Modification of the analytic hierarchy process (AHP) method using fuzzy logic: Fuzzy AHP approach as a support to the decision making process concerning engagement of the group for additional hindering
Abstract
This paper presents the modification of the AHP method, which takes into account the degree of suspense of decision maker, that is it allows that decision maker, with a certain degree of conviction (which is usually less than 100%), defines which linguistic expression corresponds to optimality criteria comparison. To determine the criteria weights and alternative values, fuzzy numbers are used since they are very suitable for the expression of vagueness and uncertainty. In this way, after applying the AHP method, we obtained values of criterion functions for each of the examined alternatives, which corresponds to the value determined by the degree of conviction. This provides that for different values of the degree of conviction can be made generation of different sets of criterion functions values. The set model was tested on choosing directions of action of the Group for additional hindering, as a procedure wich is often accompanied by greater or lesser degree of uncertainty of criteria that are necessary in relevant decision making.
References
Anagnostopoulos, K., Doukas, H., & Psarras, J. (2008). Linguistic multicriterria analysis system combining fuzzy sets theory, ideal and anti-ideal points for location site selection. Experts System with Applications, 35, 2041–2048.
Arslan, T., & Khisty, C.J.A. (2006). Rational approach to handling fuzzy perceptions in route choice. European Journal of Operational Research, 168 (2), 571–583.
Boender, C.G.E., De Graan, J.G., & Lootsma, F.A. (1989). Multi-criteria decision analysis with fuzzy pairwise comparisons. Fuzzy Sets and Systems, 29 (2), 133–143.
Božanić, D., Pamučar, D., Đorović, B., Milić, A. & Lukovac, V. (2011). Application of fuzzy AHP method on selection of actions direction of the Group for supplementary obstacle placing. In Proceedings of the 38th Symposium on operational research SYM-OP-IS 2011, Zlatibor, Serbia, 556-559.
Božanić, D., Pamučar, D., & Đorović, B. (2013). Modification of Analytic Hierarchy Process (AHP) method and its application in the defence decision making. Tehnika-Mandzment, 63, 327–334.
Božanić, D., & Pamučar, D. (2010). Evaluating locations for river crossing using fuzzy logic. Military Technical Courier, 58 (1), 129–145.
Chang, W. (1981). Ranking of fuzzy utilities with triangular membership functio. International conference on policy analisys and information systems, 263–276.
Chang, Y.H., & Yeh, C.H. (2012). A survey analysis of service quality for domestic airlines. European Journal of Operational Research, 149 (1), 166–177.
Chen, S.M., & Tan, J.M. (2014). Handing multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems, 74, 163–72.
Chen, C.T. (2000). Extensions of the TOPSIS for group decision making problem under fuzzy environment. Fuzzy Sets and Systems, 114 (1), 1–9.
Chen, M.F., & Tzeng, G.H. (2014). Combining grey relation and TOPSIS concepts for selecting an expatriate host country. Mathematical and Computer Modeling, 50 (13), 1473–1490.
Chen, S.M. (1997). A new method for tool steel materials selection under fuzzy environment. Fuzzy Sets and Systems, 92 (3), 265–274.
Chiadamrong, N. (2013). An integrated fuzzy multicriteria decision making under fuzzy environment. Computers and Industrial Engineering, 51 (1–2), 433–436.
Devetak, S., & Terzić, M. (2011). Application of the analytic hierarchy process method in the selection of optimal tactical radio communication systems. Military Technical Courier, 59 (3), 161–176.
Ding, J.F., & Liang, G.S. (2015). Using fuzzy MCDM to select partners of strategic alliances for liner shipping. Information Sciences, 183 (13), 197–225.
Dubois, D., & Prade, H. (1978). Operation on fuzzy number. International Journal of Systems Science, 9, 613–626.
Dubois, D., & Prade, H. (1987). The mean value of a fuzzy number. Fuzzy Sets and Systems, 24, 279–300.
Fan, Z.P., & Liu, Y. (2015). A method for group decision-making based on multi-granularity uncertain linguistic information. Experts System with Applications, 37, 4000–4008.
Gau, W.L., & Buehrer, D.J. (2013). Vague sets. IEEE Transactions on Systems Manufacturing and Cybernetics, 23, 610–614.
Grzegrorzewski, P. (2013). The hamming distance between intuitionistic fuzzy sets. In Proceedings of the 10th IFSA world congress, Istanbul, Turkey, 35–38.
