IEEE Computational Intelligence Magazine - February 2023 - 83
3) Type-reduction: When the popular
center-of-sets type-reducer [3] is
used, the type-reduced output is:
YðxÞ¼½yl; yr;
yl ¼ min
l2½1;K1
Pl
Pl
Pr
k¼1fkyk þ
k¼1fk þ
yr ¼ max
r2½1;K1
Pr
k¼1fkyk þ
k¼1fk þ
PK
PK
k¼rþ1fkyk
k¼rþ1fk
: (8)
PK
PK
k¼lþ1fkyk
k¼lþ1fk
; (7Þ
(6Þ
4) Defuzzification: The defuzzified output
is yðxÞ¼ ylþyr
2 .
IV. Conclusion
Fuzzy sets are suitable for modeling
human linguistic uncertainties, and the
resulting fuzzy systems can then be used
to perform inferences based on a linguistic
rulebase. This short paper has
introduced the basic concepts ofT1 and
IT2 fuzzy sets and systems. More details
and examples can be found in the
online full paper at IEEE Xplore.
Acknowledgment
This work was supported by the National
Natural Science Foundation of China
under Grant 61873321.
References
[1] L. A. Zadeh, " Fuzzy sets, " Inf. Control,vol.8,
pp. 338-353, 1965.
[2] L. A. Zadeh, " The concept of a linguistic variable
and its application to approximate reasoning-1, " Inf.
Sci., vol. 8, pp. 199-249, 1975.
[3] J. M. Mendel, Uncertain Rule-Based Fuzzy Systems:
Introduction and New Directions, 2nd ed. Berlin, Germany:
Springer, 2017.
FEBRUARY 2023 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 83
http://ieeefoundation.org/what-to-support
IEEE Computational Intelligence Magazine - February 2023
Table of Contents for the Digital Edition of IEEE Computational Intelligence Magazine - February 2023
Contents
IEEE Computational Intelligence Magazine - February 2023 - Cover1
IEEE Computational Intelligence Magazine - February 2023 - Cover2
IEEE Computational Intelligence Magazine - February 2023 - Contents
IEEE Computational Intelligence Magazine - February 2023 - 2
IEEE Computational Intelligence Magazine - February 2023 - 3
IEEE Computational Intelligence Magazine - February 2023 - 4
IEEE Computational Intelligence Magazine - February 2023 - 5
IEEE Computational Intelligence Magazine - February 2023 - 6
IEEE Computational Intelligence Magazine - February 2023 - 7
IEEE Computational Intelligence Magazine - February 2023 - 8
IEEE Computational Intelligence Magazine - February 2023 - 9
IEEE Computational Intelligence Magazine - February 2023 - 10
IEEE Computational Intelligence Magazine - February 2023 - 11
IEEE Computational Intelligence Magazine - February 2023 - 12
IEEE Computational Intelligence Magazine - February 2023 - 13
IEEE Computational Intelligence Magazine - February 2023 - 14
IEEE Computational Intelligence Magazine - February 2023 - 15
IEEE Computational Intelligence Magazine - February 2023 - 16
IEEE Computational Intelligence Magazine - February 2023 - 17
IEEE Computational Intelligence Magazine - February 2023 - 18
IEEE Computational Intelligence Magazine - February 2023 - 19
IEEE Computational Intelligence Magazine - February 2023 - 20
IEEE Computational Intelligence Magazine - February 2023 - 21
IEEE Computational Intelligence Magazine - February 2023 - 22
IEEE Computational Intelligence Magazine - February 2023 - 23
IEEE Computational Intelligence Magazine - February 2023 - 24
IEEE Computational Intelligence Magazine - February 2023 - 25
IEEE Computational Intelligence Magazine - February 2023 - 26
IEEE Computational Intelligence Magazine - February 2023 - 27
IEEE Computational Intelligence Magazine - February 2023 - 28
IEEE Computational Intelligence Magazine - February 2023 - 29
IEEE Computational Intelligence Magazine - February 2023 - 30
IEEE Computational Intelligence Magazine - February 2023 - 31
IEEE Computational Intelligence Magazine - February 2023 - 32
IEEE Computational Intelligence Magazine - February 2023 - 33
IEEE Computational Intelligence Magazine - February 2023 - 34
IEEE Computational Intelligence Magazine - February 2023 - 35
IEEE Computational Intelligence Magazine - February 2023 - 36
IEEE Computational Intelligence Magazine - February 2023 - 37
IEEE Computational Intelligence Magazine - February 2023 - 38
IEEE Computational Intelligence Magazine - February 2023 - 39
IEEE Computational Intelligence Magazine - February 2023 - 40
IEEE Computational Intelligence Magazine - February 2023 - 41
IEEE Computational Intelligence Magazine - February 2023 - 42
IEEE Computational Intelligence Magazine - February 2023 - 43
IEEE Computational Intelligence Magazine - February 2023 - 44
IEEE Computational Intelligence Magazine - February 2023 - 45
IEEE Computational Intelligence Magazine - February 2023 - 46
IEEE Computational Intelligence Magazine - February 2023 - 47
IEEE Computational Intelligence Magazine - February 2023 - 48
IEEE Computational Intelligence Magazine - February 2023 - 49
IEEE Computational Intelligence Magazine - February 2023 - 50
IEEE Computational Intelligence Magazine - February 2023 - 51
IEEE Computational Intelligence Magazine - February 2023 - 52
IEEE Computational Intelligence Magazine - February 2023 - 53
