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2018 | OriginalPaper | Chapter

Strengthened Ordered Directional and Other Generalizations of Monotonicity for Aggregation Functions

Authors : Mikel Sesma-Sara, Laura De Miguel, Julio Lafuente, Edurne Barrenechea, Radko Mesiar, Humberto Bustince

Published in: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations

Publisher: Springer International Publishing

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Abstract

A tendency in the theory of aggregation functions is the generalization of the monotonicity condition. In this work, we examine the latest developments in terms of different generalizations. In particular, we discuss strengthened ordered directional monotonicity, its relation to other types of monotonicity, such as directional and ordered directional monotonicity and the main properties of the class of functions that are strengthened ordered directionally monotone. We also study some construction methods for such functions and provide a characterization of usual monotonicity in terms of these notions of monotonicity.

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previous chapter Penalty-Based Functions Defined by Pre-aggregation Functions

next chapter A Study of Different Families of Fusion Functions for Combining Classifiers in the One-vs-One Strategy

Beliakov, G., Calvo, T., Wilkin, T.: Three types of monotonicity of averaging functions. Knowl.-Based Syst. 72, 114–122 (2014). https://doi.org/10.1016/j.knosys.2014.08.028CrossRef

Beliakov, G., Špirková, J.: Weak monotonicity of Lehmer and Gini means. Fuzzy Sets Syst. 299, 26–40 (2016). https://doi.org/10.1016/j.fss.2015.11.006MathSciNetCrossRefMATH

Bullen, P.S.: Handbook of Means and Their Inequalities, vol. 560. Springer, Dordrecht (2013). https://doi.org/10.1007/978-94-017-0399-4CrossRefMATH

Bustince, H., Barrenechea, E., Sesma-Sara, M., Lafuente, J., Dimuro, G.P., Mesiar, R., Kolesárová, A.: Ordered directionally monotone functions. Justification and application. IEEE Trans. Fuzzy Syst. (in press). https://doi.org/10.1109/TFUZZ.2017.2769486

Bustince, H., Fernandez, J., Kolesárová, A., Mesiar, R.: Directional monotonicity of fusion functions. Eur. J. Oper. Res. 244(1), 300–308 (2015). https://doi.org/10.1016/j.ejor.2015.01.018MathSciNetCrossRefMATH

Calvo, T., Kolesárová, A., Komornıková, M., Mesiar, R.: A Review of Aggregation Operators. Servicio de Publicaciones de la UAH, Madrid (2001)

Choquet, G.: Theory of capacities. Ann. de l’institut Fourier 5, 131–295 (1954). https://doi.org/10.5802/aif.53MathSciNetCrossRefMATH

De Miguel, L., Sesma-Sara, M., Elkano, M., Asiain, M., Bustince, H.: An algorithm for group decision making using n-dimensional fuzzy sets, admissible orders and OWA operators. Inf. Fusion 37, 126–131 (2017). https://doi.org/10.1016/j.inffus.2017.01.007CrossRef

García-Lapresta, J., Martínez-Panero, M.: Positional voting rules generated by aggregation functions and the role of duplication. Int. J. Intell. Syst. 32(9), 926–946 (2017). https://doi.org/10.1002/int.21877CrossRef

10.

Klir, G., Folger, T.: Fuzzy Sets, Uncertainty, and Information. Prentice Hall, Upper Saddle River (1988)MATH

11.

Lucca, G., Sanz, J., Dimuro, G., Bedregal, B., Asiain, M.J., Elkano, M., Bustince, H.: CC-integrals: choquet-like copula-based aggregation functions and its application in fuzzy rule-based classification systems. Knowl.-Based Syst. 119, 32–43 (2017). https://doi.org/10.1016/j.knosys.2016.12.004CrossRef

12.

Menger, K.: Statistical metrics. Proc. Nat. Acad. Sci. 28(12), 535–537 (1942)MathSciNetCrossRef

13.

Mesiar, R., Kolesárová, A., Stupňanová, A.: Quo vadis aggregation? Int. J. Gen Syst 47(2), 97–117 (2018). https://doi.org/10.1080/03081079.2017.1402893MathSciNetCrossRef

14.

Paternain, D., Fernandez, J., Bustince, H., Mesiar, R., Beliakov, G.: Construction of image reduction operators using averaging aggregation functions. Fuzzy Sets Syst. 261, 87–111 (2015). https://doi.org/10.1016/j.fss.2014.03.008MathSciNetCrossRefMATH

15.

Sesma-Sara, M., Bustince, H., Barrenechea, E., Lafuente, J., Kolsesárová, A., Mesiar, R.: Edge detection based on ordered directionally monotone functions. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K.T., Krawczak, M. (eds.) IWIFSGN/EUSFLAT -2017. AISC, vol. 643, pp. 301–307. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-66827-7_27CrossRef

16.

Sesma-Sara, M., Lafuente, J., Roldán, A., Mesiar, R., Bustince, H.: Strengthened ordered directionally monotone functions. Links between the different notions of monotonicity. Fuzzy Sets and Systems (submitted for publication)

17.

Sklar, A.: Fonctions de répartition à n dimensions et leurs marges (1959)

18.

Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010). https://doi.org/10.1002/int.20418CrossRefMATH

19.

Wilkin, T., Beliakov, G.: Weakly monotonic averaging functions. Int. J. Intell. Syst. 30(2), 144–169 (2015). https://doi.org/10.1002/int.21692CrossRef

20.

Yager, R.: On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988). https://doi.org/10.1109/21.87068MathSciNetCrossRefMATH

Title: Strengthened Ordered Directional and Other Generalizations of Monotonicity for Aggregation Functions
Authors: Mikel Sesma-Sara
Laura De Miguel
Julio Lafuente
Edurne Barrenechea
Radko Mesiar
Humberto Bustince
Publisher: Springer International Publishing
Book: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations
Print ISBN: 978-3-319-91475-6

Electronic ISBN: 978-3-319-91476-3

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-91476-3_35

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