Title of paper:

Some algebraic properties of the matrix representation of intuitionistic fuzzy modal operators

Author(s):

Sinem Yılmaz

Department of Mathematics, University of Mersin, Turkey

sinemyilmaz@gmail.com

Gökhan Çuvalcioğlu

Department of Mathematics, University of Mersin, Turkey

gcuvalcioglu@gmail.com

Arif Bal

Department of Mathematics, University of Mersin, Turkey

arif.bal.math@gmail.com


Presented at:

19th International Conference on Intuitionistic Fuzzy Sets, 4–6 June 2015, Burgas, Bulgaria

Published in:

"Notes on Intuitionistic Fuzzy Sets", Volume 21, 2015, Number 2, pages 6—18

Download:

PDF (187 Kb, File info)

Abstract:

Intuitionistic fuzzy sets were introduced by Atanassov in 1983 [1]. He defined Intuitionistic Fuzzy Modal Operators on IFSs. Intuitionistic fuzzy modal operators were separated in three types called onetwouni type modal operators on Intuitionistic Fuzzy Sets with the help of some authors’ studies [3, 5]. A study named Matrix Representation of the Second Type of Intuitionistic Fuzzy Modal Operators introduced in [4]. In this study, our purpose is to examine some new algebraic properties of matrix representation sets of Intuitionistic Fuzzy Modal Operators which is a monoid with the matrix product and give the concept of generator in this algebraic structure.

Keywords:

Intuitionisic fuzzy sets, Intuitionistic fuzzy modal operators, Matrix representation of IFMOs on IFSs, Algebraic properties of matrix representation of IFMOs on IFSs.

AMS Classification:

03E72, 47S40.

References:

 Atanassov, K., Intuitionistic fuzzy sets, Proc. of VII ITKR’s Session, Sofia (deposed June 1983, in Bulgarian)
 Atanassov, K., Intuitionistic Fuzzy Sets, Springer, Heidelberg, 1999.
 Çuvalcioğlu, G., On the Diagram of One Type Modal Operatorss on Intuitionistic Fuzzy Sets: Last Expanding with [math]\displaystyle{ Z^{\omega,\theta}_{\alpha,\beta} }[/math] , Iranian J. of Fuzzy Systems, 10(1), 2013, 89–106.
 Çuvalcıoğlu, G., S. Yılmaz and K. Atanassov. Matrix representation of the second type of intuitionistic fuzzy modal operators, Notes on Intuitionistic Fuzzy Sets, 20(5), 2014, 9–16.
 Dencheva K. Extension of intuitionistic fuzzy modal operators ⊞ and ⊠. Proceedings of the Second Int. IEEE Symposium: Intelligent Systems, Varna, June 2224, 2004, Vol. 3, 2122.
 Hungerford, T. W. Algebra, SpringerVerlag NY Inc, 1974
 L. A. Zadeh, Fuzzy sets, Information and Control, 8 , 1965, 338353.

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