Abstract
The structure of ordinal sums of conjunctive and disjunctive functions is convenient for classification into the classes Yes, No and Maybe containing a tendency to the classes Yes and No. It especially holds when task is expressed by short vague requirements. The averaging part is covered by any averaging function. Concerning this part (class Maybe), functions having annihilator 0 usually are not suitable due to \(A(1,0)=A(0,1)=0\). The dual observation holds for functions having annihilator equal to 1. The classification by uninorms has reached to the same conclusion. This work proposes a parametric class of quasi–arithmetic means with the convex combination of the geometric mean and its dual geometric mean. Regarding classification into classes Yes and No, the parametrized family of nilpotent t–norms and t–conorms is proposed. This consideration creates the frame for learning function’s parameter from the user inputs and labelled data. This research activity also contributes to the field of explainable computational intelligence. The results are supported by illustrative example. Finally, the discussion and the future research activities conclude the paper.
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Acknowledgments
This paper was partially supported by SGS project No. SP2022/113 of the Ministry of Education, Youth and Sports of the Czech Republic. Also the supports of the projects APVV-18-0052, KEGA No. 025EU-4/2021 and VEGA No. 1/0466/19 of the Ministry of Education, Science, Research and Sport of the Slovak Republic are kindly announced.
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Hudec, M., Mináriková, E., Mesiar, R. (2022). Aggregation Functions in Flexible Classification by Ordinal Sums. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1601. Springer, Cham. https://doi.org/10.1007/978-3-031-08971-8_31
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