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Subtractions over intuitionistic fuzzy sets: Difference between revisions
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(; "What Links Here" References {{Special:WhatLinksHere/{{PAGENAME}}|namespace=102|hidetrans=1|hideredirs=1}}) |
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For the various definitions of subtraction of over [[intuitionistic fuzzy sets]], the functions sg and {{overline|sg}} have been used: | |||
{ | <math> | ||
\text{sg}(x) = \left \{ \begin{array}{c c} 1 & \text{if } x > 0 \\ | |||
0 & \text{if } x \leq 0 | |||
\end{array},</math> <math> | |||
\overline{\text{sg}}(x) = \left \{ \begin{array}{c c} 1 & \text{if } x < 0 \\ | |||
0 & \text{if } x \geq 0 | |||
\end{array}.</math> | |||
== List of intuitionistic fuzzy subtractions of —<sub><i>i</i></sub> type == | |||
=== Alternative separated view === | |||
== List of intuitionistic fuzzy subtractions of —<sub><i>i</i></sub>′ type == | |||
{| width="100%" class="wikitable sortable" style="font-family:Courier; font-size:120%;" | {| width="100%" class="wikitable sortable" style="font-family:Courier; font-size:120%;" | ||
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| | | | ||
| {<x, <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x))</font>, <font color=red>max(ν<sub>A</sub>(x), 1 - ν<sub>B</sub>(x))</font>>|x ∈ E} | | {<x, <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x))</font>, <font color=red>max(ν<sub>A</sub>(x), 1 - ν<sub>B</sub>(x))</font>>|x ∈ E} | ||
|- valign="top" | |- valign="top" | ||
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| | | | ||
| {<x, <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x), sg(μ<sub>B</sub>(x)))</font>, <font color=red>max(ν<sub>A</sub>(x), min(μ<sub>B</sub>(x), sg(ν<sub>B</sub>(x))))</font>>|x ∈ E} | | {<x, <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x), sg(μ<sub>B</sub>(x)))</font>, <font color=red>max(ν<sub>A</sub>(x), min(μ<sub>B</sub>(x), sg(ν<sub>B</sub>(x))))</font>>|x ∈ E} | ||
|- valign="top" | |||
| —<sub>19</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x), sg(μ<sub>B</sub>(x)))</font>, <font color=red>ν<sub>A</sub>(x)</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>20</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x))</font>, <font color=red>ν<sub>A</sub>(x)</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>21</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), 1 - μ<sub>B</sub>(x), sg(μ<sub>B</sub>(x)))</font>, <font color=red>max(ν<sub>A</sub>(x), min(μ<sub>B</sub>(x), sg(1 - μ<sub>B</sub>(x))))</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>22</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), 1 - μ<sub>B</sub>(x), sg(μ<sub>B</sub>(x)))</font>, <font color=red>ν<sub>A</sub>(x)</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>23</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), 1 - μ<sub>B</sub>(x))</font>, <font color=red>ν<sub>A</sub>(x)</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>24</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x), sg(1 - ν<sub>B</sub>(x)))</font>, <font color=red>max(ν<sub>A</sub>(x), min(1 - ν<sub>B</sub>(x), sg(ν<sub>B</sub>(x))))</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>25</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x), sg(1 - ν<sub>B</sub>(x)))</font>, <font color=red>ν<sub>A</sub>(x)</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>26</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x))</font>, <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x).ν<sub>B</sub>(x) + {{overline|sg}}(1 - μ<sub>B</sub>(x)))</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>27</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), 1 - μ<sub>B</sub>(x))</font>, <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x).(1 - μ<sub>B</sub>(x)) + {{overline|sg}}(1 - μ<sub>B</sub>(x)))</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>28</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x))</font>, <font color=red>max(ν<sub>A</sub>(x), (1 - ν<sub>B</sub>(x)).ν<sub>B</sub>(x) + {{overline|sg}}(ν<sub>B</sub>(x)))</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>29</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), max(0, μ<sub>B</sub>(x).ν<sub>B</sub>(x) + {{overline|sg}}(1 - ν<sub>B</sub>(x))))</font>, <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x).