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Issue:A new geometrical interpretation of some concepts in the intuitionistic fuzzy logic

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Title of paper: A new geometrical interpretation of some concepts in the intuitionistic fuzzy logic
Author(s):
Anestis Hatzimichailidis
Department of Civil Engineering, Democritus University of Thrace, GR-671 00 Xanthi, Greece
hatz_aneAt sign.pnghol.gr
Basil Papadopoulos
Department of Civil Engineering, Democritus University of Thrace, GR-671 00 Xanthi, Greece
papadobAt sign.pngcivil.duth.gr
Presented at: 9th ICIFS, Sofia, 7—8 May 2005
Published in: Conference proceedings, "Notes on IFS", Volume 11 (2005) Number 2, pages 38—46
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Abstract: We provide a new geometrical interpretation of some concepts in the intuitionistic fuzzy sets (briefly IFSs). Using the new geometrical interpretation, we can give the corresponding geometrical interpretations of some operations and operators over the elements of the IFSs. With the new geometrical interpretation we can have an abstract picture of operations and relations over IFSs. This can be observed in an arbitrary triangle without the restrictions of other geometrical interpretations, which are known to work in a unit rectangle, in an isosceles triangle, and in an equilateral triangle.
Keywords: Intuitionistic fuzzy sets, Intuitionistic fuzzy logic, Geometrical interpretations of intuitionistic fuzzy sets
References:
  1. K. T. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications, Springer-Verlag, Berlin, 1998.
  2. Atanassov K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol.20 (1986), No.1, 87-96.
  3. Atanassov K., More on intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol.33 (1989), No.1, 37-46.
  4. Atanassov K., New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol.61 (1994), No.2, 137-142
  5. Danchev S., A new geometrical interpretation of some concepts in the intuitionistic fuzzy logics, Notes on Intuitionistic Fuzzy Sets, Vol. 1 (1995), No 2, 116-118.
  6. A. G. Hatzimichailidis, B. K. Papadopoulos., A new implication in the intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, Vol. 8 (2002), No 4, 79-104
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