A Distribution-Based Next-Generation Multi-Criteria Performance Measurement Method: Bhattacharyya Distance Performance Measurement (BDPM)

Öz

Multi-criteria decision-making (MCDM) problems, the reliable ranking of alternatives remains a fundamental challenge, particularly in environments characterized by heterogeneous criterion distributions, where classical additive, multiplicative, and purely geometric distance-based approaches often exhibit limited discriminative power. To address this limitation, this study proposes a novel framework termed Bhattacharyya Distance Performance Measurement (BDPM), which integrates Bhattacharyya distributional divergence into a reference-based performance evaluation structure. Unlike conventional methods that quantify proximity to ideal and anti-ideal profiles solely through magnitude differences, BDPM measures the degree of distributional overlap and separation between criterion profiles, thereby introducing a missing information-based discrimination mechanism into MCDM literature. The empirical validity of BDPM is examined using the 2024 Global Innovation Index dataset and two additional case studies focusing on bank financial performance and university institutional performance. Sensitivity analyses, including weight perturbation and rank-reversal scenarios, indicate that the proposed method exhibits an ideal level of sensitivity, maintaining stable rankings under substantial parameter variations. The high Spearman correlation coefficients obtained from comparative analyses demonstrate that BDPM produces reliable and systematically consistent results in line with established MCDM techniques. Furthermore, simulation experiments and ANOM–Levene tests confirm that the method remains structurally stable across diverse scenario configurations. By redefining performance measurement through a distribution-based discrimination perspective, BDPM fills a significant methodological gap in the existing literature and provides a more selective and informative evaluation mechanism for heterogeneous decision environments. Future research is encouraged to extend the method to fuzzy and dynamic decision contexts and to investigate its integration into automated decision-support systems.

Anahtar Kelimeler

• MCDM
• Bhattacharyya Distance
• BDPM

Dağılım-Temelli Yeni Nesil Bir Çok Kriterli Performans Ölçüm Yöntemi: Bhattacharyya Uzaklık Performan Ölçümü (BDPM)

Öz

Çok kriterli karar verme (MCDM) problemlerinde alternatiflerin güvenilir biçimde sıralanması, özellikle kriter dağılımlarının heterojen olduğu karar ortamlarında, klasik toplamsal, çarpımsal ve salt geometrik uzaklık temelli yaklaşımlar açısından temel bir zorluk oluşturmaktadır. Bu sınırlılığı aşmak amacıyla bu çalışmada, Bhattacharyya dağılım ayrışımını referans-temelli performans değerlendirme yapısına entegre eden ve Bhattacharyya Distance Performance Measurement (BDPM) olarak adlandırılan yeni bir çerçeve önerilmektedir. BDPM, alternatiflerin ideal ve anti-ideal profillere olan yakınlığını yalnızca büyüklük farkları üzerinden değil, kriter profilleri arasındaki dağılımsal örtüşme ve ayrışım düzeyleri üzerinden nicelleyerek, MCDM literatüründe eksikliği hissedilen bilgi-temelli bir ayrıştırma mekanizmasını karar sürecine kazandırmaktadır. Yöntemin ampirik geçerliliği, 2024 Küresel İnovasyon Endeksi verileri ile banka finansal performansı ve üniversite kurumsal performansına ilişkin iki ek vaka çalışması üzerinden sınanmıştır. Ağırlık perturbasyonu ve rank-reversal senaryolarını içeren duyarlılık analizleri, önerilen yöntemin ideal düzeyde bir hassasiyet sergileyerek önemli parametre değişimleri altında dahi sıralama istikrarını koruduğunu göstermiştir. Karşılaştırmalı analizlerde elde edilen yüksek Spearman korelasyon katsayıları, BDPM’nin yerleşik MCDM yöntemleriyle uyumlu, güvenilir ve sistematik sonuçlar ürettiğini ortaya koymuştur. Ayrıca simülasyon deneyleri ve ANOM–Levene testleri, yöntemin farklı senaryo koşullarında yapısal olarak kararlı ve robust olduğunu doğrulamaktadır. Bu yönleriyle BDPM, performans ölçümünü dağılım-temelli ayrışım perspektifiyle yeniden tanımlayarak literatürde önemli bir metodolojik boşluğu doldurmakta ve heterojen karar ortamları için daha seçici bir değerlendirme mekanizması sunmaktadır. Gelecek çalışmalarda yöntemin bulanık ve dinamik karar problemlerine uyarlanması ve otomatik karar destek sistemlerine entegrasyonu önerilmektedir.

Anahtar Kelimeler

• ÇKKV
• Bhattacharyya Uzaklık
• BDPM

Kaynakça

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