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Ranking with Statistical Variance Procedure based Analytic Hierarchy Process

Year 2017, Volume: 1 Issue: 1, 31 - 38, 01.06.2017

Abstract

This study introduces an
objective multicriteria ranking method based on the Analytic Hierarchy Process
(AHP). Different multicriteria decision analysis methods generate different
solutions for the same ranking problem because of their varying mathematical
models. In AHP, decision makers construct positive comparison matrices from
their preferences by using a scale of 1-9. However, even a simple ranking
problem requires numerous comparison matrices while subjective judgments lead
to inconsistent rankings. As a simplified version of the AHP, the Statistical Variance
Procedure (SVP) based AHP (SVP-AHP) extracts the ranking of alternatives from a
multicriteria dataset without referring to costly survey processes. SVP-AHP uses
pairwise comparison matrices, the powerful tool of AHP, and it does not need to
measure consistency. For an objective ranking of alternatives, SVP-AHP embeds
vector normalization and SVP into the AHP. SVP determines criteria weights
while pairwise comparison matrices for alternatives are constructed using the
normalized observations. In SVP-AHP, it is sufficient to know only criteria and
alternative values, unlike AHP, where the model requires decision makers’ judgments.
Results of the AHP and SVP-AHP for the example in this study point out that
SVP-AHP is an efficient ranking method because of its computational efficieny
and objectivity.

References

  • [1] Esen, H. Ö., 2008, “Applied Operational Research” (“Uygulamalı Yöneylem Araştırması”), (S. Tolun, Ed.), Çağlayan Kitabevi.
  • [2] Roy, B., & Vanderpooten, D., 1997, “An overview on “The European school of MCDA: Emergence, basic features and current works”, European Journal of Operational Research, 99, 26–27.
  • [3] Tayalı, H. A., 2016, “Statistical variance procedure based analytic hierarcy process: An application on multicriteria facility location selection”, Retrieved from https://tez.yok.gov.tr/UlusalTezMerkezi/.
  • [4] Ömürbek, N., & Mercan, Y., 2014, “Performance Evaluation of Sub-manufacturing Sectors Using TOPSIS and ELECTRE Methods”, Cankiri Karatekin University Journal of the Faculty of Economics and Administrative Sciences, 4(1), 237–266.
  • [5] Xidonas, P., Mavrotas, G., & Psarras, J., 2009, “A multicriteria methodology for equity selection using financial analysis”, Computers and Operations Research, 36(12), 3187–3203.
  • [6] Zopounidis, C., & Doumpos, M., 2002, “Multicriteria classification and sorting methods: A literature review”, European Journal of Operational Research, 138(2), 229–246.
  • [7] Tsoukiàs, A., 2008, “From decision theory to decision aiding methodology”, European Journal of Operational Research, 187(1), 138–161.
  • [8] Saaty, T. L., 1977, “A scaling method for priorities in hierarchical structures”, Journal of Mathematical Psychology, 15(3), 234–281.
  • [9] Sipahi, S., & Timor, M., 2010, “The analytic hierarchy process and analytic network process: An overview of applications”, Management Decision, 48(5), 775–808.
  • [10] Nelson, D., 2008, “The Penguin Dictionary of Mathematics”, Penguin UK.
  • 11] Alonso, J. A., & Lamata, M. T., 2006, “Consistency in the analytic hierarchy process: a new approach”, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 14(4), 445–459.
  • [12] Farkas, A., 2007, “The analysis of the principal eigenvector of pairwise comparison matrices”, Acta Polytechnica Hungarica, 4(2), 99–115.
  • [13] Taha, H. A., 2007, “Operations Research: An Introduction”, Pearson Education International.
  • [14] Saaty, T. L., 2003, “Decision-making with the AHP: Why is the principal eigenvector necessary”, European Journal of Operational Research, 145(1), 85–91.
  • [15] Saaty, T. L., 2008, “Relative measurement and its generalization in decision making; why pairwise comparisons are central in mathematics for the measurement of intangible factors”, Revista de La Real Academia de Ciencias Exactas, Fisicas Y Naturales. Serie A. Matematicas, 102(2), 251–318.
  • [16] Peláez, J. I., & Lamata, M. T., 2003, “A new measure of consistency for positive reciprocal matrices”, Computers and Mathematics with Applications, 46(12), 1839–1845.
  • [17] Opricovic, S., & Tzeng, G. H., 2004, “Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS”, European Journal of Operational Research, 156(2), 445–455.
  • [18] Özdağoğlu, A., 2013, “The effects of different normalization methods to decision making process in TOPSIS” (“Farklı normalizasyon yöntemlerinin TOPSIS’te karar verme sürecine etkisi”), Ege Academic Review, 13(2), 245–257.
  • [19] Pavlicic, D. M., 2001, “Normalisation affects the results of MADM methods”, Yugoslav Journal of Operations Research, 11(2), 251–265.
  • [20] Tervonen, T., Figueira, J., Lahdelma, R., & Dias, J., 2009, “A stochastic method for robustness analysis in sorting problems”, European Journal of Operational Research, 192(1), 236–242.
  • [21] Zardari, N. H., Ahmed, K., Shirazi, S. M., & Yusop, Z. Bin., 2015, “Weighting Methods and their Effects on Multi-Criteria Decision Making Model Outcomes in Water Resources Management”, Springer International Publishing.
  • [22] Rao, R., & Patel, B., 2010, “A subjective and objective integrated multiple attribute decision making method for material selection”, Materials & Design, 31(10), 4738–4747.
  • [23] Charilas, D. E., Panagopoulos, A. D., & Ourania, M. I., 2014, “A Unified Network Selection Framework Using Principal Component Analysis and Multi Attribute Decision Making”, Wireless Personal Communications, 74(1), 147–165.
  • [24] Timor, M., 2011, “Analytic Hierarchy Process” (“Analitik Hiyerarşi Prosesi”) Istanbul, Türkmen Kitapevi.
  • [25] Sánchez-Lozano, J., & Teruel-Solano, J., 2013, “Geographical Information Systems (GIS) and Multi-Criteria Decision Making (MCDM) methods for the evaluation of solar farms locations: Case study in south-eastern Spain”, Renewable and Sustainable Energy Reviews, 24, 544–556.

