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Subtractions over intuitionistic fuzzy sets

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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), sgB(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), sgB(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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