Submit your research to the International Journal "Notes on Intuitionistic Fuzzy Sets". Contact us at nifs.journal@gmail.com
Call for Papers for the 27th International Conference on Intuitionistic Fuzzy Sets is now open!
Conference: 5–6 July 2024, Burgas, Bulgaria • EXTENDED DEADLINE for submissions: 15 APRIL 2024.

Subtractions over intuitionistic fuzzy sets: Difference between revisions

From Ifigenia, the wiki for intuitionistic fuzzy sets and generalized nets
Jump to navigation Jump to search
VisualWikitext
mNo edit summary
mNo edit summary
(2 intermediate revisions by the same user not shown)
Line 1: Line 1:
For the various definitions of subtraction of over [[intuitionistic fuzzy sets]], the functions sg and {{overline|sg}} have been used:
For the various definitions of subtraction of over [[intuitionistic fuzzy sets]], the functions sg and {{overline|sg}} have been used:


{|
<math>
|-valign="middle"
\text{sg}(x) = \left \{ \begin{array}{c c} 1 & \text{if } x > 0 \\
| rowspan="2" | sg(x) = <span style="font-size:350%;">{</span>
0 & \text{if } x \leq 0
| 1 || if x > 0
\end{array},</math>&nbsp;&nbsp;&nbsp;<math>
|-
\overline{\text{sg}}(x) = \left \{ \begin{array}{c c} 1 & \text{if } x < 0 \\
| 0 || if x ≤ 0
0 & \text{if } x \geq 0
|}
\end{array}.</math>
 
== List of intuitionistic fuzzy subtractions of &#8212;<sub><i>i</i></sub> type ==


{|
=== Alternative separated view ===  
|-valign="middle"
| rowspan="2" | {{overline|sg}}(x) = <span style="font-size:350%;">{</span>
| 1 || if x < 0
|-
| 0 || if x ≥ 0
|}


== List of intuitionistic fuzzy subtractions of &#8212;<sub><i>i</i></sub>&#8242; type ==
== List of intuitionistic fuzzy subtractions of &#8212;<sub><i>i</i></sub>&#8242; type ==
Line 492: Line 488:


|}
|}
== List of intuitionistic fuzzy subtractions of &#8212;<sub><i>i</i></sub>&#8242;&#8242; type ==
=== Alternative separated view ===


== Approaches to defining intuitionistic fuzzy subtractions ==
== Approaches to defining intuitionistic fuzzy subtractions ==

Revision as of 14:42, 5 November 2013

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

See also

Ifigenia stub This article is a stub. You can help Ifigenia by expanding it.
Retrieved from "https://ifigenia.org/index.php?title=Subtractions_over_intuitionistic_fuzzy_sets&oldid=6648"