Issue:On the intuitionistic fuzzy sets with metric type relation between the membership and non-membership functions

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Title of paper: On the intuitionistic fuzzy sets with metric type relation between the membership and non-membership functions Author(s): Peter Vassilev Bioinformatics and Mathematical Modelling Department, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., Sofia 1113, Bulgaria peter.vassilev@gmail.com Presented at: 16th ICIFS, Sofia, 9-10 September 2012 Published in: Conference proceedings, "Notes on IFS", Volume 18 (2012) Number 3, pages 30—38 Download:  PDF (169  Kb, Info) Abstract: In the paper the so-called dφ-intuitionistic fuzzy set (dφ-IFS), over the non-empty universe E are considered for the case when φ is R2-metric induced by an arbitrary fixed absolute normalized R2-norm φ. It is proved that there exists a bijective isomorphism between the class of all such sets and the class of all intuitionistic fuzzy sets over E. Keywords: Intuitionistic fuzzy set, d-intuitionistic fuzzy set, dφ-intuitionistic fuzzy set, Norm, Absolute norm, Normalized norm, Absolute normalized norm, Injection, Surjection, Bijection, Isomorphism. AMS Classification: 03E72 References: Atanassov, K. Intuitionistic Fuzzy Sets. Springer Physica-Verlag, Heidelberg, 1999. Bonsall, F., J. Duncan. Numerical Ranges II, London Math. Soc., Lecture Notes Ser., Vol. 10, 1973. Kato, M., T. Tamura. Weakly nearly uniform smoothness and worth property of Ψ-direct sums of Banach spaces. Comment. Math. Prace Mat., Vol. 46, 2006, 113—129. Mitani K., K. Saito, T. Suzuki. Smoothness of absolute norms on ℂn, J. Convex Anal. Vol. 10, 2003, 89–107. Saito, K.-S., M. Kato, Y. Takahashi. Absolute norms on ℂn, J. Math. Anal. Appl., Vol. 252, 2000, 879-905. Suzuki, T., A. Yamano, M. Kato. The James Constant of 2-Dimensional Lorentz Sequence Spaces. Bull. Kyushu Inst. Tech. Pure Appl. Math. Vol. 53, 2006, 15–24. Takahashi, Y., M. Kato, K.-S. Saito. Strict convexity of absolute norms on ℂ2 and direct sums of Banach spaces, J. Inequal. Appl. Vol. 7, 2002, 179–186. Vassilev, P. A Metric Approach To Fuzzy Sets And Intuitionistic Fuzzy Sets. Proc. of. First Int. Workshop on IFSs, GNs, KE, Sept. 2006, 31–38. Zuo, Z. The Ptolemy constant of absolute normalized norms on ℝ2: Journal of Inequalities and Applications, 2012, 2012:107. Citations: Issue:Operators similar to operators defined over intuitionistic fuzzy sets ‎ (← links) The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.