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Subtractions over intuitionistic fuzzy sets: Difference between revisions
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== List of intuitionistic fuzzy subtractions == | |||
{| | |||
|-valign="middle" | |||
| rowspan="2" | sg(x) = <span style="font-size:350%;">{</span> | |||
| 1 || if x > 0 | |||
|- | |||
| 0 || if x ≤ 0 | |||
|} | |||
{| | |||
|-valign="middle" | |||
| rowspan="2" | {{overline|sg}}(x) = <span style="font-size:350%;">{</span> | |||
| 1 || if x < 0 | |||
|- | |||
| 0 || if x ≥ 0 | |||
|} | |||
{| 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%" | Subtraction<br/> | |||
|- valign="top" | |||
| —<sub>1</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x))</font>, <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x))</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>2</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), {{overline|sg}}(μ<sub>B</sub>(x)))</font>, <font color=red>max(ν<sub>A</sub>(x), sg(μ<sub>B</sub>(x)))</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>3</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x))</font>, <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x).ν<sub>B</sub>(x) + μ<sub>B</sub>(x)<sup>2</sup>)</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>4</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x))</font>, <font color=red>max(ν<sub>A</sub>(x), 1 - ν<sub>B</sub>(x))</font>>|x ∈ E} | |||
|} | |||
=== Alternative separated view === | |||
{| width="100%" class="wikitable" style="font-family:Courier; font-size:120%;" | |||
|- valign="top" | |||
! width="5%" | No. | |||
! width="5%" | Ref. | |||
! width="5%" | Year | |||
! width="85%" | Subtraction: | |||
{<x, <font color=green>Subtraction MEMBERSHIP expression</font>, <font color=red>Subtraction NON-MEMBERSHIP expression</font> >|x ∈ E} | |||
|} | |||
{| width="100%" class="wikitable sortable" style="font-family:Courier; font-size:120%;" | |||
|- valign="top" | |||
! width="5%" | No. | |||
! width="5%" | Ref. | |||
! width="5%" | Year | |||
! width="40%" | Subtraction MEMBERSHIP expression<br/> | |||
! width="45%" | Subtraction NON-MEMBERSHIP expression<br/> | |||
|- valign="top" | |||
| —<sub>1</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x))</font> | |||
| <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x))</font> | |||
|- valign="top" | |||
| —<sub>2</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), {{overline|sg}}(μ<sub>B</sub>(x)))</font> | |||
| <font color=red>max(ν<sub>A</sub>(x), sg(μ<sub>B</sub>(x)))</font> | |||
|- valign="top" | |||
| —<sub>3</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x))</font> | |||
| <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x).ν<sub>B</sub>(x) + μ<sub>B</sub>(x)<sup>2</sup>)</font> | |||
|- valign="top" | |||
| —<sub>4</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x))</font> | |||
| <font color=red>max(ν<sub>A</sub>(x), 1 - ν<sub>B</sub>(x))</font> | |||
|} | |||
== References == | == References == | ||
* [[Issue:Remark on operation "subtraction" over intuitionistic fuzzy sets|Remark on operation "subtraction" over intuitionistic fuzzy sets]], Krassimir Atanassov, 2009 | * [[Issue:Remark on operation "subtraction" over intuitionistic fuzzy sets|Remark on operation "subtraction" over intuitionistic fuzzy sets]], Krassimir Atanassov, 2009 | ||
Revision as of 17:29, 22 August 2011
List of intuitionistic fuzzy subtractions
| sg(x) = { | 1 | if x > 0 |
| 0 | if x ≤ 0 |
| sg(x) = { | 1 | if x < 0 |
| 0 | if x ≥ 0 |
| No. | Ref. | Year | Subtraction |
|---|---|---|---|
| —1′ | {<x, min(μA(x), νB(x)), max(νA(x), μB(x))>|x ∈ E} | ||
| —2′ | {<x, min(μA(x), sg(μB(x))), max(νA(x), sg(μB(x)))>|x ∈ E} | ||
| —3′ | {<x, min(μA(x), νB(x)), max(νA(x), μB(x).νB(x) + μB(x)2)>|x ∈ E} | ||
| —4′ | {<x, min(μA(x), νB(x)), max(νA(x), 1 - νB(x))>|x ∈ E} |
Alternative separated view
| No. | Ref. | Year | Subtraction:
{<x, Subtraction MEMBERSHIP expression, Subtraction NON-MEMBERSHIP expression >|x ∈ E} |
|---|
| No. | Ref. | Year | Subtraction MEMBERSHIP expression |
Subtraction NON-MEMBERSHIP expression |
|---|---|---|---|---|
| —1′ | min(μA(x), νB(x)) | max(νA(x), μB(x)) | ||
| —2′ | min(μA(x), sg(μB(x))) | max(νA(x), sg(μB(x))) | ||
| —3′ | min(μA(x), νB(x)) | max(νA(x), μB(x).νB(x) + μB(x)2) | ||
| —4′ | min(μA(x), νB(x)) | max(νA(x), 1 - νB(x)) |
References
- Remark on operation "subtraction" over intuitionistic fuzzy sets, Krassimir Atanassov, 2009
- On intuitionistic fuzzy subtraction, generated by an implication from Kleene-Dienes type, Lilija Atanassova, 2009
- On intuitionistic fuzzy subtraction, related to intuitionistic fuzzy negation ¬11, Beloslav Riečan, Diana Boyadzhieva, Krassimir Atanassov, 2009
- On intuitionistic fuzzy subtraction, related to intuitionistic fuzzy negation ¬4, Beloslav Riečan, Magdaléna Renčová, Krassimir Atanassov, 2009
- Equalities with intuitionistic fuzzy subtractions and negations, Krassimir Atanassov, Magdaléna Renčová, Dimitar Dimitrov, 2010
