-based addition preserving linearity of t -sums of fuzzy intervals, Mathware and Soft Computing 5 (1998), 97–98. MR1632755
  13. Triangular norm-based addition of linear fuzzy numbers, Tatra Mountains Math. Publ. 6 (1995), 75–82. MR1363985
  14. T -sum of L - R -fuzzy numbers, Fuzzy Sets and Systems 85 (1996), 379–384. MR1428314
  15. A note to the addition of fuzzy numbers based on a continuous Archimedean T -norm, Fuzzy Sets and Systems 91 (1997), 253–258. 
  16. A note on the T -sum of L R fuzzy numbers, Fuzzy Sets and Systems 79 (1996), 259–261. MR1388398
  17. Shape preserving additions of fuzzy intervals, Fuzzy Sets and Systems 86 (1997), 73–78. Zbl0921.04002MR1438439
  18. Triangular-norm-based addition of fuzzy intervals, Fuzzy Sets and Systems 91 (1997), 231–237. Zbl0919.04011MR1480048
  19. Associative functions and abstract semigroups, Publ. Math. Debrecen 10 (1963), 69–81. MR0170967
  20. The concept of a linguistic variable and its applications to approximate reasoning, Parts, I, II, III, Inform. Sci. 8 (1975), 199–251, 301–357; 9 (1975) 43–80. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.