Aggregation and related functions in fuzzy set theory: dualities and monotonicity-based generalizations

• Autorzy: Mesiar R. , Kolesarova A.

Identyfikatory

DOI

10.14313/JAMRIS_3-2017/29

• Języki publikacji: EN

Abstrakty

EN

We discuss several extensions of binary Boolean functions acting on the domain [0, 1]. Formally, there are 16 disjoint classes of such functions, covering a majority of binary functions considered in fuzzy set theory. We introduce and discuss dualities in this framework, stressing the links between different subclasses of considered functions, e.g., the link between conjunctive and implication functions. Special classes of considered functions are characterized, among others, by particular kinds of monotonicity. Relaxing these constraints by considering monotonicity in one direction only, we generalize standard classes of aggregation functions, implications, semicopulas, etc., into larger classes called pre-aggregations, pre-implications, pre-semicopulas, etc. Note that the dualities discussed for the standard classes also relate the new extended classes of pre-functions.

Słowa kluczowe

EN

aggregation function; conjuctor; directional monotonicity; disjunctor; duality; implication function; pre-aggregation function; pre-implication function

• Wydawca: Łukasiewicz Industrial Research Institute for Automation and Measurements PIAP
• Czasopismo: Journal of Automation Mobile Robotics and Intelligent Systems
• Rocznik: 2017
• Tom: Vol. 11, No. 3
• Strony: 58--61
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Mesiar R.

• Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, Slovakia

autor

Kolesarova A.

• Faculty of Chemical and Food Technology, Slovak University of Technology, Radlinského 9, 812 37 Bratislava, Slovakia

Bibliografia

• [1] Bustince, H., Fernandez, J., Kolesárová , A., Mesiar,R., ”Directional monotonicity of fusion functions”, European Journal of Operational Research, vol. 244, 2015, no. 1, 300–308. DOI:10.1016/j.ejor.2015.01.018.
• [2] Bustince, H., Pagola, M., Mesiar, R., Hüllermeier, E., Herrera, F., ”Grouping, Overlap, and Generalized Bientropic Functions for Fuzzy Modeling of Pairwise Comparisons”, IEEE Transactions on Fuzzy Systems, vol. 20, 2012, no.3, 405–415. DOI:10.1109/TFUZZ.2011.2173581.
• [3] Bustince, H., Fernandez, J., Mesiar, R., Montero, J., Orduna, R., ”Overlap functions. Nonlinear Analysis: Theory”, Methods and Applications, vol. 72, 2010, no. 3–4, 1488–1499. DOI:10.1016/j.na.2009.08.033.
• [4] Dimuro, G.P., Bustince, H., Fernandez, J., Mesiar,R., Bedregal, B., ”New Results on Pre-aggregation Functions: introducing (light) pre-t-norms”. In: IFSA-SCIS 2017, Otsu, 2017.
• [5] Durante, F. Sempi, C., ”Semicopulæ”, Kybernetika ,vol. 41, 2005, no.3, 315–328.
• [6] Genest C., Molina L., Lallena, L., Sempi C., ”A characterization of quasi-copulas”, J. Multivariate Anal., no. 69, 1999, 1193–1205. DOI:10.1006/jmva.1998.1809.
• [7] Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E., Aggregation Functions: Encyclopedia of Mathematics, Cambridge University Press 2009.
• [8] Mesiar, R., Kolesárová , A., Bustince, H., Fernandez, J., Dualities in the class of extended Boolean functions. ”Fuzzy Sets and Systems”, in press. Available online 20 April 2017. DOI:10.1016/j.fss.2017.04.008.
• [9] Lucca, G., Sanz, J. A., Pereira-Dimuro, G., Bedregal,B., Mesiar, R., Kolesárová , A., Bustince, H., ”Pre-aggregation functions: construction and an application”, IEEE Trans. on Fuzzy Systems, vol. 24, 2016, no.2, 260-–272. DOI:10.1109/TFUZZ.2015.2453020.
• [10] Pradera, A., Beliakov, G., Bustince, H., De Baets,B., ”A review of the relationships between implication, negation and aggregation functions from the point of view of material implication”, Information Sciences, no. 329, 2016, 357–380. DOI:10.1016/j.ins.2015.09.033.
• [11] Zadeh, L. A., ”Fuzzy Sets”, Information and Control”, 1965,no. 8, 338–358.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).