An alternate method to determine λ0-measure values prior to applying Choquet integral in a multi-attribute decision making environment

Krishnan, A.; Wahab, S.; Kasim, M.; Bakar, E.

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Decision Science Letters

ISSN 1929-5812 (Online) - ISSN 1929-5804 (Print) Quarterly Publication Volume 8 Issue 2 pp. 193-210 , 2019

An alternate method to determine λ0-measure values prior to applying Choquet integral in a multi-attribute decision making environment Pages 193-210 Download PDF

Authors: Anath Rau Krishnan, Siti Nur Aqilah Ab Wahab, Maznah Mat Kasim, Engku Muhammad Nazri Engku Abu Bakar

DOI: 10.5267/j.dsl.2018.6.001

Keywords: Choquet integral, Fuzzy measure, Interpretive structural modelling, Multi-attribute decision problems

Abstract: Determining 2n values of fuzzy measure prior to applying Choquet integral normally turns into a complex undertaking, especially when the decision problem entails a large number of evaluation attributes, n. Many patterns of fuzzy measure have thus been suggested to deal with this complexity. λ0-measure is one such pattern. However, the original λ0-measure identification method was found to be unsuccessful in providing clear-cut indications on the relationships held by the attributes. A revised version of the method was then introduced to tackle this issue, but unfortunately it requires a large amount of initial data from the respondents compared to the original method. This paper therefore proposes an alternate version of λ0-measure identification method that synchronously compensates the shortcomings associated with each existing method. The proposed method uses interpretive structural modelling (ISM) to uncover the actual relationships held by the attributes. The outputs of ISM (i.e. digraph, driving power and dependence power) are then utilised to determine the inputs required to identify the complete set of λ0-measure values. A supplier selection problem was used to demonstrate the feasibility of the method. Also, the usability of the method was compared over the existing ones.

How to cite this paper

 Krishnan, A., Wahab, S., Kasim, M & Bakar, E. (2019). An alternate method to determine λ0-measure values prior to applying Choquet integral in a multi-attribute decision making environment.Decision Science Letters , 8(2), 193-210.