Heilpern, S. (1992). The expected value of a fuzzy number. Fuzzy Sets and Systems, 47 (1), 81–86.
Hong, D.H., & Choi, C.H. (2014). Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems, 128, 103–113.
Jae, M., & Moon, J.H. (2002). Use of a fuzzy decision-making method in evaluating severe accident management strategies. Annals of Nuclear Energy, 29, 1597–1606.
Jantzen, J. (1998). Design of Fuzzy Controllers. Tech report. no 98-E 864. Technical University of Denmark, Department of Automation.
Kaufmann, A., & Gupta, M. (1985). Introduktion to Fuzzy Arithmetic. Van Nostrand Reinhold Company, New York.
Kickert, W.J.M. (1978). Fuzzy theories on decision making: A critical review. Boston: Kluwer Academic Publishers.
Kujačić, M. (2001). Selection of the best options in designing the organization of postal traffic using the Analytic Network Process. Ph.D. Thesis. Belgrade: Faculty of Transport and Traffic Engineering, University of Belgrade.
Kuo, M.S., Tzeng, G.H., & Huang, W.C. (2007). Group decision making based on concepts of ideal and anti-ideal points in a fuzzy environment. Mathematical and Computer Modelling, 45 (34), 324–339.
Laarhoven, P.J.M., & Pedrycz, W. (2003). A fuzzy extension of Saaty’s priority theory. Fuzzy Sets and Systems, 11, 229–241.
Li, R.J. (1999). Fuzzy method in group decision making. Computers and Mathematics with Applications, 38 (1), 91–101.
Liu, H.W., & Wang, G.J. (2007). Multi-criteria decision-making methods based on intuitionistic fuzzy sets. European Journal of Operational Research, 179, 220–233.
Lootsma, F.A. (1988). Numerical scaling of human judgment in pairwise–comparison methods for fuzzy multi–criteria decision analysis, Mathematical Models for Decision Support. NATO ASI Series F, Computer and System Sciences, Springer–Verlag, Berlin, Germany, 57–88.
Lootsma, F.A., Mensch, T.C.A., & Vos, F.A. (1990). Multi–criteria analysis and budget reallocation in long–term research planning. European Journal of Operational Research, 47 (3), 293–305.
Ma, D., & Zheng, X. (1991). 9/9–9/1 scale method of the AHP. Proceedings of the 2nd International Symposium on the AHP, Pittsburgh, 197–202.
Miller, G.A. (1956). The magical number seven plus or minus two: some limits on our capacity for processing information. Psychological Review, 63 (2), 81–97.
Military Lexicon. (1981). Military Paper Office. Belgrade.
Nehi, H.M. & Maleki, H.R. (2005). Intuitionistic fuzzy numbers and it’s applications in fuzzy optimization problem. In Proceedings of the 9th WSEAS International Conference on Systems, Athens, Greece.
Pamučar, D., Ćirović, G., & Sekulović D. (2015). Development of an integrated transport system in distribution centres: A FA'WOT analysis. Tehnical gazette, 22 (3), accepted for publication.
Pamučar, D., Božanić, D., & Đorović B. (2011a). Fuzzy logic in decision making process in the Armed forces of Serbia. Lambert Academic Publishing GmbH & Co. KG, Germany.
Pamučar, D., Božanić, D., Đorović, B., & Milić, A. (2011b). Modelling of the fuzzy logical system for offering support in making decisions within the engineering units of the Serbian army. International journal of the physical sciences, 6 (3), 592–609.
Pamučar, D., Ćirović, G., Sekulović, D., & Ilić, A. (2011c). A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in a SWOT analysis. Scientific Research and Essays, 6 (25), 5374–5386.
Pamučar, D., Đorović, B., Božanić, D., & Ćirović, G. (2012). Modification of the dynamic scale of marks in analytic hierarchy process (AHP) and analytic network approach (ANP) through application of fuzzy approach. Scientific Research and Essays, 7 (1), 24–37.
Pamučar, D. (2010). Using fuzzy logic and neural networks during a decision making proces in transport. Military Technical Courier, 58 (3), 125–143.
Peneva, V., & Popchev, I. (1998). Comparison of cluster from fuzzy numbers. Fuzzy Sets and Systems, 97 (1), 75–81.
