Abstract
In this study, we propose an approach to derive a group assessment of an item as its weight vector on multiple viewpoints. When there are a group of decision makers who give the judgments of the item as comparison matrices on the viewpoints, it is reasonable that the weight vector of the item is the core of those by all the decision makers. Each decision maker’s weight vector basically includes his/her given comparison matrix, which represents only a part of his/her thinking. Namely, there is an inclusion relation between a comparison and a ratio of the corresponding weights. In addition, there are items other than the target one. A decision maker gives the comparison matrices of some of the other items if s/he knows them, as well as the target one. It is natural that there is a correlation between the judgment of the target item to those of the others. The correlation is taken into consideration from the aspect of consistency of his/her judgments. We define a fuzzy degree of the consistency with all the comparison matrices s/he gives. As the consistency degree for a comparison matrix increases, it may become unable to satisfy the inclusion relation between the comparison matrix and the weight vector. Hence, we introduce a fuzzy degree of inclusion relation in order to relax it. There is a trade-off between them. Therefore, by maximizing both degrees we obtain the weight vector of the target item from the comparison matrices of the target item considering the consistency of each decision maker’s judgments. The proposed approach is applicable even in the case that a group of given comparison matrices is incomplete such that some comparisons in a comparison matrix are missing and/or the comparison matrices of some items are missing.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Haker, P.T.: Incomplete pairwise comparisons in the analytic hierarchy process. Math. Model. 9(11), 837–848 (1987)
Bozóki, S., Fülöp, J.: Efficient weight vectors from pairwise comparison matrices. Eur. J. Oper. Res. 264(2), 419–427 (2018)
Saaty, T.L.: The Analytic Hierarchy Process. McGraw-Hill, New York (1980)
Jensen, R.E.: An alternative scaling method for priorities in hierarchical structures. J. Math. Psychol. 28(3), 317–332 (1984)
Saaty, T.L., Vargas, L.G.: Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios. Math. Model. 5(5), 309–324 (1984)
Ishizaka, A., Siraj, S.: Are multi-criteria decision-making tools useful? An experimental comparative study of three methods. Eur. J. Oper. Res. 264(2), 462–471 (2018)
Sugihara, K., Tanaka, H.: Interval evaluations in the analytic hierarchy process by possibilistic analysis. Comput. Intell. 17(3), 567–579 (2001)
Entani, T., Sugihara, K.: Uncertainty index based interval assignment by interval AHP. Eur. J. of Oper. Res. 219(2), 379–385 (2012)
Inuiguchi, M., Innan, S.: Improving interval weight estimations in interval AHP by relaxations. J. Adv. Comput. Intell. Intell. Inform. 21, 1135–1143 (2017)
Jalao, E.R., Wu, T., Shunk, D.: An intelligent decomposition of pairwise comparison matrices for large-scale decisions. Eur. J. Oper. Res. 238(1), 270–280 (2014)
Brunelli, M., Fedrizzi, M.: Axiomatic properties of inconsistency indices for pairwise comparisons. J. Oper. Res. Soc. 66, 1–15 (2015)
Ramík, J., Korviny, P.: Inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean. Fuzzy Sets Syst. 161(11), 1604–1613 (2010)
Kubler, S., Derigent, W., Voisin, A., Robert, J., Traon, Y.L., Viedma, E.H.: Measuring inconsistency and deriving priorities from fuzzy pairwise comparison matrices using the knowledge-based consistency index. Knowl.-Based Syst. 162, 147–160 (2018). Special Issue on Intelligent Decision-Making and Consensus Under Uncertainty in Inconsistent and Dynamic Environments
Siraj, S., Mikhailov, L., Keane, J.A.: Contribution of individual judgments toward inconsistency in pairwise comparisons. Eur. J. Oper. Res. 242(2), 557–567 (2015)
Fedrizzi, M., Giove, S.: Incomplete pairwise comparison and consistency optimization. Eur. J. Oper. Res. 183(1), 303–313 (2007)
Forman, E., Peniwati, K.: Aggregating individual judgments and priorities with the Analytic hierarchy process. Eur. J. Oper. Res. 108(1), 165–169 (1998)
Wan, S., Wang, F., Dong, J.: Additive consistent interval-valued atanassov intuitionistic fuzzy preference relation and likelihood comparison algorithm based group decision making. Eur. J. Oper. Res. 263(2), 571–582 (2017)
Wan, S., Wang, F., Dong, J.: A group decision making method with interval valued fuzzy preference relations based on the geometric consistency. Inf. Fusion 40, 87–100 (2018)
Brunelli, M., Fedrizzi, M.: Boundary properties of the inconsistency of pairwise comparisons in group decisionsy. Eur. J. Oper. Res. 240, 765–773 (2015)
Entani, T., Inuiguchi, M.: Pairwise comparison based interval analysis for group decision aiding with multiple criteria. Fuzzy Sets Syst. 274(1), 79–96 (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Entani, T. (2019). Group Assessment of Comparable Items from the Incomplete Judgments. In: Kearfott, R., Batyrshin, I., Reformat, M., Ceberio, M., Kreinovich, V. (eds) Fuzzy Techniques: Theory and Applications. IFSA/NAFIPS 2019 2019. Advances in Intelligent Systems and Computing, vol 1000. Springer, Cham. https://doi.org/10.1007/978-3-030-21920-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-21920-8_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21919-2
Online ISBN: 978-3-030-21920-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)