This paper deals with the calculation of a vector of reliable weights of decision
alternatives on the basis of interval pairwise comparison judgments of experts.
These weights are used to construct the ranking of decision alternatives and to
solve selection problems, problems of ratings construction, resources allocation
problems, scenarios evaluation problems, and other decision making problems. A
comparative analysis of several popular models, which calculate interval
weights on the basis of interval pairwise comparison matrices (IPCMs), was
performed. The features of these models when they are applied to IPCMs with
different inconsistency levels were identified. An algorithm is proposed which
contains the stages for analyzing and increasing the IPCM inconsistency,
calculating normalized interval weights, and calculating the ranking of
decision alternatives on the basis of the resulting interval weights. It was
found that the property of weak order preservation usually allowed identifying
order-related intransitive expert pairwise comparison judgments. The correction
of these elements leads to the removal of contradictions in resulting weights
and increases the accuracy and reliability of results.
References
[1]
Pankratova, N.D. and Nedashkovskaya, N.I. (2010) Models and Methods of Analysis of Hierarchies. Theory and Applications. Kiev. (In Ukrainian)
[2]
Mikhailov, L. (2003) Deriving Priorities from Fuzzy Pairwise Comparison Judgements. Fuzzy Sets and Systems, 134, 365-385. http://dx.doi.org/10.1016/S0165-0114(02)00383-4
[3]
Wang, Y.M. and Elhag, T.M.S. (2007) A Goal Programming Method for Obtaining Interval Weights from an Interval Comparison Matrix. European Journal of Operational Research, 177, 458-471. http://dx.doi.org/10.1016/j.ejor.2005.10.066
[4]
Wang, Y.M. and Chin, K.S. (2008) A Linear Goal Programming Priority Method for Fuzzy Analytic Hierarchy Process and Its Applications in New Product Screening. International Journal of Approximate Reasoning, 49, 451-465. http://dx.doi.org/10.1016/j.ijar.2008.04.004
[5]
Sugihara, K., Ishii, H. and Tanaka, H. (2004) Interval Priorities in AHP by Interval Regression Analysis. European Journal of Operational Research, 158, 745-754. http://dx.doi.org/10.1016/S0377-2217(03)00418-1
[6]
Wang, Y.-M., Luo, Y. and Hua, Z. (2008) On the Extent Analysis Method for Fuzzy AHP and Its Applications. European Journal of Operational Research, 186, 735-747. http://dx.doi.org/10.1016/j.ejor.2007.01.050
[7]
Wang, Y.M., Yang, J.B. and Xu, D.L. (2005) A Two-Stage Logarithmic Goal Programming Method for Generating Weights from Interval Comparison Matrices. Fuzzy Sets and Systems, 152, 475-498. http://dx.doi.org/10.1016/j.fss.2004.10.020
[8]
Chandran, B., Golden, B. and Wasil, E. (2005) Linear Programming Models for Estimating Weights in the Analytic Hierarchy Process. Computers & Operations Research, 32, 2235-2254. http://dx.doi.org/10.1016/j.cor.2004.02.010
[9]
Chang, D.Y. (1996) Applications of the Extent Analysis Method on Fuzzy AHP. European Journal of Operational Research, 95, 649-655. http://dx.doi.org/10.1016/0377-2217(95)00300-2
[10]
Saaty, T.L. and Vargas, L.G. (2006) Decision Making with the Analytic Network Process: Economic, Political, Social and Technological Applications with Benefits, Opportunities, Costs and Risks. Springer, New York.
[11]
Pankratova, N.D. and Nedashkovskaya, N.I. (2016) Estimation of Consistency of Fuzzy Pairwise Comparison Matrices Using a Defuzzification Method. In: Zgurovsky, M.Z. and Sadovnihiy, V.A., Eds., Springer, 161-172.
[12]
Nedashkovskaya, N.I. (2013) Method of Consistent Pairwise Comparisons When Estimating Decision Alternatives in Terms of Qualitative Criterion. System Research and Information Technologies, 4, 67-79. (In Ukrainian) http://journal.iasa.kpi.ua/article/view/33943
[13]
Pankratova, N. and Nedashkovskaya, N. (2015) Methods of Evaluation and Improvement of Consistency of Expert Pairwise Comparison Judgements. International Journal of Information Theories and Applications, 22, 203-223. http://www.foibg.com/ijita/vol22/ijita22-03-p01.pdf
[14]
Nedashkovskaya, N.I. (2015) The М_Outflow Method for Finding the Most Inconsistent Elements of a Pairwise Comparison Matrix. System Analysis and Information Technologies: Materials of International Scientific and Technical Conference SAIT, Kyiv, 22-25 June 2015, 95. (In Russian) http://sait.kpi.ua/books/
[15]
Pankratova, N.D. and Nedashkovskaya, N.I. (2013) The Method of Estimating the Consistency of Paired Comparisons. International Journal of Information Technologies and Knowledge, 7, 347-361. http://www.foibg.com/ijitk/ijitk-vol07/ijitk07-04-p05.pdf
[16]
Chen, S.J. and Hwang, C.L. (1992) Fuzzy Multiple Attribute Decision Making: Methods and Applications. Springer, New York. http://dx.doi.org/10.1007/978-3-642-46768-4
[17]
Ishibuchi, H. and Tanaka, H. (1990) Multiobjective Programming in Optimization of the Interval Objective Function. European Journal of Operational Research, 48, 219-225. http://dx.doi.org/10.1016/0377-2217(90)90375-L
[18]
Sengupta, A. and Pal, T.K. (2000) On Comparing Interval Numbers. European Journal of Operational Research, 127, 28-43. http://dx.doi.org/10.1016/S0377-2217(99)00319-7
[19]
Xu, Z.S. and Da, Q.L. (2002) The Uncertain OWA Operator. International Journal of Intelligent Systems, 17, 569-575. http://dx.doi.org/10.1002/int.10038
[20]
Xu, Z. and Chen, J. (2008) Some Models for Deriving the Priority Weights from Interval Fuzzy Preference Relations. European Journal of Operational Research, 184, 266-280. http://dx.doi.org/10.1016/j.ejor.2006.11.011
[21]
Wang, Z.-J. and Li, K.W. (2012) Goal Programming Approaches to Deriving Interval Weights Based on Interval Fuzzy Preference Relations. Information Sciences, 193, 180-198. http://dx.doi.org/10.1016/j.ins.2012.01.019
[22]
Wang, Y.-M. and Elhag, T.M.S. (2006) On the Normalization of Interval and Fuzzy Weights. Fuzzy Sets and Systems, 157, 2456-2471. http://dx.doi.org/10.1016/j.fss.2006.06.008
[23]
Nedashkovskaya, N. (2015) Pairwise Comparison Models on the Basis of Interval Expert Judgments. Questions of Applied Mathematics and Mathematical Modeling, 15, 121-137. (In Russian)
