A new interactive approach to multiple criteria sorting problems: An application in energy sector

Year 2021, Volume: 36 Issue: 4, 2239 - 2254, 02.09.2021

Ali Özarslan Gülşah Karakaya

https://doi.org/10.17341/gazimmfd.737908

Abstract

In this study, an interactive approach with the decision maker is proposed for sorting alternatives evaluated by multiple criteria. The preferences of the decision maker are assumed to be consistent with an additive utility function which is commonly used in literature. In the proposed approach, alternatives are assigned to categories by the decision maker through iterations. Based on the information obtained from the decision maker, mathematical models are solved in order to determine the worst and best possible categories of the alternatives. Accordingly, the probabilities of assigning alternatives to categories are calculated. Relative entropy, which is a measure of information theory, is used to measure the assignment ambiguity of the alternatives and select the alternative to be asked the decision maker. Alternatives with a certain level of assignment probability are probabilistically assigned to categories without consulting the decision maker. Assignment information from the decision maker is gathered iteratively until there are no alternative left. Our approach is compared against another approach from literature on a data set in the energy sector. The results show that the proposed approach is successful in reducing the cognitive burden of the decision maker.

Keywords

multi-criteria sorting problems, relative entropy, interactive probabilistic method, additive utility function, energy trilemma index

Çok kriterli sınıflandırma problemlerine yeni bir etkileşimli yöntem: Enerji sektöründe bir uygulama

Abstract

Bu çalışmada birden fazla kriterle değerlendirilen alternatiflerin sınıflandırması için karar verici ile etkileşimli bir yaklaşım önerilmektedir. Karar vericinin tercihlerinin literatürde sıklıkla kullanılan toplamsal fayda fonksiyonu ile tutarlı olduğu varsayılmaktadır. Önerilen yaklaşımda, iterasyonlar boyunca karar vericiye alternatifler sunularak bu alternatiflerin kategori bilgisi alınmaktadır. Karar vericiden alınan bilgiler kullanılarak alternatiflerin atanabilecekleri olası en kötü ve en iyi kategorileri belirlemek için matematiksel modeller çözülmektedir. Bu modellerden bilgi toplayarak alternatiflerin kategorilere atanma olasılıkları hesaplanmaktadır. Karar vericiye sunulacak alternatif belirlenirken atanma belirsizliğini ölçmek için bir bilgi kuramı ölçüsü olan göreceli entropiden yararlanılmaktadır. Alternatiflerin atanma belirsizlikleri belirli bir seviyenin altına düşünce atanma olasılıkları belirli bir seviyeden yüksek olan alternatifler karar vericiye sorulmadan olasılıksal olarak kategorilere atanmaktadır. Tüm alternatifler sınıflandırılana kadar karar vericiden aşamalı olarak atama bilgisi alınmaktadır. Yaklaşımımız literatürden başka bir yöntem ile enerji sektöründe bir veri seti üzerinde test edilerek performans kıyaslaması yapılmıştır. Sonuçlar, karar vericinin bilişsel yükünü azaltmada önerilen yaklaşımın başarılı olduğunu göstermektedir.

Keywords

çok kriterli sınıflandırma problemleri, göreceli entropi, etkileşimli olasılıksal yöntem, toplamsal fayda fonksiyonu, enerji üçlemi endeksi