Refrences

Agrawal, A. K., Kumar, D., & Rahman, Z. (2017). An ISM approach for modelling the enablers of sustainability in market-oriented firms. International Journal of Business Excellence, 12(1), 23-45.
Angilella, S., Greco, S., Lamantia, F., & Matarazzo, B. (2004). Assessing non-additive utility for multicriteria decision aid. European Journal of Operational Research, 158(3), 734-744.
Berrah, L., Mauris, G., & Montmain, J. (2008). Monitoring the improvement of an overall industrial performance based on a Choquet integral aggregation. Omega, 36(3), 340-351.
Bhadani, A. K., Shankar, R., & Rao, D. V. (2016). Modeling the factors and their inter-dependencies for investment decision in Indian mobile service sector. Journal of Modelling in Management, 11(1), 189-212.
Bottero, M., Ferretti, V., & Mondini, G. (2013). A Choquet integral-based approach for assessing the sustainability of a new waste incinerator. International Journal of Multicriteria Decision Making, 3(2-3), 157-177.
Chen, S. J., & Hwang, C. L. (1992). Fuzzy multiple attribute decision making methods. Springer, Berlin Heidelberg
Choquet, G. (1954). Theory of capacities. In Annales de l'institut Fourier (Vol. 5, pp. 131-295).
Demirel, N. Ç., Demirel, T., Deveci, M., & Vardar, G. (2017). Location selection for underground natural gas storage using Choquet integral. Journal of Natural Gas Science and Engineering, 45, 368-379.
Detyniecki, M. (2000). Mathematical aggregation operators and their application to video querying. Dissertation, University of Paris VI
Dwivedi, Y. K., Janssen, M., Slade, E. L., Rana, N. P., Weerakkody, V., Millard, J.,& Snijders, D. (2017). Driving innovation through big open linked data (BOLD): Exploring antecedents using interpretive structural modelling. Information Systems Frontiers, 19(2), 197-212.
Feng, C. M., Wu, P. J., & Chia, K. C. (2010). A hybrid fuzzy integral decision-making model for locating manufacturing centers in China: A case study. European Journal of Operational Research, 200(1), 63-73.
Grabisch, M. (1996). The application of fuzzy integrals in multicriteria decision making. European journal of operational research, 89(3), 445-456.
Grabisch, M., & Labreuche, C. (2010). A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. Annals of Operations Research, 175(1), 247-286.
Gürbüz, T., Alptekin, S. E., & Alptekin, G. I. (2012). A hybrid MCDM methodology for ERP selection problem with interacting criteria. Decision Support Systems, 54(1), 206-214.
Hu, Y. C., & Chen, H. C. (2010). Choquet integral-based hierarchical networks for evaluating customer service perceptions on fast food stores. Expert Systems with Applications, 37(12), 7880-7887.
Harary, F., Norman, R. Z., & Cartwight, D. (1965). Structural models: An introduction to the theory of directed graphs. Wiley, New York.
Huang, J. J., Tzeng, G. H., & Ong, C. S. (2005). Multidimensional data in multidimensional scaling using the analytic network process. Pattern Recognition Letters, 26(6), 755-767.
Hung, S. J. (2011). Activity-based divergent supply chain planning for competitive advantage in the risky global environment: A DEMATEL-ANP fuzzy goal programming approach. Expert Systems with Applications, 38(8), 9053-9062.
Ishii, K., & Sugeno, M. (1985). A model of human evaluation process using fuzzy measure. International Journal of Man-Machine Studies, 22(1), 19-38.
Kojadinovic, I. (2008). Unsupervized aggregation of commensurate correlated attributes by means of the Choquet integral and entropy functionals. International Journal of Intelligent Systems, 23(2), 128-154.
Krishnan, A. R., Aqilah, S. N., Kasim, M. M., Nazri, E. M., & Char, A. K. (2017). A revised procedure to identify λ0-measure values for applying Choquet integral in solving multi-attribute decision problems. OPSEARCH, 54(3), 637-650.
Krishnan, A. R., Kasim, M. M., & Bakar, E. M. N. E. A. (2015). A short survey on the usage of Choquet integral and its associated fuzzy measure in multiple attribute analysis. Procedia Computer Science, 59, 427-434.
Larbani, M., Huang, C. Y., & Tzeng, G. H. (2011). A novel method for fuzzy measure identification. International Journal of Fuzzy Systems, 13(1).
Malone, D. W. (1975). An introduction to the application of interpretive structural modeling. Proceedings of the IEEE, 63(3), 397-404.
Mandal, A., & Deshmukh, S. G. (1994). Vendor selection using interpretive structural modelling (ISM). International Journal of Operations & Production Management, 14(6), 52-59.
Marichal, J. L. (2000a). Behavioral analysis of aggregation in multicriteria decision aid. In Preferences and decisions under incomplete knowledge (pp. 153-178). Physica, Heidelberg.
Marichal, J. L. (2000b). An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria. IEEE Transactions on Fuzzy Systems, 8(6), 800-807.
Murofushi, T., & Sugeno, M. (1989). An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure. Fuzzy sets and Systems, 29(2), 201-227.
Sage A.P. (1977). Interpretive structural modeling: Methodology for large scale systems. New York, NY: McGraw-Hill.
Shieh, J. I., Wu, H. H., & Huang, K. K. (2010). A DEMATEL method in identifying key success factors of hospital service quality. Knowledge-Based Systems, 23(3), 277-282.
Singh, B., Grover, S., & Singh, V. (2017). A benchmarking model for Indian service industries using MICMAC and WISM approach. International Journal of System Assurance Engineering and Management, 8(2), 1266-1281.
Singh, M. D., & Kant, R. (2008). Knowledge management barriers: An interpretive structural modeling approach. International Journal of Management Science and Engineering Management, 3(2), 141-150.
Sugeno, M. (1974). Theory of fuzzy integrals and its applications. Doctoral Thesis, Tokyo Institute of Technology.
Tzeng, G. H., Yang, Y. P. O., Lin, C. T., & Chen, C. B. (2005). Hierarchical MADM with fuzzy integral for evaluating enterprise intranet web sites. Information Sciences, 169(3-4), 409-426.
Warfield, J. N. (1974). Developing subsystem matrices in structural modeling. IEEE Transactions on Systems, Man, and Cybernetics, (1), 74-80.
Zhang, L., Xu, Y., Yeh, C. H., Liu, Y., & Zhou, D. (2016). City sustainability evaluation using multi-criteria decision making with objective weights of interdependent criteria. Journal of Cleaner Production, 131, 491-499.