Abstract
In this chapter we present the results connected with multicriteria (or similarly multiagent) decision making problems under uncertainty. The aspects of decision making form a wide branch of considerations both in fuzzy sets theory and its extensions (cf. [1,2,3]). We consider only some of the basic concepts for the case of interval-valued fuzzy relations. Here, there is examined preservation of transitivity properties by aggregation operators. Similar considerations may be performed for the remaining properties. We concentrate on transitivity as an exemplary property since this is one of the most important properties which may guarantee consistency of choices of decision makers. Namely, following crisp notion of transitivity we see that if x is preferred to y and y is preferred to z, mathematically R(x, y) and R(y, z), then x should be preferred to z, in mathematical notions it means that R(x, z) holds. This is intuitive and natural assumption. We provide the results connected with the notions of pos-B-transitivity, nec-B-transitivity and preservation of these properties by aggregation operators in decision making. We propose to apply the respective notion of transitivity and aggregation method, depending on the requirements of the given problem. Namely, if for a given problem we require that at least one element in the first interval is smaller or equal to at least one element in the second interval, then the notions related to \(\preceq _{\pi }\) would be suitable (pos-B-transitivity, pos-aggregation function). If for a given problem we require that each element in the first interval is smaller or equal to each element in the second interval, then the notions related to \(\preceq _{\nu }\) would be suitable (nec-B-transitivity, nec-aggregation function). We think that such approach may lead to the more meaningful results and better choice of the solution alternatives (however, please note that the mentioned classes of aggregation operators are not disjoint, cf. Corollary 2.2 and Theorem 2.9).
The speed of decision making is the essence of good governance.
Piyush Goyal
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Kacprzyk, J.: Group decision making with a fuzzy linguistic majority. Fuzzy Sets Syst. 18(2), 105–118 (1986)
Szmidt, E., Kacprzyk, J.: Using intuitionistic fuzzy sets in group decision making. Control. Cybern. 78, 183–195 (1996)
Szmidt, E., Kacprzyk, J.: A new approach to ranking alternatives expressed via intuitionistic fuzzy sets. In: Ruan, D., et al. (eds.) Computational Intelligence in Decision and Control, pp. 265–270. World Scientific, Singapore (2008)
Bentkowska, U.: New types of aggregation functions for interval-valued fuzzy setting and preservation of pos-B and nec-B-transitivity in decision making problems. Inf. Sci. 424, 385–399 (2018)
Bentkowska, U., Pȩkala, B., Bustince, H., Fernandez, J., Jurio, A., Balicki, J.: N-reciprocity property for interval-valued fuzzy relations with an application to group decision making problems in social networks. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 25(Suppl. 1), 43–72 (2017)
Xu, Z.: On compatibility of interval fuzzy preference relations. Fuzzy Optim. Decis. Mak. 3, 217–225 (2004)
Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)
Montero, J., Tejada, J., Cutello, C.: A general model for deriving preference structures from data. Eur. J. Oper. Res. 98, 98–110 (1997)
Bilgiç, T.: Interval-valued preference structures. Eur. J. Oper. Res. 105, 162–183 (1998)
Barrenechea, E., Fernandez, J., Pagola, M., Chiclana, F., Bustince, H.: Construction of interval-valued fuzzy preference relations from ignorance functions and fuzzy preference relations: application to decision making. Knowl. Based Syst. 58, 33–44 (2014)
Pȩkala, B.: Uncertainty Data in Interval-Valued Fuzzy Set Theory. Properties, Algorithms and Applications. Studies in fuzziness and soft computing. Springer, Cham (2019)
Bentkowska, U., Bustince, H., Jurio, A., Pagola, M., Pȩkala, B.: Decision making with an interval-valued fuzzy preference relation and admissible orders. Appl. Soft Comput. 35, 792–801 (2015)
Orlovsky, S.A.: Decision-making with a fuzzy preference relation. Fuzzy Sets Syst. 1(3), 155–167 (1978)
Hüllermeier, E., Brinker, K.: Learning valued preference structures for solving classification problems. Fuzzy Sets Syst. 159, 2337–2352 (2008)
Hüllermeier, E., Vanderlooy, S.: Combining predictions in pairwise classification: an optimal adaptive voting strategy and its relation to weighted voting. Pattern Recognit. 43(1), 128–142 (2010)
Bustince, H., Galar, M., Bedregal, B., Kolesárová, A., Mesiar, R.: A new approach to interval-valued Choquet integrals and the problem of ordering in interval-valued fuzzy sets applications. IEEE Trans. Fuzzy Syst. 21(6), 1150–1162 (2013)
Dubois, D.: The role of fuzzy sets in decision sciences: old techniques and new directions. Fuzzy Sets Syst. 184, 3–28 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Bentkowska, U. (2020). Decision Making Using Interval-Valued Aggregation. In: Interval-Valued Methods in Classifications and Decisions. Studies in Fuzziness and Soft Computing, vol 378. Springer, Cham. https://doi.org/10.1007/978-3-030-12927-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-12927-9_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-12926-2
Online ISBN: 978-3-030-12927-9
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)