Polinomlara dayalı çok kriterli karar verme yöntemleri: Hermite ve Legendre polinomları.
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| Title: | Polinomlara dayalı çok kriterli karar verme yöntemleri: Hermite ve Legendre polinomları. |
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| Alternate Title: | Polynomial based multi-criteria decision-making methods: Hermite and Legendre polynomials. |
| Authors: | Polat, Yadigar1 yadigarpolat@kilis.edu.tr |
| Source: | Journal of the Faculty of Engineering & Architecture of Gazi University / Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi,. Mar2026, Vol. 41 Issue 1, p639-649. 11p. |
| Subjects: | Hermite polynomials, Legendre's polynomials, Multiple criteria decision making, Orthogonal polynomials, Rank correlation (Statistics), Analytic hierarchy process |
| Abstract (English): | This study aims to evaluate the applicability of newly developed MCDM models based on the integration of Hermite and Legendre polynomials into the decision process. By embedding orthogonal polynomial structures, the reliability of decision-making is enhanced, particularly in data environments with asymmetry, noise, and outliers. The proposed models, named Hermite MCDM and Legendre MCDM, were applied to data from 15 small ruminant farms in Kilis Province and compared with the classical VIKOR method. Up to the fifth degree, Hermite and Legendre polynomials were employed to construct decision matrices, where AHP-weighted criteria were normalized using polynomial functions. The resulting rankings were evaluated via Spearman's rank correlation coefficient. Findings indicate that ?? and ?? yielded the highest similarity to VIKOR. [ABSTRACT FROM AUTHOR] |
| Abstract (Turkish): | Bu çalışma, ÇKKV sürecine Hermite ve Legendre polinomlarının entegrasyonu ile geliştirilen yeni karar modellerinin uygulanabilirliğini değerlendirmeyi amaçlamaktadır. Ortogonal polinomların karar modellerine entegrasyonu sayesinde, özellikle asimetrik, gürültülü ve uç değer içeren veri yapılarında karar verme güvenilirliğinin artırılması hedeflenmiştir. Kilis ilinde faaliyet gösteren 15 küçükbaş hayvan işletmesine ait veriler kullanılarak geliştirilen Hermite ÇKKV ve Legendre ÇKKV modelleri, klasik bir yöntem olan VIKOR ile karşılaştırılmıştır. Uygulamada, beşinci dereceye kadar Hermite ve Legendre polinomları kullanılarak karar matrisleri oluşturulmuş, AHP ile ağırlıklandırılmış kriterler polinom fonksiyonlarıyla normalize edilmiştir. Sıralama sonuçları Spearman sıralama korelasyon katsayısı ile VIKOR yöntemiyle karşılaştırılmıştır. Bulgular, özellikle H4(x) ve P5 (x) polinomlarının VIKOR ile yüksek düzeyde uyum gösterdiğini ortaya koymuştur. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of the Faculty of Engineering & Architecture of Gazi University / Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, is the property of Gazi University, Faculty of Engineering & Architecture and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 192992964 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Polinomlara dayalı çok kriterli karar verme yöntemleri: Hermite ve Legendre polinomları. – Name: TitleAlt Label: Alternate Title Group: TiAlt Data: Polynomial based multi-criteria decision-making methods: Hermite and Legendre polynomials. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Polat%2C+Yadigar%22">Polat, Yadigar</searchLink><relatesTo>1</relatesTo><i> yadigarpolat@kilis.edu.tr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+the+Faculty+of+Engineering+%26+Architecture+of+Gazi+University+%2F+Gazi+Üniversitesi+Mühendislik+Mimarlık+Fakültesi+Dergisi%2C%22">Journal of the Faculty of Engineering & Architecture of Gazi University / Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi,</searchLink>. Mar2026, Vol. 41 Issue 1, p639-649. 11p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Hermite+polynomials%22">Hermite polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Legendre's+polynomials%22">Legendre's polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Multiple+criteria+decision+making%22">Multiple criteria decision making</searchLink><br /><searchLink fieldCode="DE" term="%22Orthogonal+polynomials%22">Orthogonal polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Rank+correlation+%28Statistics%29%22">Rank correlation (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Analytic+hierarchy+process%22">Analytic hierarchy process</searchLink> – Name: Abstract Label: Abstract (English) Group: Ab Data: This study aims to evaluate the applicability of newly developed MCDM models based on the integration of Hermite and Legendre polynomials into the decision process. By embedding orthogonal polynomial structures, the reliability of decision-making is enhanced, particularly in data environments with asymmetry, noise, and outliers. The proposed models, named Hermite MCDM and Legendre MCDM, were applied to data from 15 small ruminant farms in Kilis Province and compared with the classical VIKOR method. Up to the fifth degree, Hermite and Legendre polynomials were employed to construct decision matrices, where AHP-weighted criteria were normalized using polynomial functions. The resulting rankings were evaluated via Spearman's rank correlation coefficient. Findings indicate that ?? and ?? yielded the highest similarity to VIKOR. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Abstract (Turkish) Group: Ab Data: Bu çalışma, ÇKKV sürecine Hermite ve Legendre polinomlarının entegrasyonu ile geliştirilen yeni karar modellerinin uygulanabilirliğini değerlendirmeyi amaçlamaktadır. Ortogonal polinomların karar modellerine entegrasyonu sayesinde, özellikle asimetrik, gürültülü ve uç değer içeren veri yapılarında karar verme güvenilirliğinin artırılması hedeflenmiştir. Kilis ilinde faaliyet gösteren 15 küçükbaş hayvan işletmesine ait veriler kullanılarak geliştirilen Hermite ÇKKV ve Legendre ÇKKV modelleri, klasik bir yöntem olan VIKOR ile karşılaştırılmıştır. Uygulamada, beşinci dereceye kadar Hermite ve Legendre polinomları kullanılarak karar matrisleri oluşturulmuş, AHP ile ağırlıklandırılmış kriterler polinom fonksiyonlarıyla normalize edilmiştir. Sıralama sonuçları Spearman sıralama korelasyon katsayısı ile VIKOR yöntemiyle karşılaştırılmıştır. Bulgular, özellikle H4(x) ve P5 (x) polinomlarının VIKOR ile yüksek düzeyde uyum gösterdiğini ortaya koymuştur. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of the Faculty of Engineering & Architecture of Gazi University / Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, is the property of Gazi University, Faculty of Engineering & Architecture and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.17341/gazimmfd.1738216 Languages: – Code: tur Text: Turkish PhysicalDescription: Pagination: PageCount: 11 StartPage: 639 Subjects: – SubjectFull: Hermite polynomials Type: general – SubjectFull: Legendre's polynomials Type: general – SubjectFull: Multiple criteria decision making Type: general – SubjectFull: Orthogonal polynomials Type: general – SubjectFull: Rank correlation (Statistics) Type: general – SubjectFull: Analytic hierarchy process Type: general Titles: – TitleFull: Polinomlara dayalı çok kriterli karar verme yöntemleri: Hermite ve Legendre polinomları. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Polat, Yadigar IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 13001884 Numbering: – Type: volume Value: 41 – Type: issue Value: 1 Titles: – TitleFull: Journal of the Faculty of Engineering & Architecture of Gazi University / Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, Type: main |
| ResultId | 1 |
