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Issue:T-Lower level set and t-upper level set of an intuitionistic fuzzy set

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Title of paper: t-Lower level set and t-upper level set of an intuitionistic fuzzy set
Author(s):
Ümit Deniz
Department of Mathematics, Faculty of Art and Science, Recep Tayyip Erdogan University, Rize, Türkiye
umit.deniz@erdogan.edu.tr
Presented at: 8th IFS and Contemporary Mathematics (IFSCOM) Conference, 16–19 June 2022, Türkiye
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 28 (2022), Number 4, pages 375–380
DOI: https://doi.org/10.7546/nifs.2022.28.4.375-380
Download:  PDF (157  Kb, File info)
Abstract: In this paper we give the definitions of t-lower level set (Lt(A)) and t-upper level set (Ut(A)) of an Intuitionistic fuzzy set. [1] A t-lower level set is defined by giving a lower boundary on μA(x) + νA(x). A t-upper level set is defined by giving an upper boundary on μA(x) + νA(x). If A is an Intuitionistic fuzzy set of X, then Lt(A) and Ut(A) are subsets of X. In this paper we give some theorems by using t-lower level sets and t-upper level sets and prove them.
Keywords: Intuitionistic fuzzy sets, t-lower level sets, t-upper level sets, Cut of intuitionistic fuzzy set.
AMS Classification: 03F55, 03G25, 13C05, 13C13, 13A15.
References:
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  2. Çuvalcıoğlu, G. (2014). Some properties of controlled set theory. Notes on Intuitionistic Fuzzy Sets, 20(2), 37–42, (2014).
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  4. Rosenfeld, A. (1971). Fuzzy groups. Journal of Mathematical Analysis and Application, 35, 512–517.
  5. Sharma, P. K. (2011). (α, β)-Cut of intuitionistic fuzzy groups. International Mathematical Forum, 6(53), 2605–2614.
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