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Neural Processing Letters
Published in: Neural Processing Letters 2/2016

01-10-2016

Rectifying the Inconsistent Fuzzy Preference Matrix in AHP Using a Multi-Objective BicriterionAnt

Authors: Abba Suganda Girsang, Chun-Wei Tsai, Chu-Sing Yang

Published in: Neural Processing Letters | Issue 2/2016

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Abstract

Analytic hierarchy process (AHP) is a decision making tool regarding the criteria analysis to obtain a priority alternative. One of the important issues in comparison matrix of AHP is the consistency. The inconsistent comparison matrix cannot be used to make decision. This paper proposes an algorithm using a modified BicriterionAnt to pursue two objectives intended to rectify the inconsistent fuzzy preference matrix, called MOBAF. The two objectives include minimizing the consistent ratio (CR) and minimizing the deviation matrix, which are in conflict with each other when rectifying the inconsistent matrix. This study uses two pheromone matrices and two heuristic distances matrices to generate the ants tour. To see the performance, MOBAF is implemented to rectify on some inconsistent fuzzy preference matrices. As a result, in addition to being able to rectify the CR, the proposed algorithm also successfully generates some non-dominated solutions that can be considered as optimal solutions.
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Literature
1.
Bozóki S, Fülöp J, Rónyai L (2010) On optimal completion of incomplete pairwise comparison matrices. Math Comput Model 52(1):318–333MathSciNetCrossRefMATH
2.
Chaharsooghi SK, Kermani AM (2008) An intelligent multi-colony multi-objective ant colony optimization (aco) for the 0–1 knapsack problem. In: Evolutionary computation, 2008. CEC 2008. (IEEE World Congress on Computational Intelligence). IEEE Congress on IEEE, pp 1195–1202
3.
Chiclana F, Herrera F, Herrera-Viedma E (2001) Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations. Fuzzy Sets Syst 122(2):277–291MathSciNetCrossRefMATH
4.
Coello CAC, Lechuga MS (2002) MOPSO: a proposal for multiple objective particle swarm optimization. In: Proceeding of congress evolutionary computation (CEC), IEEE, vol 2, pp 1051–1056
5.
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRef
6.
Doerner K, Gutjahr WJ, Hartl RF, Strauss C, Stummer C (2004) Pareto ant colony optimization: a metaheuristic approach to multiobjective portfolio selection. Ann Oper Res 131(1–4):79–99MathSciNetCrossRefMATH
7.
Dorigo M, Gambardella LM (1997) Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evol Comput 1(1):53–66CrossRef
8.
Ergu D, Kou G, Peng Y, Shi Y (2011) A simple method to improve the consistency ratio of the pair-wise comparison matrix in ANP. Eur J Oper Res 213(1):246–259MathSciNetCrossRefMATH
9.
García-Martínez C, Cordón O, Herrera F (2007) A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria tsp. Eur J Oper Res 180(1):116–148CrossRefMATH
10.
Girsang AS, Tsai CW, Yang CS (2014) Ant colony optimization for reducing the consistency ratio in comparison matrix. In: International conference on advances in engineering and technology (ICAET), pp 577–582
11.
Girsang AS, Tsai CW, Yang CS (2015) Ant algorithm for modifying an inconsistent pairwise weighting matrix in an analytic hierarchy process. Neural Comput Appl 26(2):313–327CrossRef
12.
Herrera-Viedma E, Herrera F, Chiclana F, Luque M (2004) Some issues on consistency of fuzzy preference relations. Eur J Oper Res 154(1):98–109MathSciNetCrossRefMATH
13.
Iredi S, Merkle D, Middendorf M (2001) Bi-criterion optimization with multi colony ant algorithms. In: Coello CAC, Aguirre AH, Zitzler E (eds) Evolutionary multi-criterion optimization. Springer, New York, pp 359–372CrossRef
14.
