Polynomial based multi-criteria decision-making methods: Hermite and Legendre polynomials

Yıl 2026, Cilt: 41 Sayı: 1 , 639 - 650 , 31.03.2026

Yadigar Polat

https://doi.org/10.17341/gazimmfd.1738216

https://izlik.org/JA46XK64WR

Öz

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 H_4 (x) and P_5 (x) yielded the highest similarity to VIKOR.

Anahtar Kelimeler

Hermite polynomials , legendre polynomials , multi-criteria decision-making

Polinomlara dayalı çok kriterli karar verme yöntemleri: Hermite ve Legendre polinomları

https://izlik.org/JA46XK64WR

Öz

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 H_4 (x) ve P_5 (x) polinomlarının VIKOR ile yüksek düzeyde uyum gösterdiğini ortaya koymuştur.

Anahtar Kelimeler

Hermite polinomları , legendre polinomları , çok kriterli karar verme

Kaynakça

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