Developing Stochastic Additive Utility Method (UTA) Considering the Possible Dependency among Criteria

Document Type : Research Paper


1 Assistant Prof, Department of Industrial Management, Faculty of Management, University of Tehran, Tehran, Iran

2 Prof, Department of Industrial Management, Faculty of Management, University of Tehran, Tehran, Ira

3 PhD Candidate, Department of Industrial Management, Alborz Campus, University of Tehran, Karaj, Iran

4 Associate Prof., Department of Public Management, Faculty of Management, University of Tehran, Tehran, Iran


Objective: One of the well-known methods as to Multi Attribute Utility Theory (MAUT) in the field of decision making is Utility Additive Method (UTA), which has been developed over time. Two main deficiencies of such methods are first, ignoring the uncertainty embedded in the values of different criteria and second, disregarding the possibility of dependencies among various criteria. The uncertainty problem, either fuzzy or stochastic, has been discussed in various developments including, fuzzy UTA and stochastic UTA models, respectively. Although it seems unlikely to apply in real world problems, the criteria independency is the primary assumption of all these models. Thus, this paper is aimed at developing stochastic UTA model so as to consider the possibility of dependency among different criteria.
Methods: In this paper, conditional probability is applied in developing the UTA model, so that the probability of values of each criterion is considered with respect to probable values of other criteria.
Results: The developed model is presented in 12 steps, and its applicability in practice is shown using a real example based upon the data extracted from three main criteria of stock investments for three petrochemical companies.
Conclusion: The proposed model addresses the deficiency of ignoring the probable dependencies among criteria in stochastic UTA model, and covers the research gap posed by previous researchers.


Abadian, M., Shajari, H. (2017). Multi-attribute method for selecting the optimal stock portfolio using fundamental analysis variables in the petrochemical companies members of Stock Exchange. Financial Engineering and Portfolio Management, 7(26), 1-26. (in Persian)
Amini, H., Rasti, B.M. (2017). The interactivity between the criteria in MCDM problemJournal of Indusrial Management8(4), 515-532. (in Persian)
Angilella, S., Greco, S., Lamantia, F., & Matarazzo, B. (2003). Assessing non-additive utility for multicriteria decision aid. European Journal of Operational Research, 3(158), 734–744.
Beuthe, M. Scannella, G. (2001). Comparative analysis of UTA multi-criteria methods. European Journal of Operational Research, (130), 246-262.
Despotis, D.K., Zopounidis, C. (1993). Building additive utilities in the presence of non-monotonic.: Building additive utilities in the presence of non-monotonic preference. In: Pardalos, P.M., Siskos, Y, Zopounidis, C. (eds.) Advances in Multicriteria Analysis, 101–114. Kluwer Academic, Dordrecht.
Eberhard, A., Schreider, S., & Stojkov, L. (2007). Construction of the utility function using a non-linear best fit optimisation approach In Proceedings of the International congress on modelling and simulation MODSIM07. Christchurch, 10–14, December 2007.
Figueira, J., Salvatore, G., & Matthias, E. (2005). Multiple Criteria Decision Analysis. Springer, New York, NY.
Figueira, J. R, Greco, S., & SÅ‚owinski, R. (2009). Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method. European Journal of Operational Research, (195), 460–486.
Jacquet-Lagreze, E., Siskos, J. (1982). Assessing a set of additive utility functions for multicriteria decision-making, the UTA method. European journal of operational research, 10 (2), 151-164.
Mehregan, M. R. (2013), Multiple Objective Decision Making Models, University of Tehran Press, Tehran. (in Persian)
Nguyen, D.V. (2013). Global maximization of UTA functions in multi-objective optimization. European Journal of Operational Research, (228), 397–404.
Pachauri, B., Kumar, A., Dhar, J. (2014). Oftware reliability growth modeling with dynamic faults and release time optimization using GA and MAUT. Applied Mathematics and Computation, (242), 500–509.
Patiniotakis, I., Apostolou, D., Mentzas, G. (2011). Fuzzy UTASTAR: A method for discovering utility functions from fuzzy data. Expert Systems with Applications, (38), 15463–15474.
Salati, M., Makoui, A. (2015). Offer the value function (utility) to prioritize research projects in R & D centers using the UTA method (Case of Water Resources company in Iran). Industrial Management Studies11(31), 19-33. (in Persian)
Scholza, M., Franz, N., Hinz, O. (2017). Effects of decision space information on MAUT-based systems that support purchase decision processes. Decision Support Systems, (97), 43–57.
Shanmuganathan, M., Kajendran, K., Sasikumar, A.N., Mahendran, M. (2018). Multi Attribute Utility Theory – An Over View. International Journal of Scientific & Engineering Research, 9(3), 698-706.
Siskos, J. (1983). Analyse de systèmes de décision multicritère en univers aléatoire. Control Eng. 10(3–4), 193–212.
Siskos, Y., & Jacquet, L. (1982). Assessing a set of additive utility functions for multi criteria decision making, The UTA method. European Journal of Operational Research, 10(2), 151–164.
Siskos, Y., Yannacopoulos, D. (1985). UTASTAR: An ordinal regression method for building additive value functions. Investigaçao Operacional, 5 (1), 39-53.
Siskos, Y., Grigoroudis, E. & Matsatsinis, N.F. (2016). UTA methods. Multiple criteria decision analysis, pp. 315-362. Springer, New York, NY.
Sorourkhah, A., Azar, A., Babaie-Kafaki, S., Shafiei Nik Abadi, M. (2017). Using Weighted-Robustness Analysis in Strategy Selection (Case Study: Saipa Automotive Research and Innovation Center). Industrial Management Journal, 9(4), 665-690. (in Persian)