İstatistiksel Varyans Prosedürü Temelli Analitik Hiyerarşi Prosesi ile Sıralama

Year 2017, Volume: 1 Issue: 1, 31 - 38, 01.06.2017

Abstract

Bu çalışmada çok
kriterli karar analizi yöntemlerinden Analitik Hiyerarşi Prosesi (AHP) ile
sıralama yöntemini temel alan çok kriterli bir nesnel sıralama yöntemi
sunulmaktadır.
Çok kriterli karar
analizi yöntemleri, matematiksel altyapılarındaki farklılıklar nedeniyle, aynı
sıralama problemi için farklı sıralama çözümleri üretebilmektedir.
AHP ile sıralama yönteminde karar vericilerin 1-9 ölçeğinde belirttiği
tercihler ile pozitif karşılaştırmalar matrisleri oluşturulmaktadır. Ancak karar
vericiler ufak çaplı bir sıralama problemi için bile çok sayıda karşılaştırma yaparken
öznel yargılar tutarsız sıralamalara neden olabilmektedir. Bu çalışmada sunulan
AHP’nin sadeleştirilmiş hali olan İstatistiksel Varyans Prosedürü (İVP) temelli
AHP (İVP-AHP), çok kriterli bir veri setindeki alternatiflerin sıralamasını maliyetli
anket süreçlerine başvurmadan kriter değerlerine göre belirlemektedir. Nesnel
bir sıralama için İVP ve vektörel normalizasyonu AHP ile bütünleştiren İVP-AHP
yönteminde kriter ağırlıkları İVP ile belirlenirken alternatiflerin
karşılaştırmalar matrisleri normalize edilmiş gözlem değerlerinden oluşmaktadır.
İVP-AHP ile sıralama yöntemi, AHP ile sıralama yönteminin güçlü özelliği olan karşılaştırmalar
matrislerini kullanırken tutarlılık ölçümlerine ihtiyaç duymamaktadır. İVP-AHP
yönteminde sadece sıralanması istenen alternatifler, seçimi etkileyen kriterler
ve alternatiflerin kriter değerlerinin bilinmesi yeterli olup bu parametreler
için –AHP yönteminde olduğu gibi– karar verici yargılarına ihtiyaç
bulunmamaktadır. Bu çalışmada örnek bir veri setinden AHP ve İVP-AHP yöntemleri
ile elde edilen karşılaştırmalı bulgular, işlem kolaylığı ve AHP yöntemindeki öznelliği
gidermesi açısından İVP-AHP sıralama yönteminin etkin ve nesnel bir sıralama
yöntemi olduğuna işaret etmektedir.

