Implications over intuitionistic fuzzy sets - Revision history

Vassia Atanassova: ; "What Links Here" References {{Special:WhatLinksHere/{{PAGENAME}}|namespace=102|hidetrans=1|hideredirs=1}}

2022-04-29T07:41:23Z

; "What Links Here" References {{Special:WhatLinksHere/{{PAGENAME}}|namespace=102|hidetrans=1|hideredirs=1}}

← Older revision		Revision as of 10:41, 29 April 2022
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	* [[Issue:On some two-parametric intuitionistic fuzzy implications\|On some two-parametric intuitionistic fuzzy implications]], Piotr Dworniczak, 2011		* [[Issue:On some two-parametric intuitionistic fuzzy implications\|On some two-parametric intuitionistic fuzzy implications]], Piotr Dworniczak, 2011
	* [[Issue:Second Zadeh's intuitionistic fuzzy implication\|Second Zadeh's intuitionistic fuzzy implication]], Krassimir Atanassov, 2011		* [[Issue:Second Zadeh's intuitionistic fuzzy implication\|Second Zadeh's intuitionistic fuzzy implication]], Krassimir Atanassov, 2011

			; "What Links Here" References

			{{Special:WhatLinksHere/{{PAGENAME}}\|namespace=102\|hidetrans=1\|hideredirs=1}}

	== See also ==		== See also ==

2021-03-11T07:45:08Z

Alternative separated view

← Older revision		Revision as of 10:45, 11 March 2021
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	=== ~~Alternative separated view~~ ===		=== List of implications ===


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	== References ==		== References ==

2021-03-11T07:44:36Z

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	\| {<x, <font color=green>μ<sub>B</sub>(x)+ν<sub>A</sub>(x).(1-ν<sub>A</sub>(x))-μ<sub>B</sub>(x).</font>, <font color=red></font>>\|x ∈ E}		\| {<x, <font color=green>μ<sub>B</sub>(x)+ν<sub>A</sub>(x).(1-ν<sub>A</sub>(x))-μ<sub>B</sub>(x).</font>, <font color=red></font>>\|x ∈ E}
	\|}		\|}
			-->


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	</font>		</font>
	\|}~~-->~~		\|}

	== References ==		== References ==

2021-03-11T07:43:52Z

List of intuitionistic fuzzy implications

← Older revision		Revision as of 10:43, 11 March 2021
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	\end{cases}.</math>		\end{cases}.</math>

	== List of intuitionistic fuzzy implications ==		<!-- == List of intuitionistic fuzzy implications ==

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	== References ==		== References ==

2016-05-05T09:10:02Z

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	0 \text{ if } x \leq 0		0 \text{ if } x \leq 0
	\end{cases},</math>   <math>		\end{cases},</math>   <math>
	\overline{\text{sg}}(x) = \begin{cases} 1 \text{ if } x < 0 \\		\overline{\text{sg}}(x) = \begin{cases} 0 \text{ if } x > 0 \\
	0 \text{ if } x \~~geq~~ 0		1 \text{ if } x \leq 0
	\end{cases}.</math>		\end{cases}.</math>

2015-06-30T14:41:23Z

List of intuitionistic fuzzy implications: up to 147

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+|
+|
-| <font color=green>μ<sub>B</sub>(x)+ν<sub>A</sub>(x).(1-ν<sub>A</sub>(x))-μ<sub>B</sub>(x).</font> || <font color=red></font>
+| <font color=green>μ<sub>B</sub>(x)+ν<sub>A</sub>(x).(1-ν<sub>A</sub>(x))-μ<sub>B</sub>(x).</font> || <font color=red>
 |}

2015-06-02T10:44:02Z

← Older revision		Revision as of 13:44, 2 June 2015
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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:		For the various definitions of implication of over [[intuitionistic fuzzy sets]], the functions sg(''x'') and {{overline\|sg}}(''x'') have been used:

	<math>		<math>\text{sg}(x) = \begin{cases} 1 \text{ if } x > 0 \\
	\text{sg}(x) = ~~\left \{~~ \begin{~~array}{c c~~} 1 & \text{if } x > 0 \\		0 \text{ if } x \leq 0
	0 & \text{if } x \leq 0		\end{cases},</math>   <math>
	\end{~~array~~},</math>   <math>		\overline{\text{sg}}(x) = \begin{cases} 1 \text{ if } x < 0 \\
	\overline{\text{sg}}(x) = ~~\left \{~~ \begin{~~array}{c c~~} 1 & \text{if } x < 0 \\		0 \text{ if } x \geq 0
	0 & \text{if } x \geq 0		\end{cases}.</math>
	\end{~~array~~}.</math>

	== List of intuitionistic fuzzy implications ==		== List of intuitionistic fuzzy implications ==

2015-05-26T10:20:57Z

Alternative separated view

2013-12-10T16:37:05Z

← Older revision		Revision as of 19:37, 10 December 2013
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	\end{array}.</math>		\end{array}.</math>

	ρ== List of intuitionistic fuzzy implications ==		== List of intuitionistic fuzzy implications ==

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2013-11-14T11:22:28Z

← Older revision		Revision as of 14:22, 14 November 2013
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	\|		\|
	\| {<x, <font color=green>μ<sub>B</sub>(x)+ν<sub>A</sub>(x)-μ<sub>B</sub>(x).ν<sub>A</sub>(x)</font>, <font color=red>((1-μ<sub>B</sub>(x)).μ<sub>B</sub>(x)+{{overline\|sg}}(μ<sub>B</sub>(x))).(1-ν<sub>A</sub>(x))</font>>\|x ∈ E}		\| {<x, <font color=green>μ<sub>B</sub>(x)+ν<sub>A</sub>(x)-μ<sub>B</sub>(x).ν<sub>A</sub>(x)</font>, <font color=red>((1-μ<sub>B</sub>(x)).μ<sub>B</sub>(x)+{{overline\|sg}}(μ<sub>B</sub>(x))).(1-ν<sub>A</sub>(x))</font>>\|x ∈ E}

			\|- valign="top"
			\| →<sub>138</sub>
			\|
			\|
			\| {<x, <font color=green>μ<sub>B</sub>(x)+ν<sub>A</sub>(x).(1-ν<sub>A</sub>(x))-μ<sub>B</sub>(x).</font>, <font color=red></font>>\|x ∈ E}
	\|}		\|}