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Issue:Operators similar to operators defined over intuitionistic fuzzy sets

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Title of paper: Operators similar to operators defined over intuitionistic fuzzy sets
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: 8th IWIFS, Sofia, 9 October 2012
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 18 (2012) Number 4, pages 40—47
Download:  PDF (180  Kb, File 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 dφ is R2-metric induced by an arbitrary fixed absolute normalized R2-norm φ. Using a bijective isomorphism between the class of all such sets and the class of all intuitionistic fuzzy sets over E, any operator acting over one of the mentioned classes produces a similar operator acting on the other. Some of the operators defined over the intuitionistic fuzzy sets and their corresponding similar operators are considered and studied in this paper and important limit theorems are established.
Keywords: Intuitionistic fuzzy set, d-intuitionistic fuzzy set, dφ-intuitionistic fuzzy set, Norm, Absolute norm, Normalized norm, Absolute normalized norm, Similar operator.
AMS Classification: 03E72
References:
  1. Atanassov, K. Intuitionistic Fuzzy Sets, Springer, Heidelberg, 1999.
  2. Atanassov, K. T., On Intuitionistic Fuzzy Sets Theory, Springer, Berlin, 2012.
  3. Vassilev, P. On the intuitionistic fuzzy sets with metric type relation between the membership and non-membership functions. Notes on Intuitionistic Fuzzy Sets. Vol. 18, 2012, No. 3, 30–38.
  4. Vassilev, P. A metric approach to fuzzy sets and intuitionistic fuzzy sets. Proc. of. First Int. Workshop on IFSs, GNs, KE, London, Sept. 2006, 31–38.
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