IEEE Computational Intelligence Magazine - February 2023 - 54
IEEE Computational Intelligence Magazine - February 2023 - 55
IEEE Computational Intelligence Magazine - February 2023 - 56
IEEE Computational Intelligence Magazine - February 2023 - 57
IEEE Computational Intelligence Magazine - February 2023 - 58
IEEE Computational Intelligence Magazine - February 2023 - 59
IEEE Computational Intelligence Magazine - February 2023 - 60
IEEE Computational Intelligence Magazine - February 2023 - 61
IEEE Computational Intelligence Magazine - February 2023 - 62
IEEE Computational Intelligence Magazine - February 2023 - 63
IEEE Computational Intelligence Magazine - February 2023 - 64
IEEE Computational Intelligence Magazine - February 2023 - 65
IEEE Computational Intelligence Magazine - February 2023 - 66
IEEE Computational Intelligence Magazine - February 2023 - 67
IEEE Computational Intelligence Magazine - February 2023 - 68
IEEE Computational Intelligence Magazine - February 2023 - 69
IEEE Computational Intelligence Magazine - February 2023 - 70
IEEE Computational Intelligence Magazine - February 2023 - 71
IEEE Computational Intelligence Magazine - February 2023 - 72
IEEE Computational Intelligence Magazine - February 2023 - 73
IEEE Computational Intelligence Magazine - February 2023 - 74
IEEE Computational Intelligence Magazine - February 2023 - 75
IEEE Computational Intelligence Magazine - February 2023 - 76
IEEE Computational Intelligence Magazine - February 2023 - 77
IEEE Computational Intelligence Magazine - February 2023 - 78
IEEE Computational Intelligence Magazine - February 2023 - 79
IEEE Computational Intelligence Magazine - February 2023 - 80
IEEE Computational Intelligence Magazine - February 2023 - 81
IEEE Computational Intelligence Magazine - February 2023 - 82
IEEE Computational Intelligence Magazine - February 2023 - 83
IEEE Computational Intelligence Magazine - February 2023 - 84
IEEE Computational Intelligence Magazine - February 2023 - 85
IEEE Computational Intelligence Magazine - February 2023 - 86
IEEE Computational Intelligence Magazine - February 2023 - 87
IEEE Computational Intelligence Magazine - February 2023 - 88
IEEE Computational Intelligence Magazine - February 2023 - 89
IEEE Computational Intelligence Magazine - February 2023 - 90
IEEE Computational Intelligence Magazine - February 2023 - 91
IEEE Computational Intelligence Magazine - February 2023 - 92
IEEE Computational Intelligence Magazine - February 2023 - 93
IEEE Computational Intelligence Magazine - February 2023 - 94
IEEE Computational Intelligence Magazine - February 2023 - 95
IEEE Computational Intelligence Magazine - February 2023 - 96
IEEE Computational Intelligence Magazine - February 2023 - 97
IEEE Computational Intelligence Magazine - February 2023 - 98
IEEE Computational Intelligence Magazine - February 2023 - 99
IEEE Computational Intelligence Magazine - February 2023 - 100
IEEE Computational Intelligence Magazine - February 2023 - 101
IEEE Computational Intelligence Magazine - February 2023 - 102
IEEE Computational Intelligence Magazine - February 2023 - 103
IEEE Computational Intelligence Magazine - February 2023 - 104
IEEE Computational Intelligence Magazine - February 2023 - Cover3
IEEE Computational Intelligence Magazine - February 2023 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202311
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202308
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202305
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202302
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202211
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202208
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202205
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202202
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202111
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202108
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202105
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202102
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202011
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202008
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202005
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202002
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201911
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201908
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201905
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201902
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201811
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201808
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201805
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201802
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter12
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall12
https://www.nxtbookmedia.com