(μ<sub>B</sub>(x).ν<sub>B</sub>(x) + {{overline|sg}}(1 - ν<sub>B</sub>(x))) + {{overline|sg}}(1 - μ<sub>B</sub>(x)))</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>30</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), μ<sub>B</sub>(x).ν<sub>B</sub>(x)</font>, <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x).(μ<sub>B</sub>(x).ν<sub>B</sub>(x) + {{overline|sg}}(1 - ν<sub>B</sub>(x))) + {{overline|sg}}(1 - μ<sub>B</sub>(x)))</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>31</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), (1 - μ<sub>B</sub>(x)).μ<sub>B</sub>(x) + {{overline|sg}}(μ<sub>B</sub>(x)))</font>, <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x).((1 - μ<sub>B</sub>(x)).μ<sub>B</sub>(x) + {{overline|sg}}(μ<sub>B</sub>(x))) + {{overline|sg}}(1 - μ<sub>B</sub>(x)))</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>32</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), (1 - μ<sub>B</sub>(x)).μ<sub>B</sub>(x)</font>, <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x).((1 - μ<sub>B</sub>(x)).μ<sub>B</sub>(x) + {{overline|sg}}(μ<sub>B</sub>(x))) + {{overline|sg}}(1 - μ<sub>B</sub>(x)))</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>33</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x).(1 - ν<sub>B</sub>(x)) + {{overline|sg}}(1 - ν<sub>B</sub>(x)))</font>, <font color=red>max(ν<sub>A</sub>(x), (1 - ν<sub>B</sub>(x)).(ν<sub>B</sub>(x).(1 - ν<sub>B</sub>(x)) + {{overline|sg}}(1 - ν<sub>B</sub>(x))) + {{overline|sg}}(ν<sub>B</sub>(x)))</font>>|x ∈ E} | |||
|- valign="top" | |||
| —<sub>34</sub>′ | |||
| | |||
| | |||
| {<x, <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x).(1 - ν<sub>B</sub>(x)))</font>, <font color=red>max(ν<sub>A</sub>(x), (1 - ν<sub>B</sub>(x)).(ν<sub>B</sub>(x).(1 - ν<sub>B</sub>(x)) + {{overline|sg}}(1 - ν<sub>B</sub>(x))) + {{overline|sg}}(ν<sub>B</sub>(x)))</font>>|x ∈ E} | |||
|} | |} | ||
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| | | | ||
| | | | ||
| | | style= "color: green;" | min(μ<sub>A</sub>(x), ν<sub>B</sub>(x)) | ||
| | | style= "color: red;" | max(ν<sub>A</sub>(x), μ<sub>B</sub>(x)) | ||
|- valign="top" | |- valign="top" | ||
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| <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x), sg(μ<sub>B</sub>(x)))</font> | | <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x), sg(μ<sub>B</sub>(x)))</font> | ||
| <font color=red>max(ν<sub>A</sub>(x), min(μ<sub>B</sub>(x), sg(ν<sub>B</sub>(x))))</font> | | <font color=red>max(ν<sub>A</sub>(x), min(μ<sub>B</sub>(x), sg(ν<sub>B</sub>(x))))</font> | ||
|- valign="top" | |||
| —<sub>19</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x), sg(μ<sub>B</sub>(x)))</font> | |||
| <font color=red>ν<sub>A</sub>(x)</font> | |||
|- valign="top" | |||
| —<sub>20</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x))</font> | |||
| <font color=red>ν<sub>A</sub>(x)</font> | |||
|- valign="top" | |||
| —<sub>21</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), 1 - μ<sub>B</sub>(x), sg(μ<sub>B</sub>(x)))</font> | |||
| <font color=red>max(ν<sub>A</sub>(x), min(μ<sub>B</sub>(x), sg(1 - μ<sub>B</sub>(x))))</font> | |||
|- valign="top" | |||
| —<sub>22</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), 1 - μ<sub>B</sub>(x), sg(μ<sub>B</sub>(x)))</font> | |||
| <font color=red>ν<sub>A</sub>(x)</font> | |||
|- valign="top" | |||
| —<sub>23</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), 1 - μ<sub>B</sub>(x))</font> | |||
| <font color=red>ν<sub>A</sub>(x)</font> | |||
|- valign="top" | |||
| —<sub>24</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x), sg(1 - ν<sub>B</sub>(x)))</font> | |||
| <font color=red>max(ν<sub>A</sub>(x), min(1 - ν<sub>B</sub>(x), sg(ν<sub>B</sub>(x))))</font> | |||
|- valign="top" | |||
| —<sub>25</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x), sg(1 - ν<sub>B</sub>(x)))</font> | |||
| <font color=red>ν<sub>A</sub>(x)</font> | |||
|- valign="top" | |||
| —<sub>26</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x))</font> | |||
| <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x).ν<sub>B</sub>(x) + {{overline|sg}}(1 - μ<sub>B</sub>(x)))</font> | |||
|- valign="top" | |||
| —<sub>27</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), 1 - μ<sub>B</sub>(x))</font> | |||
