Issue:Compass-and-straightedge constructions in the intuitionistic fuzzy interpretational triangle: two new intuitionistic fuzzy modal operators

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Title of paper: Compass-and-straightedge constructions in the intuitionistic fuzzy interpretational triangle: two new intuitionistic fuzzy modal operators Author(s): Vassia Atanassova Department of Bioinformatics and Mathematical Modelling Institute of Biophysics and Biomedical Engineering Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, Sofia 1113, Bulgaria vassia.atanassova@gmail.com Lyubka Doukovska Intelligent Systems Department Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev str., Bl. 2, 1113 Sofia, Bulgaria doukovska@iit.bas.bg Presented at: 21st International Conference on Intuitionistic Fuzzy Sets, 22–23 May 2017, Burgas, Bulgaria Published in: "Notes on IFS", Volume 23, 2017, Number 2, pages 1—7 Download:  PDF (157 Kb  Kb, File info) Abstract: The idea about the two new intuitionistic fuzzy modal operators, proposed here, was inspired by a review of the modal operators defined over intuitionistic fuzzy sets and the observation that graphically all of them are constructed by orthogonal projections. Here for the first time, we propose a new method of constructing two different modal operators, using a compass-andstraightedge construction, producing for each point from the intuitionistic fuzzy interpretational triangle, the two points onto the triangle’s hypothenuse that are respectively equidistant from the Truth and the Falsity as the point itself. The properties of these so-constructed new intuitionistic fuzzy operators are studied and formulated in two theorems. Keywords: Intuitionistic fuzzy modal operator, Intuitionistic fuzzy interpretational triangle, Ruler-and-compass construction, InterCriteria Analysis. AMS Classification: 03E72. References: Atanassov, K. (1989). Geometrical interpretation of the elements of the intuitionistic fuzzy objects, Preprint IM-MFAIS-1-89, Sofia, 1989, Reprinted: Int J Bioautomation. 2016, 20(S1), S27–S42. Atanassov, K. (2017). Intuitionistic Fuzzy Logics. Springer, Cham. Atanassov, K., Szmidt, E., & Kacprzyk, J. (2013). On intuitionistic fuzzy pairs, Notes on Intuitionistic Fuzzy Sets, 19(3), 1–13. Atanassov, K. (2005). On one type of intuitionistic fuzzy modal operators. Notes on Intuitionistic Fuzzy Sets, 11(5), 24–28. Atanassov, K. (2004). On the modal operators defined over intuitionistic fuzzy sets . Notes on Intuitionistic Fuzzy Sets, 10(1), 7–12. Atanassov, K. (2006). 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