Pythagorean Fuzzy \((l,u)\)-Level Cuts and Their Applications to Fuzzy Normed Subrings

Authors

  • Amal Kumar Adak Department of Mathematics, Ganesh Dutt College (affiliated to Lalit Narayan Mithila University), Begusarai 851101, Bihar, India https://orcid.org/0000-0002-3644-782X
  • Gauri Kant Kumar Department of Mathematics, Lalit Narayan Mithila University, Darbhanga 846008, Bihar, India https://orcid.org/0009-0004-8915-8927

DOI:

https://doi.org/10.26713/cma.v16i3.3371

Keywords:

Intuitionistic fuzzy set, Pythagorean fuzzy set, t-norm, s-norm, (l,u)-level sets, Pythagorean fuzzy normed subring

Abstract

When attempting to quantify an ill-quantity, the Pythagorean Fuzzy Set (PFS) notion is essential. This study provides a \((l,u)\)-level cut of Pythagorean Fuzzy Sets (PFSs). We define \((l,u)\)-level cuts of a PFS \((P)\) as crisp sets consisting of elements \((x)\) for which the membership value is greater than \((l)\) and non-membership value is less than \((u)\). The concept of Pythagorean fuzzy normed subring is introduced and its properties are investigated. Additionally, the relationship between PFNSRs and Pythagorean fuzzy \((l,u)\)-level sets is analyzed.

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Published

30-10-2025
CITATION

How to Cite

Adak, A. K., & Kumar, G. K. (2025). Pythagorean Fuzzy \((l,u)\)-Level Cuts and Their Applications to Fuzzy Normed Subrings. Communications in Mathematics and Applications, 16(3), 703–716. https://doi.org/10.26713/cma.v16i3.3371

Issue

Vol. 16 No. 3 (2025)

Section

Research Article

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