Please check our Instructions to Authors and send your manuscripts to nifs.journal@gmail.com. Next issue: March 2025.
Subtractions over intuitionistic fuzzy sets
(Redirected from Intuitionistic fuzzy subtractions)
For the various definitions of subtraction of over intuitionistic fuzzy sets, the functions sg and sg have been used:
[math]\displaystyle{ \text{sg}(x) = \left \{ \begin{array}{c c} 1 & \text{if } x \gt 0 \\ 0 & \text{if } x \leq 0 \end{array}, }[/math] [math]\displaystyle{ \overline{\text{sg}}(x) = \left \{ \begin{array}{c c} 1 & \text{if } x \lt 0 \\ 0 & \text{if } x \geq 0 \end{array}. }[/math]
List of intuitionistic fuzzy subtractions of —i type
Alternative separated view
List of intuitionistic fuzzy subtractions of —i′ type
| 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} | ||
| —19′ | {<x, min(μA(x), νB(x), sg(μB(x))), νA(x)>|x ∈ E} | ||
| —20′ | {<x, min(μA(x), νB(x)), νA(x)>|x ∈ E} | ||
| —21′ | {<x, min(μA(x), 1 - μB(x), sg(μB(x))), max(νA(x), min(μB(x), sg(1 - μB(x))))>|x ∈ E} | ||
| —22′ | {<x, min(μA(x), 1 - μB(x), sg(μB(x))), νA(x)>|x ∈ E} | ||
| —23′ | {<x, min(μA(x), 1 - μB(x)), νA(x)>|x ∈ E} | ||
| —24′ | {<x, min(μA(x), νB(x), sg(1 - νB(x))), max(νA(x), min(1 - νB(x), sg(νB(x))))>|x ∈ E} | ||
| —25′ | {<x, min(μA(x), νB(x), sg(1 - νB(x))), νA(x)>|x ∈ E} | ||
| —26′ | {<x, min(μA(x), νB(x)), max(νA(x), μB(x).νB(x) + sg(1 - μB(x)))>|x ∈ E} | ||
| —27′ | {<x, min(μA(x), 1 - μB(x)), max(νA(x), μB(x).(1 - μB(x)) + sg(1 - μB(x)))>|x ∈ E} | ||
| —28′ | {<x, min(μA(x), νB(x)), max(νA(x), (1 - νB(x)).νB(x) + sg(νB(x)))>|x ∈ E} | ||
| —29′ | {<x, min(μA(x), max(0, μB(x).νB(x) + sg(1 - νB(x)))), max(νA(x), μB(x).(μB(x).νB(x) + sg(1 - νB(x))) + sg(1 - μB(x)))>|x ∈ E} | ||
| —30′ | {<x, min(μA(x), μB(x).νB(x), max(νA(x), μB(x).(μB(x).νB(x) + sg(1 - νB(x))) + sg(1 - μB(x)))>|x ∈ E} | ||
| —31′ | {<x, min(μA(x), (1 - μB(x)).μB(x) + sg(μB(x))), max(νA(x), μB(x).((1 - μB(x)).μB(x) + sg(μB(x))) + sg(1 - μB(x)))>|x ∈ E} | ||
| —32′ | {<x, min(μA(x), (1 - μB(x)).μB(x), max(νA(x), μB(x).((1 - μB(x)).μB(x) + sg(μB(x))) + sg(1 - μB(x)))>|x ∈ E} | ||
| —33′ | {<x, min(μA(x), νB(x).(1 - νB(x)) + sg(1 - νB(x))), max(νA(x), (1 - νB(x)).(νB(x).(1 - νB(x)) + sg(1 - νB(x))) + sg(νB(x)))>|x ∈ E} | ||
| —34′ | {<x, min(μA(x), νB(x).(1 - νB(x))), max(νA(x), (1 - νB(x)).(νB(x).(1 - νB(x)) + sg(1 - νB(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)))) | ||
| —19′ | min(μA(x), νB(x), sg(μB(x))) | νA(x) | ||
| —20′ | min(μA(x), νB(x)) | νA(x) | ||
| —21′ | min(μA(x), 1 - μB(x), sg(μB(x))) | max(νA(x), min(μB(x), sg(1 - μB(x)))) | ||
| —22′ | min(μA(x), 1 - μB(x), sg(μB(x))) | νA(x) | ||
| —23′ | min(μA(x), 1 - μB(x)) | νA(x) | ||
| —24′ | min(μA(x), νB(x), sg(1 - νB(x))) | max(νA(x), min(1 - νB(x), sg(νB(x)))) | ||
| —25′ | min(μA(x), νB(x), sg(1 - νB(x))) | νA(x) | ||
| —26′ | min(μA(x), νB(x)) | max(νA(x), μB(x).νB(x) + sg(1 - μB(x))) | ||
| —27′ | min(μA(x), 1 - μB(x)) | max(νA(x), μB(x).(1 - μB(x)) + sg(1 - μB(x))) | ||
| —28′ | min(μA(x), νB(x)) | max(νA(x), (1 - νB(x)).νB(x) + sg(νB(x))) | ||
| —29′ | min(μA(x), max(0, μB(x).νB(x) + sg(1 - νB(x)))) | max(νA(x), μB(x).(μB(x).νB(x) + sg(1 - νB(x))) + sg(1 - μB(x))) | ||
| —30′ | min(μA(x), μB(x).νB(x) | max(νA(x), μB(x).(μB(x).νB(x) + sg(1 - νB(x))) + sg(1 - μB(x))) | ||
| —31′ | min(μA(x), (1 - μB(x)).μB(x) + sg(μB(x))) | max(νA(x), μB(x).((1 - μB(x)).μB(x) + sg(μB(x))) + sg(1 - μB(x))) | ||
| —32′ | min(μA(x), (1 - μB(x)).μB(x) | max(νA(x), μB(x).((1 - μB(x)).μB(x) + sg(μB(x))) + sg(1 - μB(x))) | ||
| —33′ | min(μA(x), νB(x).(1 - νB(x)) + sg(1 - νB(x))) | max(νA(x), (1 - νB(x)).(νB(x).(1 - νB(x)) + sg(1 - νB(x))) + sg(νB(x))) | ||
| —34′ | min(μA(x), νB(x).(1 - νB(x))) | max(νA(x), (1 - νB(x)).(νB(x).(1 - νB(x)) + sg(1 - νB(x))) + sg(νB(x))) |
List of intuitionistic fuzzy subtractions of —i′′ type
Alternative separated view
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
- On Łukasiewicz's intuitionistic fuzzy subtraction, Beloslav Riečan, Krassimir Atanassov, 2011
- On Zadeh's intuitionistic fuzzy subtraction, Beloslav Riečan, Krassimir Atanassov, 2011
- "What Links Here" References