Ke L, Zhang Q, Battiti R (2013) Moea/d-aco: a multiobjective evolutionary algorithm using decomposition and antcolony. IEEE T Cybern 43(6):1845–1859CrossRef
15.
Lin CC, Wang WC, Yu WD (2008) Improving AHP for construction with an adaptive AHP approach (A\(^{ 3}\)). Autom Constr 17(2):180–187MathSciNetCrossRef
16.
Liu X, Pan Y, Xu Y, Yu S (2012) Least square completion and inconsistency repair methods for additively consistent fuzzy preference relations. Fuzzy Sets Syst 198:1–19MathSciNetCrossRefMATH
17.
López-Ibáñez M, Stützle T (2010) Automatic configuration of multi-objective aco algorithms. In: Swarm intelligence, Springer, pp 95–106
18.
López-Ibáñez M, Stützle T (2010) The impact of design choices of multiobjective antcolony optimization algorithms on performance: an experimental study on the biobjective tsp. In: Proceedings of the 12th annual conference on genetic and evolutionary computation, ACM pp 71–78
19.
Ma J, Fan ZP, Jiang YP, Mao JY, Ma L (2006) A method for repairing the inconsistency of fuzzy preference relations. Fuzzy Sets Syst 157(1):20–33MathSciNetCrossRefMATH
20.
Ma W (1994) A practical approach to modify pair wise comparison matrices and two criteria of modificatory effectiveness. J Sci Syst Eng 4:37–58
21.
Mahfouf M, Chen MY, Linkens DA (2004) Adaptive weighted particle swarm optimisation for multi-objective optimal design of alloy steels. In: Parallel problem solving from nature-PPSN VIII, Springer, pp 762–771
22.
Mytakidis T, Vlachos A (2008) Maintenance scheduling by using the bi-criterion algorithm of preferential anti-pheromone. Leonardo J Sci 12(16):143–164
23.
24.
Pinto D, Barán B (2005) Solving multiobjective multicast routing problem with a new ant colony optimization approach. In: Proceedings of the 3rd international IFIP/ACM Latin American conference on networking, ACM, pp 11–19
25.
Saaty TL (1980) The analytic hierarchy process: planning, priority setting, resources allocation. McGraw-Hill, New YorkMATH
26.
Srinivas N, Deb K (1994) Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3):221–248CrossRef
27.
T’kindt V, Monmarché N, Tercinet F, Laügt D (2002) An ant colony optimization algorithm to solve a 2-machine bicriteria flowshop scheduling problem. Eur J Oper Res 142(2):250–257MathSciNetCrossRefMATH
28.
Wu Z, Xu J (2012) A consistency and consensus based decision support model for group decision making with multiplicative preference relations. Decis Support Syst 52(3):757–767CrossRef
29.
Xu Y, Da Q, Wang H (2011) A note on group decision-making procedure based on incomplete reciprocal relations. Soft Comput 15(7):1289–1300CrossRefMATH
30.
31.
Xu Y, Patnayakuni R, Wang H (2013) Logarithmic least squares method to priority for group decision making with incomplete fuzzy preference relations. Appl Math Model 37(4):2139–2152MathSciNetCrossRef
32.
Xu Y, Wang H (2013) Eigenvector method, consistency test and inconsistency repairing for an incomplete fuzzy preference relation. Appl Math Model 37(7):5171–5183MathSciNetCrossRef
33.
34.
Xu Z, Da Q (2003) An approach to improving consistency of fuzzy preference matrix. Fuzzy Optim Decis Mak 2(1):3–12MathSciNetCrossRef
35.
Yager RR (1982) Fuzzy set possibility theory recent developments, vol 1. Pergamon, New YorkMATH
36.
Yang I, Wang WC, Yang TI (2012) Automatic repair of inconsistent pairwise weighting matrices in analytic hierarchy process. Autom Constr 22:290–297CrossRef
37.
Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195CrossRef
Metadata
Title
Rectifying the Inconsistent Fuzzy Preference Matrix in AHP Using a Multi-Objective BicriterionAnt
Authors
Abba Suganda Girsang
Chun-Wei Tsai
Chu-Sing Yang
Publication date
01-10-2016
Publisher
Springer US
Published in
Neural Processing Letters / Issue 2/2016
Print ISSN: 1370-4621
Electronic ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-015-9474-x

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