References

  • [1] Esen, H. Ö., 2008, “Applied Operational Research” (“Uygulamalı Yöneylem Araştırması”), (S. Tolun, Ed.), Çağlayan Kitabevi.
  • [2] Roy, B., & Vanderpooten, D., 1997, “An overview on “The European school of MCDA: Emergence, basic features and current works”, European Journal of Operational Research, 99, 26–27.
  • [3] Tayalı, H. A., 2016, “Statistical variance procedure based analytic hierarcy process: An application on multicriteria facility location selection”, Retrieved from https://tez.yok.gov.tr/UlusalTezMerkezi/.
  • [4] Ömürbek, N., & Mercan, Y., 2014, “Performance Evaluation of Sub-manufacturing Sectors Using TOPSIS and ELECTRE Methods”, Cankiri Karatekin University Journal of the Faculty of Economics and Administrative Sciences, 4(1), 237–266.
  • [5] Xidonas, P., Mavrotas, G., & Psarras, J., 2009, “A multicriteria methodology for equity selection using financial analysis”, Computers and Operations Research, 36(12), 3187–3203.
  • [6] Zopounidis, C., & Doumpos, M., 2002, “Multicriteria classification and sorting methods: A literature review”, European Journal of Operational Research, 138(2), 229–246.
  • [7] Tsoukiàs, A., 2008, “From decision theory to decision aiding methodology”, European Journal of Operational Research, 187(1), 138–161.
  • [8] Saaty, T. L., 1977, “A scaling method for priorities in hierarchical structures”, Journal of Mathematical Psychology, 15(3), 234–281.
  • [9] Sipahi, S., & Timor, M., 2010, “The analytic hierarchy process and analytic network process: An overview of applications”, Management Decision, 48(5), 775–808.
  • [10] Nelson, D., 2008, “The Penguin Dictionary of Mathematics”, Penguin UK.
  • 11] Alonso, J. A., & Lamata, M. T., 2006, “Consistency in the analytic hierarchy process: a new approach”, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 14(4), 445–459.
  • [12] Farkas, A., 2007, “The analysis of the principal eigenvector of pairwise comparison matrices”, Acta Polytechnica Hungarica, 4(2), 99–115.
  • [13] Taha, H. A., 2007, “Operations Research: An Introduction”, Pearson Education International.
  • [14] Saaty, T. L., 2003, “Decision-making with the AHP: Why is the principal eigenvector necessary”, European Journal of Operational Research, 145(1), 85–91.
  • [15] Saaty, T. L., 2008, “Relative measurement and its generalization in decision making; why pairwise comparisons are central in mathematics for the measurement of intangible factors”, Revista de La Real Academia de Ciencias Exactas, Fisicas Y Naturales. Serie A. Matematicas, 102(2), 251–318.
  • [16] Peláez, J. I., & Lamata, M. T., 2003, “A new measure of consistency for positive reciprocal matrices”, Computers and Mathematics with Applications, 46(12), 1839–1845.
  • [17] Opricovic, S., & Tzeng, G. H., 2004, “Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS”, European Journal of Operational Research, 156(2), 445–455.
  • [18] Özdağoğlu, A., 2013, “The effects of different normalization methods to decision making process in TOPSIS” (“Farklı normalizasyon yöntemlerinin TOPSIS’te karar verme sürecine etkisi”), Ege Academic Review, 13(2), 245–257.
  • [19] Pavlicic, D. M., 2001, “Normalisation affects the results of MADM methods”, Yugoslav Journal of Operations Research, 11(2), 251–265.
  • [20] Tervonen, T., Figueira, J., Lahdelma, R., & Dias, J., 2009, “A stochastic method for robustness analysis in sorting problems”, European Journal of Operational Research, 192(1), 236–242.
  • [21] Zardari, N. H., Ahmed, K., Shirazi, S. M., & Yusop, Z. Bin., 2015, “Weighting Methods and their Effects on Multi-Criteria Decision Making Model Outcomes in Water Resources Management”, Springer International Publishing.
  • [22] Rao, R., & Patel, B., 2010, “A subjective and objective integrated multiple attribute decision making method for material selection”, Materials & Design, 31(10), 4738–4747.
  • [23] Charilas, D. E., Panagopoulos, A. D., & Ourania, M. I., 2014, “A Unified Network Selection Framework Using Principal Component Analysis and Multi Attribute Decision Making”, Wireless Personal Communications, 74(1), 147–165.
  • [24] Timor, M., 2011, “Analytic Hierarchy Process” (“Analitik Hiyerarşi Prosesi”) Istanbul, Türkmen Kitapevi.
  • [25] Sánchez-Lozano, J., & Teruel-Solano, J., 2013, “Geographical Information Systems (GIS) and Multi-Criteria Decision Making (MCDM) methods for the evaluation of solar farms locations: Case study in south-eastern Spain”, Renewable and Sustainable Energy Reviews, 24, 544–556.
There are 25 citations in total.

