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Keywords
(2)
Convex Combination
Triangular Norm
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Convex combinations of continuous tnorms with the same diagonal function
Convex combinations of continuous tnorms with the same diagonal function,10.1016/j.na.2007.08.076,Nonlinear Analysistheory Methods & Applications,R.
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Convex combinations of continuous tnorms with the same diagonal function
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Citations: 4
)
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R. Mesiar
,
A. MesiarováZemánková
The problem of whether a nontrivial
convex combination
of two continuous tnorms with the same diagonal function can be a tnorm is studied. It is shown that in both cases–of two nilpotent and of two strict tnorms–a nontrivial
convex combination
of tnorms with common diagonal function is associative only if the two tnorms involved coincide. For general continuous tnorms a similar result follows. An example of a convex class of noncontinuous tnorms is also included.
Journal:
Nonlinear Analysistheory Methods & Applications  NONLINEAR ANALTHEOR METH APP
, vol. 69, no. 9, pp. 28512856, 2008
DOI:
10.1016/j.na.2007.08.076
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Citation Context
(1)
...Certain versions of this problem have been studied in [15] and in [
21
]...
Thomas Vetterlein
.
Regular leftcontinuous tnorms
References
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Journal:
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On the convex combination of leftcontinuous tnorms
(
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Sándor Jenei
Journal:
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, vol. 72, no. 1, pp. 4759, 2006
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(
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Journal:
Proceedings of The National Academy of Sciences  PNAS
, vol. 28, no. 12, pp. 535537, 1942
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Citations
(4)
Convex combinations of strict tnorms
(
Citations: 1
)
Milan Petrík
Journal:
Soft Computing  SOCO
, vol. 14, no. 10, pp. 10531057, 2010
Convex combinations of nilpotent triangular norms
(
Citations: 3
)
Milan Petrík
,
Peter Sarkoci
Journal:
Journal of Mathematical Analysis and Applications  J MATH ANAL APPL
, vol. 350, no. 1, pp. 271275, 2009
Regular leftcontinuous tnorms
(
Citations: 5
)
Thomas Vetterlein
Journal:
Semigroup Forum
, vol. 77, no. 3, pp. 339379, 2008
Some results of weighted quasiarithmetic mean of continuous triangular norms
Yao Ouyang
,
Jinxuan Fang
Journal:
Information Sciences  ISCI
, vol. 178, no. 22, pp. 43964402, 2008