| Title of paper:
|
On the degree of intuitionistic fuzzy functions and its various classification degrees
|
| Author(s):
|
Ümit Deniz  0000-0002-9248-2769
|
| Department of Mathematics, Faculty of Art and Science, Recep Tayyip Erdoğan University, Rıze, Türkiye
|
| umit.deniz@erdogan.edu.tr
|
| Neslihan Yılmaz 0009-0002-9436-1431
|
| Department of Mathematics, Faculty of Art and Science, Recep Tayyip Erdoğan University, Rıze, Türkiye
|
| neslihan-yilmaz22@erdogan.edu.tr
|
|
| Published in:
|
Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 3, pages 320–331
|
| DOI:
|
https://doi.org/10.7546/nifs.2025.31.3.320-331
|
| Download:
|
 PDF (294 Kb, File info)
|
| Abstract:
|
In this paper, we explore the concept of degree of the intuitionistic fuzzy functions. In [4], Demirci studied gradations of fuzzy functionhood. There, for a fuzzy relation [math]\displaystyle{ f }[/math] on [math]\displaystyle{ X~\times~Y, }[/math] considering the fuzzy equalities [math]\displaystyle{ E_{X} }[/math] on [math]\displaystyle{ X }[/math] and [math]\displaystyle{ E_{Y} }[/math] on [math]\displaystyle{ Y }[/math] the degree of [math]\displaystyle{ f }[/math] of being a fuzzy fuction, being surjective, being injective and being bijective is defined. We extend this study to intuitionistic fuzzy functions. In this paper, we use intuitionistic fuzzy functions and their types defined by Lim, Choi and Hur [7] by using intuitionistic fuzzy equalities. Since an intuitionistic fuzzy function is a [math]\displaystyle{ (\mu_{A}(x,y),\nu_{A}(x,y)) }[/math] ordered pair, we define its degree of being [math]\displaystyle{ (\alpha) }[/math] and the degree of non-being [math]\displaystyle{ (\beta) }[/math] by using [math]\displaystyle{ (\alpha,\beta)\in L_{*}. }[/math] For an intuitionistic fuzzy relation [math]\displaystyle{ f }[/math] from [math]\displaystyle{ X \times Y }[/math] to [math]\displaystyle{ I^{2}, }[/math] considering the intuitionistic fuzzy equalities [math]\displaystyle{ E_{X} }[/math] on [math]\displaystyle{ X }[/math] and [math]\displaystyle{ E_{Y} }[/math] on [math]\displaystyle{ Y, }[/math] we define the degree to which [math]\displaystyle{ f }[/math] is an intuitionistic fuzzy function, the degree of it being surjective, injective and bijective, respectively. We especially analyze the degrees of some types of intuitionistic fuzzy functions. We prove some theorems using these definitions.
|
| Keywords:
|
Intuitionistic fuzzy equality, Intuitionistic fuzzy function, Gradation of intuitionistic fuzzy functions.
|
| AMS Classification:
|
03E72, 20N25, 08A72.
|
| References:
|
- Atanassov, K. T. (1983). Intuitionistic fuzzy sets. VII ITKR’s Session, Sofia, 20-23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: International Journal Bioautomation, 2016, 20(S1), S1–S6.
- Bustince, H., & Burillo, P. (1996). Structure on intuitionistic fuzzy relations. Fuzzy Sets and Systems, 78, 293–303.
- Demirci, M. (1999). Fuzzy functions and their fundamental properties. Fuzzy Sets and Systems, 106(2), 239–246.
- Demirci, M. (2001). Gradation of being fuzzy function. Fuzzy Sets and Systems, 119(3), 383–392.
- Kang, H. W., Lee, J.-G., & Hur, K. (2012). Intuitionistic fuzzy mapping and intuitionistic fuzzy equivalence relations. Annals of Fuzzy Mathematics and Informatics, 3(1), 61–87.
- Li, X.-P., & Wang, G.-J. (2011). (λ, α)-Homomorphisms of intuitionistic fuzzy groups. Hacettepe Journal of Mathematics and Statistics, 40(5), 663–672.
- Lim, P. K., Choi, G. H., & Hur, K. (2011). Fuzzy mappings and fuzzy equivalence relations. International Journal of Fuzzy Logic and Intelligent Systems, 11(3), 153–164.
- Rosenfeld, A. (1971). Fuzzy groups. Journal of Mathematical Analysis and Applications, 35(3), 512–517.
- Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.
|
| Citations:
|
The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.
|
|
