DEVELOPMENT OF MULTI CRITERIA DECISION MAKING METHOD WITH THE HELP OF LAGUERRE POLYNOMIALS

Abstract

Polynomials and polynomial approximations are frequently used in mathematics due to their wide domains of definition, ease of differentiation, and integrability. This study was conducted to demonstrate that Laguerre polynomials, a type of orthogonal polynomial commonly used in physics and engineering, can be utilized as a method for Multi-Criteria Decision Making (MCDM). In the study, an alternative ranking method based on Laguerre polynomials was developed for solving MCDM problems. To demonstrate the applicability of the method, a simulated case study was conducted in which five candidates applying for a job at a company were evaluated based on four criteria: “communication”, “work experience”, “exam performance”, and “appearance.” The data used in the application were obtained through data simulation. The criteria weights were determined using the Analytic Hierarchy Process (AHP), and the candidates’ performance rankings were calculated using the Simple Additive Weighting (SAW), Weighted Product Method (WPM), TOPSIS, WISP, and ARLON methods. The results showed that all methods produced the same alternative ranking. Furthermore, the results revealed that the Laguerre-based MCDM method (LMCDM) produced identical rankings when second-, third-, and fourth-degree Laguerre polynomials were applied. Since the results obtained from the SAW, WPM, TOPSIS, WISP, and ARLON methods were similar to those from the developed LMCDM method, it was concluded that LMCDM could be used as an alternative ranking method for solving MCDM problems. Therefore, it is recommended that researchers working on MCDM in future studies consider using the LMCDM method. It is expected that the proposed method will contribute to the MCDM literature.

Keywords

• MCDM
• Laguerre Polynomials
• LMCDM
• WISP
• ARLON

LAGUERRE POLİNOMLARI YARDIMIYLA ÇOK KRİTERLİ KARAR VERME YÖNTEMİ GELİŞTİRİLMESİ

Abstract

Polinom ve polinom yaklaşımları tanım aralıklarının geniş olması, kolay türevlenebilir ve integrallenebilir olmaları nedeniyle matematik alanında sık kullanılmaktadır. Bu polinomlardan biri olan genellikle fizik ve mühendislikte kullanılan ortogonal polinom olan Laguerre polinomlarının Çok Kriterli Karar Verme (ÇKKV) yöntemi olarak kullanılabileceğini göstermek amacıyla bu araştırma ele alınmıştır. Çalışmada ÇKKV problemlerinin çözümleri için Laguerre polinomlarına dayalı alternatif sıralama yöntemi geliştirilmiştir. Yöntemin uygulanabilirliğini göstermek amacıyla örnek olarak bir şirkete işe alınmak için başvuran beş kişinin “iletişim”, “iş deneyimi”, “sınav” ve “dış görünüş” olmak üzere dört kritere göre uygulaması ele alınmıştır. Uygulanan örneğin verileri veri simülasyonu yapılarak elde edilmiştir. Kriter ağırlıkları Analitik Hiyerarşi Prosesi (AHP) ile belirlenerek, kişilerin performans sıralaması Ağırlıklı Toplam Model (SAW), Ağırlıklı Çarpım Yöntemi (WPM), TOPSIS Yöntemi, WISP Yöntemi, ARLON Yöntemi ile yapıldığında aynı alternatif sıralama sonucunu verdiği belirlenmiştir. Ayrıca, Laguerre Polinomları yardımıyla geliştirilen yöntemin (LÇKKV) ikinci, üçüncü ve dördüncü dereceden polinomu uygulamasının alternatif sıralama sonuçlarının aynı olduğu ortaya çıkmıştır. SAW, WPM, TOPSIS, WISP, ARLON yöntemi alternatif sıralama sonuçları ile geliştirilen LÇKKV yöntemi uygulama sonuçlarının birbirlerine benzer olduğu ortaya çıktığından, çalışma sonucunda LÇKKV yönteminin ÇKKV problemlerinin çözümlerinde alternatif sıralama yöntemi olarak kullanabileceği sonucuna varılmıştır. Bu nedenle araştırma sonucunda ÇKKV yöntemleri konusunda gelecekte araştırma yapacak araştırmacılara LÇKKV yöntemini uygulayabilecekleri önerisinde bulunulmuştur. LÇKKV yönteminin literatüre katkı sağlayacağı beklenilmektedir.

Keywords

• ÇKKV
• Laguerre Polinomları
• LÇKKV
• WISP
• ARLON

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