Anyt-norm T which satisfiesthefunct

Anyt-norm T which satisfiesthefunctionalequation(3), forall x, y ∈ [0, 1], iscalledself-reversible [2,4,5,11,13].
The classofFrankt-norms [6] is awell-knownclassofself-reversiblet-norms.Thesimilarequationshavebeenalso
investigatedforuninormsandnullnorms [1]. Thenotionsofreversibilityandself-reversibilityappearintheoryoffuzzy
preference structures [3,12]. Recallthatself-reversiblecopulasplayanimportantroleinstatistics.In [12], thenotions
of reversibilityandself-reversibilitywereintroducedforarbitrarybinaryoperationdefinedontheunitinterval.The
subject ofourinterestisaclass SR of allself-reversiblebinaryoperationsontheunitinterval.Weshallalsostudyseveral
possibilities toconstructself-reversiblebinaryoperationsfromanotheronesusingsomecompositorsandconstruction
methods basedonunaryfunctions.Weshallseethatthepropertiesofshiftstabilityandcommutativityplayessential
roles insuchconstructions.Themaingoalistomakecleartherelationsbetweentheclassesofself-reversible,shift
stable, andcommutativebinaryoperationsontheunitinterval.

ผลลัพธ์ (ไทย) 1:

T Anyt ปกติ satisfiesthefunctionalequation(3), forall x, y ∈ [0, 1], ที่ iscalledself กลับ [2,4,5,11,13]ClassofFrankt-พื้นฐาน [6] awell-knownclassofself-reversiblet-บรรทัดฐานได้Thesimilarequationshavebeenalsoinvestigatedforuninormsandnullnorms [1] Thenotionsofreversibilityandself-reversibilityappearintheoryoffuzzyตั้งค่าโครงสร้าง [3,12] Recallthatself-reversiblecopulasplayanimportantroleinstatistics.In [12], thenotionsของ reversibilityandself-reversibilitywereintroducedforarbitrarybinaryoperationdefinedontheunitintervalที่ofourinterestisaclass เรื่อง SR ของ allself-reversiblebinaryoperationsontheunitintervalWeshallalsostudyseveralไป toconstructself-reversiblebinaryoperationsfromanotheronesusingsomecompositorsandconstructionbasedonunaryfunctions วิธีการWeshallseethatthepropertiesofshiftstabilityandcommutativityplayessentialบทบาท insuchconstructionsกะ Themaingoalistomakecleartherelationsbetweentheclassesofself กลับandcommutativebinaryoperationsontheunitinterval มั่นคง

ผลลัพธ์ (ไทย) 2:

T-anyt บรรทัดฐานซึ่ง satisfiesthefunctionalequation (3), forall x, y ∈ [0, 1] iscalledself-ย้อนกลับ [2,4,5,11,13].
classofFrankt-บรรทัดฐาน [6] เป็น
[1] Thenotionsofreversibilityandself-reversibilityappearintheoryoffuzzy
โครงสร้างการตั้งค่า [3.12] Recallthatself-reversiblecopulasplayanimportantroleinstatistics.In [12], thenotions
ของ
ofourinterestisaclass SR ของ allself-reversiblebinaryoperationsontheunitinterval.Weshallalsostudyseveral
ความเป็นไปได้ toconstructself-reversiblebinaryoperationsfromanotheronesusingsomecompositorsandconstruction
วิธี basedonunaryfunctions.Weshallseethatthepropertiesofshiftstabilityandcommutativityplayessential
บทบาท
andcommutativebinaryoperationsontheunitinterval

ผลลัพธ์ (ไทย) 3:

anyt บรรทัดฐานที่ ( 3 ) , T satisfiesthefunctionalequation forall x , y ∈ [ 0 , 1 ] , iscalledself ผันกลับ [ 2,4,5,11,13 ] .
classoffrankt บรรทัดฐาน [ 6 ] knownclassofself reversiblet การใช้งานปกติ thesimilarequationshavebeenalso
investigatedforuninormsandnullnorms [ 1 ] thenotionsofreversibilityandself reversibilityappearintheoryoffuzzy
ความชอบโครงสร้าง [ 3,12 ]recallthatself-reversiblecopulasplayanimportantroleinstatistics.in [ 12 ] thenotions

เรื่องของ reversibilityandself reversibilitywereintroducedforarbitrarybinaryoperationdefinedontheunitinterval . ofourinterestisaclass SR ของ allself reversiblebinaryoperationsontheunitinterval weshallalsostudyseveral
.ความเป็นไปได้ toconstructself วิธีการ reversiblebinaryoperationsfromanotheronesusingsomecompositorsandconstruction

basedonunaryfunctions . weshallseethatthepropertiesofshiftstabilityandcommutativityplayessential บทบาท insuchconstructions . themaingoalistomakecleartherelationsbetweentheclassesofself กลับกะ
มั่นคง andcommutativebinaryoperationsontheunitinterval .