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Subtractions over intuitionistic fuzzy sets: Difference between revisions

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| &#123;&#60;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>&#62;&#124;x &#8712; E&#125;
| &#123;&#60;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>&#62;&#124;x &#8712; E&#125;
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| &#8212;<sub>22</sub>&#8242;
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| &#123;&#60;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>&#62;&#124;x &#8712; E&#125;
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| &#8212;<sub>23</sub>&#8242;
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| &#123;&#60;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>&#62;&#124;x &#8712; E&#125;
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| &#8212;<sub>24</sub>&#8242;
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| &#123;&#60;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>&#62;&#124;x &#8712; E&#125;
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| &#8212;<sub>25</sub>&#8242;
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| &#123;&#60;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>&#62;&#124;x &#8712; E&#125;
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| &#8212;<sub>26</sub>&#8242;
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| &#123;&#60;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>&#62;&#124;x &#8712; E&#125;
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| &#8212;<sub>28</sub>&#8242;
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| &#123;&#60;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>&#62;&#124;x &#8712; E&#125;


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| <font color=green>min(μ<sub>A</sub>(x), 1 - μ<sub>B</sub>(x), sg(μ<sub>B</sub>(x)))</font>
| <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>
| <font color=red>max(ν<sub>A</sub>(x), min(μ<sub>B</sub>(x), sg(1 - μ<sub>B</sub>(x))))</font>
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| &#8212;<sub>22</sub>&#8242;
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| <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>
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| &#8212;<sub>23</sub>&#8242;
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| <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>
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| &#8212;<sub>24</sub>&#8242;
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| <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>
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| &#8212;<sub>25</sub>&#8242;
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| <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>
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| &#8212;<sub>26</sub>&#8242;
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| <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>
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| &#8212;<sub>27</sub>&#8242;
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| <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>
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| &#8212;<sub>28</sub>&#8242;
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| <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>


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Revision as of 17:28, 23 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
01 {<x, min(μA(x), νB(x)), max(νA(x), μB(x))>|x ∈ E}
02 {<x, min(μA(x), sgB(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), sgB(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), sgB(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), sgB(x))), max(νA(x), sg(1 - μB(x)))>|x ∈ E}
17 {<x, min(μA(x), sg(1 - νB(x))), max(νA(x), sgB(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) + sgB(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), sgB(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), sgB(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), sgB(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), sgB(x))) max(νA(x), sg(1 - μB(x)))
17 min(μA(x), sg(1 - νB(x))) max(νA(x), sgB(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) + sgB(x)))

Approaches to defining intuitionistic fuzzy subtractions

References

See also

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