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Implications over intuitionistic fuzzy sets: Difference between revisions
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For the various definitions of implication of over [[intuitionistic fuzzy sets]], the functions sg(''x'') and {{overline|sg}}(''x'') have been used: | |||
<math> | |||
\text{sg}(x) = \left \{ \begin{array}{c c} 1 & \text{if } x > 0 \\ | |||
0 & \text{if } x \leq 0 | |||
\end{array},</math> <math> | |||
\overline{\text{sg}}(x) = \left \{ \begin{array}{c c} 1 & \text{if } x < 0 \\ | |||
0 & \text{if } x \geq 0 | |||
\end{array}.</math> | |||
== List of intuitionistic fuzzy implications == | |||
{| width="100%" class="wikitable sortable" style="font-family:Courier; font-size:120%;" | |||
|- valign="top" | |||
! width="5%" | No. | |||
! width="5%" | Ref. | |||
! width="5%" | Year | |||
! width="85%" | Implication<br/> | |||
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| {<x, <font color=green> </font>, <font color=red> </font>>|x ∈ E} | |||
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|} | |||
=== Alternative separated view === | |||
== References == | == References == | ||
* [[Issue:On some properties of intuitionistic fuzzy implications|On some properties of intuitionistic fuzzy implications]], Michał Baczyński, 2003 | * [[Issue:On some properties of intuitionistic fuzzy implications|On some properties of intuitionistic fuzzy implications]], Michał Baczyński, 2003 | ||
Revision as of 13:48, 5 November 2013
For the various definitions of implication of over intuitionistic fuzzy sets, the functions sg(x) and sg(x) have been used:
[math]\displaystyle{ \text{sg}(x) = \left \{ \begin{array}{c c} 1 & \text{if } x \gt 0 \\ 0 & \text{if } x \leq 0 \end{array}, }[/math] [math]\displaystyle{ \overline{\text{sg}}(x) = \left \{ \begin{array}{c c} 1 & \text{if } x \lt 0 \\ 0 & \text{if } x \geq 0 \end{array}. }[/math]
List of intuitionistic fuzzy implications
| No. | Ref. | Year | Implication |
|---|
Alternative separated view
References
- On some properties of intuitionistic fuzzy implications, Michał Baczyński, 2003
- Intuitionistic fuzzy implications and Modus Ponens, Krassimir Atanassov, 2005
- A property of intuitionistic fuzzy implications, Yun Shi and Violeta Tasseva, 2005
- On some intuitionistic fuzzy implications, Krassimir Atanassov, 2006
- On a new intuitionistic fuzzy implication of Gaines-Rescher's type, Beloslav Riečan, Krassimir Atanassov, 2007
- A study on some intuitionistic fuzzy implications, Violeta Tasseva, Desislava Peneva, 2007
- On intuitionistic fuzzy subtraction, generated by an implication from Kleene-Dienes type, Lilija Atanassova, 2009
- A new intuitionistic fuzzy implication, Lilija Atanassova, 2009
- Intuitionistic fuzzy implications and axioms for implications, Krassimir Atanassov and Dimitar Dimitrov, 2010
- Four modal forms of intuitionistic fuzzy implication →@ and two related intuitionistic fuzzy negations. Part 1, Lilija Atanassova, 2010
- Some Remarks about L. Atanassova’s Paper “A New Intuitionistic Fuzzy Implication”, Piotr Dworniczak, 2010
- On the basic properties of the negations generated by some parametric intuitionistic fuzzy implications, Piotr Dworniczak, 2011
- On some two-parametric intuitionistic fuzzy implications, Piotr Dworniczak, 2011
- Second Zadeh's intuitionistic fuzzy implication, Krassimir Atanassov, 2011
