APPLICATION OF THE PIV METHOD IN THE PRESENCE OF NEGATIVE DATA: AN EMPIRICAL EXAMPLE FROM A REAL-WORLD CASE

Abstract

The presence of negative data in the decision matrix is a rare situation in Multiple Criteria Decision Making (MCDM) methods. In such a case, normalized matrix elements must be between 0 and 1 to adopt the Proximity Indexed Value (PIV) method. In this study, which deals with real life application, two different solutions are presented to find a solution to this problem. Firstly, negative decision matrix elements are converted to positive using a z-score standardization method. Secondly, different normalization techniques are used instead of vector normalization in the algorithm of the PIV method. According to the results obtained, the most appropriate technique to reach a result with the PIV method in the presence of negative data is the min-max technique. The model proposed in this study supports the usage the PIV method in the presence of negative data. In addition, this study is the first to test the suitability of different techniques for the PIV method.

Keywords

• MCDM
• PIV Method
• Normalization
• Standardization
• Consistency

NEGATİF VERİLERİN VARLIĞI DURUMUNDA PIV YÖNTEMİNİN UYGULANMASI: GERÇEK HAYAT UYGULAMASINA DAYALI AMPİRİK BİR ANALİZ

Öz

Çok Kriterli Karar Verme (ÇKKV) yöntemlerinde karar matrisinde negatif verilere nadir olarak rastlanılmaktadır. Böyle bir durumda Proximity Indexed Value- Yakınlık Endeksli Değer (PIV) yöntemini uygulamak için normalize edilmiş karar matrisi elemanlarının 0 ile 1 arasında olacak şekilde yeniden düzenlenmesi gerekmektedir. Gerçek hayat uygulamasının ele alındığı bu çalışmada, mevcut problemi ortadan kaldırmak amacıyla iki farklı çözüm yolu sunulmuştur. İlk olarak, negatif karar matrisi elemanları, z-skor standardizasyon yöntemi kullanılarak pozitif hale getirilmiştir. İkinci olarak, PIV yönteminin algoritmasında bulunan vektör normalizasyon tekniği yerine farklı normalizasyon teknikleri kullanılmıştır. Elde edilen sonuçlara göre karar matrisinde negatif verilerin varlığı durumunda PIV yöntemi ile sonuca ulaşmak için en uygun teknik min-max tekniğidir. Bu çalışmada önerilen model, karar matrisinde negatif verilerin bulunması durumunda PIV yönteminin kullanımını desteklemektedir. Ayrıca, bu çalışma farklı tekniklerin PIV yöntemi için uygunluğunu test eden ilk çalışmadır.

Anahtar Kelimeler

• MCDM
• PIV Method
• Normalization
• Standardization
• Consistency

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