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Subtractions over intuitionistic fuzzy sets: Difference between revisions

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| &#123;&#60;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>&#62;&#124;x &#8712; E&#125;
| &#123;&#60;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>&#62;&#124;x &#8712; E&#125;
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| &#8212;<sub>5</sub>&#8242;
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| &#123;&#60;x, <font color=green>min(μ<sub>A</sub>(x), {{overline|sg}}(1 - ν<sub>B</sub>(x)))</font>, <font color=red>max(ν<sub>A</sub>(x), sg(1 - ν<sub>B</sub>(x)))</font>&#62;&#124;x &#8712; E&#125;
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| <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x))</font>
| <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>
| <font color=red>max(ν<sub>A</sub>(x), 1 - ν<sub>B</sub>(x))</font>
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| &#8212;<sub>5</sub>&#8242;
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| <font color=green>min(μ<sub>A</sub>(x), {{overline|sg}}(1 - ν<sub>B</sub>(x)))</font>
| <font color=red>max(ν<sub>A</sub>(x), sg(1 - ν<sub>B</sub>(x)))</font>
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| &#8212;<sub>6</sub>&#8242;
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| <font color=green>min(μ<sub>A</sub>(x), {{overline|sg}}(1 - ν<sub>B</sub>(x)))</font>
| <font color=red>max(ν<sub>A</sub>(x), sg(μ<sub>B</sub>(x)))</font>
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| &#8212;<sub>7</sub>&#8242;
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| <font color=green>min(μ<sub>A</sub>(x), {{overline|sg}}(1 - ν<sub>B</sub>(x)))</font>
| <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x))</font>
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| &#8212;<sub>8</sub>&#8242;
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| <font color=green>min(μ<sub>A</sub>(x), 1 - μ<sub>B</sub>(x))</font>
| <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x))</font>
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Revision as of 19:40, 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}


—5′ {<x, min(μA(x), sg(1 - νB(x))), max(νA(x), sg(1 - νB(x)))>|x ∈ E}
—6′ {<x, min(μA(x), sg(1 - νB(x))), max(νA(x), sg(μB(x)))>|x ∈ E}
—7′ {<x, min(μA(x), sg(1 - νB(x))), max(νA(x), μB(x))>|x ∈ E}
—8′ {<x, min(μA(x), 1 - μB(x)), max(νA(x), μB(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))
—5′ min(μA(x), sg(1 - νB(x))) max(νA(x), sg(1 - νB(x)))
—6′ min(μA(x), sg(1 - νB(x))) max(νA(x), sg(μB(x)))
—7′ min(μA(x), sg(1 - νB(x))) max(νA(x), μB(x))
—8′ min(μA(x), 1 - μB(x)) max(νA(x), μB(x))

Approaches to defining intuitionistic fuzzy subtractions

References

See also

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