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Subtractions over intuitionistic fuzzy sets: Difference between revisions
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| <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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== Approaches to defining intuitionistic fuzzy subtractions == | |||
== References == | == References == | ||
Revision as of 17:40, 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} |
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
