NEW EXTENDED deadline for submissions: 15 AUGUST 2026.
Subtractions over intuitionistic fuzzy sets
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 |
|---|---|---|---|
| —01′ | {<x, min(μA(x), νB(x)), max(νA(x), μB(x))>|x ∈ E} | ||
| —02′ | {<x, min(μA(x), sg(μB(x))), max(νA(x), sg(μB(x)))>|x ∈ E} | ||
| —03′ | {<x, min(μA(x), νB(x)), max(νA(x), μB(x).νB(x) + μB(x)2)>|x ∈ E} | ||
| —04′ | {<x, min(μA(x), νB(x)), max(νA(x), 1 - νB(x))>|x ∈ E} | ||
| —05′ | {<x, min(μA(x), sg(1 - νB(x))), max(νA(x), sg(1 - νB(x)))>|x ∈ E} | ||
| —06′ | {<x, min(μA(x), sg(1 - νB(x))), max(νA(x), sg(μB(x)))>|x ∈ E} | ||
| —07′ | {<x, min(μA(x), sg(1 - νB(x))), max(νA(x), μB(x))>|x ∈ E} | ||
| —08′ | {<x, min(μA(x), 1 - μB(x)), max(νA(x), μB(x))>|x ∈ E} | ||
| —09′ | {<x, min(μA(x), sg(μB(x))), max(νA(x), μB(x))>|x ∈ E} | ||
| —10′ | {<x, min(μA(x), sg(1 - νB(x))), max(νA(x), 1 - νB(x))>|x ∈ E} | ||
| —11′ | {<x, min(μA(x), sg(νB(x))), max(νA(x), sg(νB(x)))>|x ∈ E} | ||
| —12′ | {<x, min(μA(x), νB(x).(μB(x) + νB(x))), max(νA(x), μB(x).(νB(x)2 + μB(x) + μB(x).νB(x)))>|x ∈ E} | ||
| —13′ | {<x, min(μA(x), sg(1 - μB(x))), max(νA(x), sg(1 - μB(x)))>|x ∈ E} | ||
| —14′ | {<x, min(μA(x), sg(νB(x))), max(νA(x), sg(1 - μB(x)))>|x ∈ E} | ||
| —15′ | {<x, min(μA(x), sg(1 - νB(x))), max(νA(x), sg(1 - μB(x)))>|x ∈ E} | ||
| —16′ | {<x, min(μA(x), sg(μB(x))), max(νA(x), sg(1 - μB(x)))>|x ∈ E} | ||
| —17′ | {<x, min(μA(x), sg(1 - νB(x))), max(νA(x), sg(νB(x)))>|x ∈ E} | ||
| —18′ | {<x, min(μA(x), νB(x), sg(μB(x))), max(νA(x), min(μB(x), sg(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 |
|---|---|---|---|---|
| —01′ | min(μA(x), νB(x)) | max(νA(x), μB(x)) | ||
| —02′ | min(μA(x), sg(μB(x))) | max(νA(x), sg(μB(x))) | ||
| —03′ | min(μA(x), νB(x)) | max(νA(x), μB(x).νB(x) + μB(x)2) | ||
| —04′ | min(μA(x), νB(x)) | max(νA(x), 1 - νB(x)) | ||
| —05′ | min(μA(x), sg(1 - νB(x))) | max(νA(x), sg(1 - νB(x))) | ||
| —06′ | min(μA(x), sg(1 - νB(x))) | max(νA(x), sg(μB(x))) | ||
| —07′ | min(μA(x), sg(1 - νB(x))) | max(νA(x), μB(x)) | ||
| —08′ | min(μA(x), 1 - μB(x)) | max(νA(x), μB(x)) | ||
| —09′ | min(μA(x), sg(μB(x))) | max(νA(x), μB(x)) | ||
| —10′ | min(μA(x), sg(1 - νB(x))) | max(νA(x), 1 - νB(x)) | ||
| —11′ | min(μA(x), sg(νB(x))) | max(νA(x), sg(νB(x))) | ||
| —12′ | min(μA(x), νB(x).(μB(x) + νB(x))) | max(νA(x), μB(x).(νB(x)2 + μB(x) + μB(x).νB(x))) | ||
| —13′ | min(μA(x), sg(1 - μB(x))) | max(νA(x), sg(1 - μB(x))) | ||
| —14′ | min(μA(x), sg(νB(x))) | max(νA(x), sg(1 - μB(x))) | ||
| —15′ | min(μA(x), sg(1 - νB(x))) | max(νA(x), sg(1 - μB(x))) | ||
| —16′ | min(μA(x), sg(μB(x))) | max(νA(x), sg(1 - μB(x))) | ||
| —17′ | min(μA(x), sg(1 - νB(x))) | max(νA(x), sg(νB(x))) | ||
| —18′ | min(μA(x), νB(x), sg(μB(x))) | max(νA(x), min(μB(x), sg(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