Raju, K.S., & Pillai, C.R.S. (1999). Multicriterion decision making in river basin planning and development. European Journal of Operational Research, 112 (2), 249–257.
Ray, T., & Triantaphyllou, E. (1999). Procedures for the evaluation of conflicts in rankings of alternatives. Computers and Industrial Engineering, 1, 35–44.
Saaty, T.L. (1996). Analytic network process - decision making with dependece and feedback. RWS publications, Pittsburgh, PA.
Saaty, T.L. (1990). Multicriteria Decision Making - The Analytic Hierarchy Process. RWS Publications, Pittsburgh.
Saaty, T.L. (1980). The analytic hierarchy process. McGraw-Hill, New York.
Teodorović, D., & Kikuchi, S. (1994). Fuzzy sets and applications in traffic and transport. Faculty of Transport and Traffic Engineering, University of Belgrade.
Triantaphyllou, E., & Lin, C.T. (1996). Development and evaluation of five multiattribute decision making methods. International Journal of Approximate Reasoning, 14 (4), 281–310.
Triantaphyllou, E., Shu, B., Snachez, S.N., & Ray, T. (1998). Multi–criteria decision making: An operations research approach. Encyclopedia of Electrical and Electronics Engineering, John–Njilley & Sons, New York.
Wang, J.Q., & Zhang, Z. (2014). Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multicriteria decision making problems. Journal of Systems Engineering and Electronics, 25 (2), 321–326.
Xu, Z., Shang, S., Qjan, W., & Shu, W. (2010). A method for fuzzy risk analysis based on the new similarity of trapezoidal fuzzy numbers. Experts System with Applications, 37, 1920–1927.
Yager, R.R. (1978). Fuzzy decision making including unequal objectives. Fuzzy Sets and Systems, 1, 87–95.
Yager, R.R. (1988). On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems Man and Cybernetics, 18, 183–190.
Ye, J. (2010). Improved method of multicriteria fuzzy decision-making based on vague sets. Computer-Aided Design, 39, 164–169.
Ye, J. (2014). Using an improved measure function of vague sets for multicriteria fuzzy decision making. Expert Systems With Applications, 37, 4706–4709.
Yeh, C.H., & Deng, H. (2014). A practical approach to fuzzy utilities comparison in fuzzy multicriteria analysis. International Journal of Approximate Reasoning, 45 (2), 179–194.
Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8, 338–356.
Zhu, K.J., Jing, Y., & Chang, D.Y. (1999). A discussion on extent analysis method and applications on fuzzy AHP. European Journal of Operational Research, 116 (18), 450–456.
Zimmermann, H.J. (1987). Fuzzy sets, decision making, and expert system. Boston: Kluwer Academic Publishers.
The Author wishes to submit the Work to SJM for publication. To enable SJM to publish the Work and to give effect to the parties’ intention set forth herein, they have agreed to cede the first right to publication and republication in the SJM Journal.
Cession
The Author hereby cedes to SJM, who accepts the cession, to the copyright in and to the paper.
The purpose of the cession is to enable SJM to publish the Work, as first publisher world-wide, and for republication in the SJM Journal, and to grant the right to others to publish the Work world-wide, for so long as such copyright subsists;
SJM shall be entitled to edit the work before publication, as it deems fit, subject to the Authors approval
The Author warrants to SJM that:
- the Author is the owner of the copyright in the Work, whether as author or as reassigned from the Author’s employee and that the Author is entitled to cede the copyright to SJM;
- the paper (or any of its part) is not submitted or accepted for publication in any other Journal;
- the Work is an original work created by the Author;
- the Author has not transferred, ceded, or assigned the copyright, or any part thereof, to any third party; or granted any third party a licence or other right to the copyright, which may affect or detract from the rights granted to SJM in terms of this agreement.
The Author hereby indemnifies the SJM as a body and its individual members, to the fullest extent permitted in law, against all or any claims which may arise consequent to the warranties set forth.
No monetary consideration shall be payable by SJM to the Author for the cession, but SJM shall clearly identify the Author as having produced the Work and ensure that due recognition is given to the Author in any publication of the Work.
Should SJM, in its sole discretion, elect not to publish the Work within 1 year after the date of this agreement, the cession shall lapse and be of no further effect. In such event the copyright shall revert to the Author and SJM shall not publish the Work, or any part thereof, without the Author’s prior written consent.