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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), 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))
|
Approaches to defining intuitionistic fuzzy subtractions
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
See also
