Prioritization Method in the Fuzzy Analytic Network Process by Fuzzy Preferences Programming Method

Authors: Tarifa S. Almulhim, Ludmil Mikhailov, Dong-Ling Xu

Abstract:

In this paper, a method for deriving a group priority vector in the Fuzzy Analytic Network Process (FANP) is proposed. By introducing importance weights of multiple decision makers (DMs) based on their experiences, the Fuzzy Preferences Programming Method (FPP) is extended to a fuzzy group prioritization problem in the FANP. Additionally, fuzzy pair-wise comparison judgments are presented rather than exact numerical assessments in order to model the uncertainty and imprecision in the DMs- judgments and then transform the fuzzy group prioritization problem into a fuzzy non-linear programming optimization problem which maximize the group satisfaction. Unlike the known fuzzy prioritization techniques, the new method proposed in this paper can easily derive crisp weights from incomplete and inconsistency fuzzy set of comparison judgments and does not require additional aggregation producers. Detailed numerical examples are used to illustrate the implement of our approach and compare with the latest fuzzy prioritization method.

Keywords: Fuzzy Analytic Network Process (FANP), Fuzzy Non-linear Programming, Fuzzy Preferences Programming Method (FPP), Multiple Criteria Decision-Making (MCDM), Triangular Fuzzy Number.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330737

References:

[1] T. L. Saaty, "Axiomatic foundation of the analytic hierarchy process," Management Sciences, vol. 32, no. 7, pp. 841-855, July 1987.
[2] T. L. Saaty, and L. G. Vargas, "Decision making with the analytic network process," New York: Spring Science Publisher, 2006.
[3] G. Singh, and L. Mikhailov, "Fuzzy analytic network process and its application to the development of decision support system," IEEE Translations on system, vol. 33, pp. 33-41, February 2003.
[4] R. Tuzkaya , and S. Önüt, "A fuzzy analytic network process based approach to transportation-mode selection between Turkey and Germany: A case study," Information Sciences, vol. 178, no. 15, pp. 3133-3146, August 2008.
[5] M. A. B. Promentilla, T. Furuichi, K. Ishii, and N. Tanikawa, "A fuzzy analytic network process for multi-criteria evaluation of contaminated site remedial countermeasures," Journal of Environmental Management, vol. 88, pp. 479-495, August 2008.
[6] I. Yuksel and M. Dagdeviren, "Using the fuzzy analytic network process (ANP) for Balanced Scorecard (BSC): a case study for a manufacturing firm," Expert Systems with Applications, vol. 37, pp. 1270-1278, March 2010.
[7] Z. Ayag, and R.G. Ozdemir, "A hybrid approach to concept selection through fuzzy analytical network process," Computers and Industrial Engineering, vol. 56, pp. 368-379, February 2009.
[8] Z. Ayag, and R.G. Ozdemir, "An intelligent approach to machine tool selection through fuzzy analytic network process," Journal of Intelligent Manufacturing, vol. 22, pp. 163-177, November 2011.
[9] T. L. Saaty, "Fundamental of the analytic network process- dependence and feedback in decision making with a single network," Journal of system science and system engineering, vol. 13, pp. 129-157, April 2004.
[10] J. K. Levy, and K. Taji, "Group decision support for hazards planning and emergency management: a Group Analytic Network Process (GANP) approach," Mathematical and Computer Modeling, vol. 46, pp. 906-917, October 2007.
[11] H. Rafiei, and M. Rabbani, "Project selection using fuzzy group analytic network process," World Academy of Science, Engineering and Technology, vol. 58, pp. 122-126, 2009.
[12] W. Z. Yang, Y. H. Ge, J.J. He, and B. Liu, "Group decision support for hazards planning and emergency management: a Group Analytic Network Process (GANP) approach," African Journal of Business Management, vol. 4, pp. 2571-2585, September 2010.
[13] L. Mikhailov, "Deriving priorities from fuzzy pair wise comparison judgments," Fuzzy Sets and System, vol. 134, pp. 365-385, July 2003.
[14] L. Mikhailov, "A fuzzy programming method for deriving priorities in the analytic hierarchy process," The Journal of the Operational Research Society, vol. 51, pp. 341-349, March 2000.
[15] R. N. Tiwari, S. Dharmar, and J. R. Rao, “Fuzzy goal programming—an additive model,” Fuzzy Sets and System, vol. 24, pp. 27–34, October 1987.
[16] L. Mikhailov, H. Didehkhani, and S. Sadi-Nezhad, “Weighted Prioritization Models in the Fuzzy Analytic Hierarchy Process,” International Journal of Information Technology & Decision Making, vol. 10, pp. 694–34, November 2011.
[17] T. L. Saaty, “Decision making with dependence and feedback: the Analytic Network Process,” PA, USA: RWA Publications, 1996, p.p. 78- 80.