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Issue:Properties of some operations defined over intuitionistic fuzzy sets

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Title of paper: Properties of some operations defined over intuitionistic fuzzy sets
Author(s):
Rangasamy Parvathi
Department of Mathematics, Vellalar College for Women, Erode - 638 012, Tamilnadu, India
paarvathis@rediffmail.com
Beloslav Riečan
Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica
Mathematical Institute of Slovak Acad. of Sciences, Štefánikova 49, SK-81473 Bratislava
riecan@mat.savba.skriecan@fpv.umb.sk
Krassimir Atanassov
Bioinformatics and Mathematical Modelling Department, IBPhBME - Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str., block 105, Sofia 1113, Bulgaria
krat@bas.bg
Published in: "Notes on IFS", Volume 18 (2012) Number 1, pages 1—4
Download:  PDF (125  Kb, Info)
Abstract: A lot of operations are defined oved the intuitionistic fuzzy sets. Here, five equalities with participation of some of these operations are introduced and proved. The paper is a continuation of [4, 5], where two new operations over Intuitionistic Fuzzy Sets (IFSs, see [1, 2]) are introduced. The operations and their properties may find applications as the operations [math]\displaystyle{ A^n }[/math], [math]\displaystyle{ n.A }[/math] and [math]\displaystyle{ \frac{1}{n}.A }[/math] find their places and play role in contrast enhancement and defining statistical tools in

intuitionistic fuzzy environment.

Keywords: Intuitionistic fuzzy sets, Operations over intuitionistic fuzzy sets
AMS Classification: 03E72
References:
  1. Atanassov, K. Intuitionistic Fuzzy Sets, Springer, Heidelberg, 1999.
  2. Atanassov, K. On Intuitionistic Fuzzy Sets Theory, Springer, Berlin, 2012 (in press).
  3. De, S. K., R. Biswas, A. R. Roy, Some operations on intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 114, 2000, No. 4, 477–484.
  4. Riečan, B., K. Atanassov. n-extraction operation over intuitionistic fuzzy sets. Notes in Intuitionistic Fuzzy Sets, Vol. 12, 2006, No. 4, 9–11.
  5. Riečan, B., K. Atanassov. Operation division by n over intuitionistic fuzzy sets. Notes in Intuitionistic Fuzzy Sets, Vol. 16, 2010, No. 4, 1–4.
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