Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

FUNDAMENTALS OF VAGUE GROUPS

  • OH, JU-MOK (Department of Mathematics, Kangnung-Wonju National University)
  • Received : 2021.06.02
  • Accepted : 2021.08.04
  • Published : 2021.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

Demirci ((1999) Vague groups. J. Math. Anal. Appl. 230, 142-156) introduced the concept of vague groups as one of uncertain reasoning structures where indistinguishable operators separate points. In this paper, we consider vague groups in which an indistinguishable operator does not need to separate points because it seems more appropriate to handle ambiguous situations. For our purposes we generalize or redefine some notions such as: vague closed subset, vague subgroup, vague kernel and vague injectiveness. Consequently we generalize most of the known results and obtain some new additional fundamental properties of vague groups, some of which are similar to ones of ordinary groups.

Keywords

Acknowledgement

This work was supported by the research grant of Gangneung-Wonju National University and the Research Institute of Natural Science of Gangneung-Wonju National Universty.

References

  1. R. Belohlavek, Fuzzy Relational Systems, Foundations and Principles, Kluwer Academic, Plenum Publishers, New York, 2002.
  2. M. Demirci, Vague groups, J. Math. Anal. Appl. 230 (1999), 142-156. https://doi.org/10.1006/jmaa.1998.6182
  3. M. Demirci and J. Recasens, Fuzzy groups, fuzzy functions and fuzzy equivalence relations, Fuzzy Sets and Systems 144 (2004), 441-458. https://doi.org/10.1016/S0165-0114(03)00301-4
  4. E.P. Klement, R. Mesiar and E. Pap, Triangular Norms, Springer, Dordrecht, 2000.
  5. J. Recasens, Indistinguishability operators, Springer-Verlag, Berlin, 2010.