References

• Roy B., Paradigm and challenges, Multiple Criteria Decision Analysis: State of the Art Surveys, Springer, Berlin, 19–39, 2016.
• Yıldırım F. ve Önder E., Çok Kriterli Karar Verme Yöntemleri, Dora Yayınları, Bursa, 2014.
• Ishizaka A. ve Nemery P., Multi-Criteria Decision Analysis Methods and Software, John Wiley & Sons Ltd., Chichester, 2013.
• Doumpos M. ve Zopounidis C., Preference disaggregation and statistical learning for multicriteria decision support: A review, European Journal of Operational Research, 209 (3), 203–214, 2011.
• Roy B., The outranking approach and the foundations of Electre methods, Journal of Theory and Decision, 31, 49–73, 1991.
• Yu W., ELECTRE TRI: Aspects methodologiques et manuel d’utilisation, document du LAMSADE, 74, Université de Paris-Dauphine, Paris, 1992.
• Leroy A., Mousseau V., Pirlot M., Learning the parameters of a multiple criteria sorting method, ADT 2011, LNCS, 6992, Editörler: Brafman R.I., Roberts F.S., Tsoukias A., Springer, Heidelberg, 219–233, 2011.
• Tervonen T., Lahdelma R., Dias J.A., Figueira J., Salminen P., SMAA-TRI: A Parameter Stability Analysis Method for ELECTRE-TRI, Environmental Security in Harbors and Coastal Areas, Editörler: Kiker G.A. ve Linkov I., Springer, Berlin, 217–231 2009.
• Nemery P. ve Lamboray C., FlowSort: a flow-based sorting method with limiting or central profiles, TOP, 16 (1), 90–113, 2008.
• Kizilkaya Aydogan E. ve Ozmen M., Two new method for multi criteria stochastic decision making: SMAA-GRA and SMAA-DEMATEL-GRA, Journal of the Faculty of Engineering and Architecture of Gazi University, 30 (4), 627–640, 2015.
• Ulu C. ve Köksalan M., An interactive approach to multicriteria sorting for quasiconcave value functions, Naval Research Logistics 61, 447–457, 2014.
• Özpeynirci Ö., Özpeynirci S., Kaya A., An interactive approach for multiple criteria selection problem, Computers & Operations Research, 78, 154–162, 2017.
• Soylu B., A multi-criteria sorting procedure with Tchebycheff utility function, Computers and Operations Research, 38 (8), 1091–1102, 2011.
• Devaud J.M., Groussaud G., Jaquet-Lagreze E., UTADIS: Une méthode de construction de fonctions d’utilité additives rendant compte de jugements globaux, Proceedings of the European working group on MCDA, Bochum, Germany, 1980.
• Jaquet-Lagreze E. ve Siskos, Y., Assessing a set of additive utility functions for multicriteria decision making: The UTA method, European Journal of Operational Research, 10, 151–164, 1982.
• Ulucan A. ve Atıcı K.B., A multiple criteria sorting methodology with multiple classification criteria and an application to country risk evaluation, Technological and Economic Development of Economy, 19 (1), 93–124, 2013.
• Zopounidis C. ve Doumpos M., Business failure prediction using the UTADIS multicriteria analysis method, Journal of the Operational Research Society, 50 (11), 1138–1148, 1999.
• Köksalan M. ve Özpeynirci S., An interactive sorting method for additive utility functions, Computers and Operations Research, 36 (9), 2565–2572, 2009.
• Ulu C. ve Köksalan M., An interactive procedure for selecting acceptable alternatives in the presence of multiple criteria, Naval Research Logistics, 48 (7), 592–606, 2001.
• Korhonen P., Wallenius J., Zionts S., Solving the discrete multiple criteria problem using convex cones, Management Science, 30 (11), 1336–1345, 1984.
• Köksalan M. ve Ulu C., An interactive approach for placing alternatives in preference classes, European Journal of Operational Research, 144 (2), 429–439, 2003.
• Buğdacı A.G., Köksalan M., Özpeynirci S., Serin Y., An Interactive probabilistic approach to multi-criteria sorting, IIE Transactions, 45, 1048–1058, 2013.
• Doumpos M. ve Zopounidis C., Developing sorting models using preference disaggregation analysis: An experimental investigation, European Journal of Operational Research, 154 (3), 585–598, 2004.
• Shannon C., The mathematical theory of communication, Bell System Technical Journal, 27 (3), 379–423, 1948. Abbas A., Entropy methods for adaptive utility elicitation, IEEE Transactions on Systems Man and Cybernetics – Part A: Systems and Humans, 34 (2), 169–178, 2004.
• Valkenhoef G. ve Tervonen T., Entropy-optimal weight constraint elicitation with additive multi-attribute utility models. Omega 64 (1), 1–12, 2016.
• Ciomek K., Kadziński M., Tervonen T., Heuristics for prioritizing pair-wise elicitation questions with additive multi-attribute value models, Omega, 71, 27–45, 2017.
• Wu J., Sun J., Liang L., Zha Y., Determination of weights for ultimate cross efficiency using shannon entropy, Expert Systems with Applications, 38 (5), 5162–5165, 2011.
• Özpeynirci S., Özpeynirci Ö., Mousseau V., An interactive algorithm for multiple criteria constrained sorting problem, Annals of Operations Research, 267 (1), 447–466, 2018.
• Savage L.J., The theory of statistical decision, Journal of the American Statistical Association, 46 (253), 55–67, 1951.
• Benabbou N., Perny P., Viappiani P., Incremental elicitation of Choquet capacities for multicriteria choice, ranking and sorting problems, Artificial Intelligence, 246, 152–180, 2017.
• World Energy Council, World Energy Trilemma Index 2019 Full Report, https://www.worldenergy.org/assets/downloads/WETrilemma_2019_Full_Report_v4_pages.pdf. Yayın tarihi Eylül 2019. Erişim tarihi Mart 20, 2020.
• Doumpos M. ve Zopounidis C., Developing sorting models using preference disaggregation analysis: An experimental investigation, Fuzzy Sets in Management, Economy and Marketing, Editörler: Zopounidis C., Pardalos P.M., Baourakis G., World Scientific, Singapore, 51–67, 2001.