Issue:On intuitionistic fuzzy version of Zadeh's extension principle

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Title of paper: On intuitionistic fuzzy version of Zadeh’s extension principle Author(s): Selami Bayeğ Industrial Engineering Department, University of Turkish Aeronautical Association, Ankara, Turkey sbayeg@thk.edu.tr Raziye Mert Department of Software Engineering, Adana Alparslan Turkes Science and Technology University, Adana, Turkey rmert@atu.edu.tr Published in: Notes on Intuitionistic Fuzzy Sets, Volume 27 (2021), Number 3, pages 9–17 DOI: https://doi.org/10.7546/nifs.2021.27.3.9-17 Download:  PDF (177  Kb, File info) Abstract: In this paper, by using [math]\displaystyle{ \alpha }[/math]- and [math]\displaystyle{ \beta }[/math]-cuts approach and the intuitionistic fuzzy Zadeh’s extension principle, we have proved a result which reveals that the [math]\displaystyle{ \alpha }[/math]- and [math]\displaystyle{ \beta }[/math]-cuts of an intuitionistic fuzzy number obtained by the intuitionistic fuzzy Zadeh’s extension principle coincide with the images of the [math]\displaystyle{ \alpha }[/math]- and [math]\displaystyle{ \beta }[/math]-cuts by the crisp function. Then we have given a corollary about monotonicity of the extension principle. Finally, we have extended these results to [math]\displaystyle{ IF_N(\mathbb{R}) \times IF_N(\mathbb{R}) }[/math]. Keywords: Intuitionistic fuzzy sets, Intuitionistic fuzzy Zadeh’s extension principle, Zadeh’s extension principle. AMS Classification: 94D05, 26E50. References: Akın, Ö., & Bayeğ, S. (2017). Intuitionistic fuzzy initial value problems: An application. Hacettepe Journal of Mathematics and Statistics, 48(6), 1682–1694. Akın, Ö., & Bayeğ, S. (2019). Some results on the fundamental concepts of fuzzy set theory in intuitionistic fuzzy environment by using [math]\displaystyle{ \alpha }[/math]- and [math]\displaystyle{ \beta }[/math]-cuts. Filomat, 33(10), 3123–3148. Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. Atanassova, L. (2006). On Intuitionistic fuzzy versions of L. Zadeh’s extension principle. Notes on Intuitionistic Fuzzy Sets, 13(3), 33–36. Dong, W. M., & Wong, F. S. (1987). Fuzzy weighted averages and implementation of the extension principle. Fuzzy Sets and Systems, 21(2), 183–199. De Barros, L. C., Bassanezi, R. C., & Tonelli, P.A. (1997). On the continuity of the Zadeh’s extension. 7th IFSA World Congress Proceedings, Prague, Czech Republic, 3–8. Hanss, M. (2002). The transformation method for the simulation and analysis of systems with uncertain parameters. Fuzzy Sets and Systems, 130(3), 277–289. Kerre, E. E. (2011). A tribute to Zadeh’s extension principle. Scientia Iranica, 18(3), 593–595. Marinov, E. (2014). On extension principle for intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 20(3), 34–41. Nguyen, H. T. (1978). A note on the extension principle for fuzzy sets. Journal of Mathematical Analysis and Applications, 64(2), 369–380. Wood, K. L., Otto, K. N., & Antonsson, E. K. (1992). Engineering design calculations with fuzzy parameters. Fuzzy Sets and Systems, 52(1), 1–20. 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.