| <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x).(1 - μ<sub>B</sub>(x)) + {{overline|sg}}(1 - μ<sub>B</sub>(x)))</font> | |||
|- valign="top" | |||
| —<sub>28</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x))</font> | |||
| <font color=red>max(ν<sub>A</sub>(x), (1 - ν<sub>B</sub>(x)).ν<sub>B</sub>(x) + {{overline|sg}}(ν<sub>B</sub>(x)))</font> | |||
|- valign="top" | |||
| —<sub>29</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), max(0, μ<sub>B</sub>(x).ν<sub>B</sub>(x) + {{overline|sg}}(1 - ν<sub>B</sub>(x))))</font> | |||
| <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x).(μ<sub>B</sub>(x).ν<sub>B</sub>(x) + {{overline|sg}}(1 - ν<sub>B</sub>(x))) + {{overline|sg}}(1 - μ<sub>B</sub>(x)))</font> | |||
|- valign="top" | |||
| —<sub>30</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), μ<sub>B</sub>(x).ν<sub>B</sub>(x)</font> | |||
| <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x).(μ<sub>B</sub>(x).ν<sub>B</sub>(x) + {{overline|sg}}(1 - ν<sub>B</sub>(x))) + {{overline|sg}}(1 - μ<sub>B</sub>(x)))</font> | |||
|- valign="top" | |||
| —<sub>31</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), (1 - μ<sub>B</sub>(x)).μ<sub>B</sub>(x) + {{overline|sg}}(μ<sub>B</sub>(x)))</font> | |||
| <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x).((1 - μ<sub>B</sub>(x)).μ<sub>B</sub>(x) + {{overline|sg}}(μ<sub>B</sub>(x))) + {{overline|sg}}(1 - μ<sub>B</sub>(x)))</font> | |||
|- valign="top" | |||
| —<sub>32</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), (1 - μ<sub>B</sub>(x)).μ<sub>B</sub>(x)</font> | |||
| <font color=red>max(ν<sub>A</sub>(x), μ<sub>B</sub>(x).((1 - μ<sub>B</sub>(x)).μ<sub>B</sub>(x) + {{overline|sg}}(μ<sub>B</sub>(x))) + {{overline|sg}}(1 - μ<sub>B</sub>(x)))</font> | |||
|- valign="top" | |||
| —<sub>33</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x).(1 - ν<sub>B</sub>(x)) + {{overline|sg}}(1 - ν<sub>B</sub>(x)))</font> | |||
| <font color=red>max(ν<sub>A</sub>(x), (1 - ν<sub>B</sub>(x)).(ν<sub>B</sub>(x).(1 - ν<sub>B</sub>(x)) + {{overline|sg}}(1 - ν<sub>B</sub>(x))) + {{overline|sg}}(ν<sub>B</sub>(x)))</font> | |||
|- valign="top" | |||
| —<sub>34</sub>′ | |||
| | |||
| | |||
| <font color=green>min(μ<sub>A</sub>(x), ν<sub>B</sub>(x).(1 - ν<sub>B</sub>(x)))</font> | |||
| <font color=red>max(ν<sub>A</sub>(x), (1 - ν<sub>B</sub>(x)).(ν<sub>B</sub>(x).(1 - ν<sub>B</sub>(x)) + {{overline|sg}}(1 - ν<sub>B</sub>(x))) + {{overline|sg}}(ν<sub>B</sub>(x)))</font> | |||
|} | |} | ||
== List of intuitionistic fuzzy subtractions of —<sub><i>i</i></sub>′′ type == | |||
=== Alternative separated view === | |||
== Approaches to defining intuitionistic fuzzy subtractions == | == Approaches to defining intuitionistic fuzzy subtractions == | ||
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* [[Issue:On intuitionistic fuzzy subtraction, related to intuitionistic fuzzy negation ¬4|On intuitionistic fuzzy subtraction, related to intuitionistic fuzzy negation ¬<sub>4</sub>]], Beloslav Riečan, Magdaléna Renčová, Krassimir Atanassov, 2009 | * [[Issue:On intuitionistic fuzzy subtraction, related to intuitionistic fuzzy negation ¬4|On intuitionistic fuzzy subtraction, related to intuitionistic fuzzy negation ¬<sub>4</sub>]], Beloslav Riečan, Magdaléna Renčová, Krassimir Atanassov, 2009 | ||
* [[Issue:Equalities with intuitionistic fuzzy subtractions and negations|Equalities with intuitionistic fuzzy subtractions and negations]], Krassimir Atanassov, Magdaléna Renčová, Dimitar Dimitrov, 2010 | * [[Issue:Equalities with intuitionistic fuzzy subtractions and negations|Equalities with intuitionistic fuzzy subtractions and negations]], Krassimir Atanassov, Magdaléna Renčová, Dimitar Dimitrov, 2010 | ||
* [[Issue:On Łukasiewicz's intuitionistic fuzzy subtraction|On Łukasiewicz's intuitionistic fuzzy subtraction]], Beloslav Riečan, Krassimir Atanassov, 2011 | |||
* [[Issue:On Zadeh's intuitionistic fuzzy subtraction|On Zadeh's intuitionistic fuzzy subtraction]], Beloslav Riečan, Krassimir Atanassov, 2011 | |||
; "What Links Here" References | |||
{{Special:WhatLinksHere/{{PAGENAME}}|namespace=102|hidetrans=1|hideredirs=1}} | |||
== See also == | == See also == |
Latest revision as of 10:41, 29 April 2022
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