A granulation of linguistic information in AHP method using modified particle swarm optimization algorithm

Document Type : Original Article

Authors

1 MSc student, Faculty of Management, University of Tehran, Tehran, Iran.

2 PhD student, Faculty of Management, University of Tehran, Tehran, Iran.

Abstract

Multi-criteria decision making methods have been of the most popular and practical areas in recent years. Among these methods, the AHP method has been considered by many researchers due to its unique features and has been used in numerous studies. This method facilitates decision-making for the decision-maker by allowing pairwise comparison between alternatives using language expressions. But this feature causes inconsistency in the decision matrix. One of the sources of inconsistency is the use of a predetermined scale to convert linguistic variables into quantitative values due to the different intellectual background of experts and their information about the problem. Therefore, the purpose of this study is to provide a customized scale for converting linguistic variables using the granularization of linguistic variables, which is in line with expert opinions and reduces the inconsistency. The unique feature of this framework is that the distribution of cut-off points is not known in advance and is determined according to expert opinions. To optimize the proposed model, a particle swarm optimization metaheuristic algorithm is used, which is modified to adapt to the specific characteristics of the problem. The results show the good performance of the proposed framework in reducing incompatibility.

Keywords

References

[1]         Y.-M. Wang and Y. Luo, “Integration of correlations with standard deviations for determining attribute weights in multiple attribute decision making,” Math. Comput. Model., vol. 51, no. 1, pp. 1–12, 2010.
[2]         A. Asakereh, M. Soleymani, and M. J. Sheikhdavoodi, “A GIS-based Fuzzy-AHP method for the evaluation of solar farms locations: Case study in Khuzestan province, Iran,” Sol. Energy, vol. 155, pp. 342–353, 2017.
[3]         A. Khadivar and F. Mojibian, “Workshops Clustering Using a Combination Approach of Data Mining and MCDM,” Mod. Res. Decis. Mak., vol. 3, no. 2, pp. 107–128, 2018.
[4]         nadia rasouli,  fatemeh marandi, and N. Nahavandi, “An Integrated approach based on MADM and MODM for supplier selection and assembler selection in supply chain management,” Mod. Res. Decis. Mak., vol. 3, no. 1, pp. 159–185, 2018.
[5]         Kh, Javani, and A. Anabostani, “Comparative Analysis of Multi Criteria ANP &AHP Decision Making green spaces in rural location,” J. Spat. Plan., vol. 19, no. 4, pp. 1–32, 2016.
[6]         A. Emrouznejad and M. Marra, “The state of the art development of AHP (1979–2017): a literature review with a social network analysis,” Int. J. Prod. Res., pp. 1–23, 2017.
[7]         F. J. Cabrerizo, E. Herrera-Viedma, and W. Pedrycz, “A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts,” Eur. J. Oper. Res., vol. 230, no. 3, pp. 624–633, 2013.
[8]         T. L. Saaty, “A scaling method for priorities in hierarchical structures,” J. Math. Psychol., vol. 15, no. 3, pp. 234–281, 1977.
[9]         M. Beynon, “An analysis of distributions of priority values from alternative comparison scales within AHP,” Eur. J. Oper. Res., vol. 140, no. 1, pp. 104–117, 2002.
[10]       Z. Pei and L. Zheng, “New unbalanced linguistic scale sets: The linguistic information representations and applications,” Comput. Ind. Eng., vol. 105, pp. 377–390, 2017.
[11]       W. Pedrycz and M. Song, “A granulation of linguistic information in AHP decision-making problems,” Inf. Fusion, vol. 17, pp. 93–101, 2014.
[12]       R. Poli, J. Kennedy, and T. Blackwell, “Particle swarm optimization,” Swarm Intell., vol. 1, no. 1, pp. 33–57, 2007.
[13]       T. L. Saaty, “The analytical hierarchical process,” J Wiley, New York, 1980.
[14]       V. Pereira and H. G. Costa, “Nonlinear programming applied to the reduction of inconsistency in the AHP method,” Ann. Oper. Res., vol. 229, no. 1, pp. 635–655, 2015.
[15]       H.-L. Li and L.-C. Ma, “Detecting and adjusting ordinal and cardinal inconsistencies through a graphical and optimal approach in AHP models,” Comput. Oper. Res., vol. 34, no. 3, pp. 780–798, 2007.
[16]       S. Siraj, L. Mikhailov, and J. A. Keane, “Contribution of individual judgments toward inconsistency in pairwise comparisons,” Eur. J. Oper. Res., vol. 242, no. 2, pp. 557–567, 2015.
[17]       P. Ji and R. Jiang, “Scale transitivity in the AHP,” J. Oper. Res. Soc., vol. 54, no. 8, pp. 896–905, 2003.
[18]       F. Herrera, E. Herrera-Viedma, and L. Martínez, “A fuzzy linguistic methodology to deal with unbalanced linguistic term sets,” IEEE Trans. fuzzy Syst., vol. 16, no. 2, pp. 354–370, 2008.
[19]       L. A. Zadeh, “Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic,” Fuzzy sets Syst., vol. 90, no. 2, pp. 111–127, 1997.
[20]       M. A. Sanchez, O. Castillo, and J. R. Castro, “Information granule formation via the concept of uncertainty-based information with Interval Type-2 Fuzzy Sets representation and Takagi–Sugeno–Kang consequents optimized with Cuckoo search,” Appl. Soft Comput., vol. 27, pp. 602–609, 2015.
[21]       K. Chatterjee and S. Kar, “Unified Granular-number-based AHP-VIKOR multi-criteria decision framework,” Granul. Comput., pp. 1–23, 2017.
[22]       Y.-F. Kuo and P.-C. Chen, “Constructing performance appraisal indicators for mobility of the service industries using Fuzzy Delphi Method,” Expert Syst. Appl., vol. 35, no. 4, pp. 1930–1939, 2008.
[23]       S. A. Jalaee, A. Ghassemi, and O. Sattari, “Simulating Consumption Function and Forecasting Iran’s Consumption until 1404 Horizon Using Genetic and Particle Swarm Optimization Algorithm,” Econ. Reseach, vol. 15, no. 2, pp. 27–47, 2015.
[24]       L. A. Zadeh, “Fuzzy sets,” Inf. Control, vol. 8, no. 3, pp. 338–353, 1965.
[25]       D.-Y. Chang, “Applications of the extent analysis method on fuzzy AHP,” Eur. J. Oper. Res., vol. 95, no. 3, pp. 649–655, 1996.
[26]       O. Gogus and T. O. Boucher, “Strong transitivity, rationality and weak monotonicity in fuzzy pairwise comparisons,” Fuzzy Sets Syst., vol. 94, no. 1, pp. 133–144, 1998.

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