Abstract
This chapter is aimed on pairwise comparison matrices with fuzzy elements. Fuzzy elements of the pairwise comparison matrix are applied whenever the decision maker is not sure about the value of his/her evaluation of the relative importance of elements in question. We particularly deal with pairwise comparison matrices with fuzzy number elements and investigate some properties of such matrices. In comparison with pairwise comparison matrices with crisp elements investigated in the previous chapter, here we investigate pairwise comparison matrices with elements from alo-group over a real interval. In some sense, this chapter is a continuation of the second part of the previous chapter. Such an approach allows for a generalization dealing with additive, multiplicative and fuzzy pairwise comparison matrices with fuzzy elements. Moreover, we deal with the problem of measuring the inconsistency of fuzzy pairwise comparison matrices by defining corresponding inconsistency indexes. Numerical examples are presented to illustrate the concepts and derived properties.
The chapter was written by “Jaroslav Ramík”.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bozbura, F.T., Beskese, A.: Prioritization of organizational capital measurement indicators using fuzzy AHP. Int. J. Approx. Reason. 44(2), 124–147 (2007)
Bozoki, S., Rapcsak, T.: On Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices. WP 2007-1. http://www.oplab.sztaki.hu/WP_2007_1_Bozoki_Rapcsak.pdf (June 2007)
Buckley, J.J.: Fuzzy hierarchical analysis. Fuzzy Sets Syst. 17(1), 233–247 (1985) [ISSN 0165-0114]
Buckley, J.J., et al.: Fuzzy hierarchical analysis revisited. Eur. J. Oper. Res. 129, 48–64 (2001)
Buyukozkan, G.: Multi-criteria decision making for e-marketplace selection. Internet Res. 14(2), 139–154 (2004)
Dagdeviren, M., Yüksel, I.: Developing a fuzzy analytic hierarchy process (AHP) model for behavior-based safety management. Inf. Sci. 178, 1717–1723 (2008)
Kulak, O., Kahraman, C.: Fuzzy multi-attribute selection among transportation companies using axiomatic design and analytic hierarchy process. Inf. Sci. 170, 191–210 (2005)
Lee, K.L., Lin, S.C.: A fuzzy quantified SWOT procedure for environmental evaluation of an international distribution center. Inf. Sci. 178(2), 531–549 (2008)
Leung, L.C., Cao, D.: On consistency and ranking of alternatives in fuzzy AHP. Eur. J. Oper. Res. 124, 102–113 (2000) [ISSN 0377-2217]
Mahmoudzadeh, M., Bafandeh, A.R.: A new method for consistency test in fuzzy AHP. J. Intell. Fuzzy Syst. 25(2), 457–461 (2013)
Mikhailov, L.: Deriving priorities from fuzzy pairwise comparison judgments. Fuzzy Sets Syst. 134, 365–385 (2003)
Mikhailov, L.: A fuzzy approach to deriving priorities from interval pairwise comparison judgements. Eur. J. Oper. Res. 159, 687–704 (2004)
Mikhailov, L., Tsvetinov, P.: Evaluation of services using a fuzzy analytic hierarchy process. Appl. Soft Comput. 5, 23–33 (2004)
Ohnishi, S., Dubois, D., et al.: A fuzzy constraint based approach to the AHP. In: Uncertainty and Intelligent Information Systems, pp. 217–228. World Scientific, Singapore (2008)
Ramik, J., Korviny, P.: Inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean. Fuzzy Sets Syst. 161, 1604–1613 (2010) [ISSN 0165-0114]
Saaty, T.L.: Multicriteria Decision Making - The Analytical Hierarchy Process, vol. I. RWS Publications, Pittsburgh (1991)
Salo, A.A.: On fuzzy ratio comparison in hierarchical decision models. Fuzzy Sets Syst. 84, 21–32 (1996) [ISSN 0165-0114]
Van Laarhoven, P.J.M., Pedrycz, W.: A fuzzy extension of Saaty’s priority theory. Fuzzy Sets Syst. 11(4), 229–241 (1983) [ISSN: 0165-0114]
Vaidya, O.S., Kumar, S.: Analytic hierarchy process: An overview of applications. Eur. J. Oper. Res. 169(1), 1–29 (2006)
Xu, Z.S., Chen, J.: Some models for deriving the priority weights from interval fuzzy preference relations. Eur. J. Oper. Res. 184, 266–280 (2008)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Gavalec, M., Ramík, J., Zimmermann, K. (2015). Preference Matrices with Fuzzy Elements in Decision Making. In: Decision Making and Optimization. Lecture Notes in Economics and Mathematical Systems, vol 677. Springer, Cham. https://doi.org/10.1007/978-3-319-08323-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-08323-0_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08322-3
Online ISBN: 978-3-319-08323-0
eBook Packages: Business and EconomicsBusiness and Management (R0)