Details

Journal Section Makaleler
Authors

Halit Alper Tayalı 0000-0002-2098-6482

Mehpare Timor

Publication Date June 1, 2017
Submission Date March 30, 2017
Published in Issue Year 2017 Volume: 1 Issue: 1

Cite

APA Tayalı, H. A., & Timor, M. (2017). Ranking with Statistical Variance Procedure based Analytic Hierarchy Process. Acta Infologica, 1(1), 31-38.
AMA Tayalı HA, Timor M. Ranking with Statistical Variance Procedure based Analytic Hierarchy Process. ACIN. June 2017;1(1):31-38.
Chicago Tayalı, Halit Alper, and Mehpare Timor. “Ranking With Statistical Variance Procedure Based Analytic Hierarchy Process”. Acta Infologica 1, no. 1 (June 2017): 31-38.
EndNote Tayalı HA, Timor M (June 1, 2017) Ranking with Statistical Variance Procedure based Analytic Hierarchy Process. Acta Infologica 1 1 31–38.
IEEE H. A. Tayalı and M. Timor, “Ranking with Statistical Variance Procedure based Analytic Hierarchy Process”, ACIN, vol. 1, no. 1, pp. 31–38, 2017.
ISNAD Tayalı, Halit Alper - Timor, Mehpare. “Ranking With Statistical Variance Procedure Based Analytic Hierarchy Process”. Acta Infologica 1/1 (June 2017), 31-38.
JAMA Tayalı HA, Timor M. Ranking with Statistical Variance Procedure based Analytic Hierarchy Process. ACIN. 2017;1:31–38.
MLA Tayalı, Halit Alper and Mehpare Timor. “Ranking With Statistical Variance Procedure Based Analytic Hierarchy Process”. Acta Infologica, vol. 1, no. 1, 2017, pp. 31-38.
Vancouver Tayalı HA, Timor M. Ranking with Statistical Variance Procedure based Analytic Hierarchy Process. ACIN. 2017;1(1):31-8.