Another look at inheritance of uniform continuity of 1-dimensional aggregation functions by their super-additive transformations

Document Type : Research Paper

Authors

1 Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Keman, Kerman, Iran

2 Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia

Abstract

In an earlier paper by Seliga, Siran and the second author (J. Mahani Math. Res. Center 8 (2019) 37–51) on lifting continuity properties of aggregation functions to their super- and sub-additive transformations it was shown that uniform continuity is preserved by super-additive transformations in dimension 1. We give a shorter and more direct proof of this result and of a related linear bound on uniformly continuous aggregation functions.

Keywords

References

[1] M. Grabisch, J. L. Marichal, R. Mesiar, E. Pap, Aggregation functions (Encyklopedia of mathematics and its applications), Cambridge University Press, 2009.
[2] S. Greco, R. Mesiar, F. Rindone, L. Sipeky, Superadditive and subadditive transformations of integrals and aggregation functions, Fuzzy Sets and Systems 291 (2016), 40{53.
[3] K. Hrinakova and A. Seliga, Remarks on super-additive and sub-additive transformations of aggregation functions, Tatra Mountains Math. Publ. 72 (2018), 55{66.
[4] F. Kouchakinejad, A. Siposova and J. Siran, Aggregation functions with given super-additive and sub-additive transformations, Intl. J. General Systems 46 (2017) 3, 225{234.
[5] R. Mesiar, A. Kolesarova and A. Stupnanova, Quo vadis aggregation? International Journal General Systems, 47 (2018), 1{21.
[6] R. L. Pouso, Uniform continuity on unbounded intervals, Int. J. Math. Educ. Sci. Tech. 39 (2008) 4, 551{557.
[7] A. Seliga, A. Siposova and J. Siran, Lifting continuity properties of aggregation functions to their super- and sub-additive transformations, Journal of Mahani Math. Res. Center 8 (2019) 37{51.
[8] A. Siposova, A note on the superadditive and the subadditive transformations of aggregation functions, Fuzzy Sets Syst. 299 (2016), 98{104.
Journal of Mahani Mathematical Research
Volume 11, Issue 3 - Serial Number 23
Special Issue dedicated to Prof. Mashaallah Mashinchi.
November 2022
Pages 191-195

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History

  • Receive Date: 20 April 2022
  • Revise Date: 29 June 2022
  • Accept Date: 24 August 2022

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