cuvalcioglu, G. (2013). On the Diagram of One Type Modal Operators on Intuitionistic fuzzy
sets: Last expanding with $Z_{alpha ,beta }^{omega ,theta. Iranian Journal of Fuzzy Systems, 10(1), 89-106. doi: 10.22111/ijfs.2013.166

g. cuvalcioglu. "On the Diagram of One Type Modal Operators on Intuitionistic fuzzy
sets: Last expanding with $Z_{alpha ,beta }^{omega ,theta". Iranian Journal of Fuzzy Systems, 10, 1, 2013, 89-106. doi: 10.22111/ijfs.2013.166

cuvalcioglu, G. (2013). 'On the Diagram of One Type Modal Operators on Intuitionistic fuzzy
sets: Last expanding with $Z_{alpha ,beta }^{omega ,theta', Iranian Journal of Fuzzy Systems, 10(1), pp. 89-106. doi: 10.22111/ijfs.2013.166

cuvalcioglu, G. On the Diagram of One Type Modal Operators on Intuitionistic fuzzy
sets: Last expanding with $Z_{alpha ,beta }^{omega ,theta. Iranian Journal of Fuzzy Systems, 2013; 10(1): 89-106. doi: 10.22111/ijfs.2013.166

On the Diagram of One Type Modal Operators on Intuitionistic fuzzy
sets: Last expanding with $Z_{alpha ,beta }^{omega ,theta

^{}department of mathematics, university of mersin, ciftlikkoy, 33016,
mersin turkey

Abstract

Intuitionistic Fuzzy Modal Operator was defined by Atanassov in cite{at3} in 1999. In 2001, cite{at4}, he introduced the generalization of these modal operators. After this study, in 2004, Dencheva cite{dencheva} defined second extension of these operators. In 2006, the third extension of these was defined in cite{at6} by Atanassov. In 2007,cite{gc1}, the author introduced a new operator over Intuitionistic Fuzzy Sets which is a generalization of Atanassov's and Dencheva's operators. At the same year, Atanassov defined an operator which is an extension of all the operators defined until 2007. The diagram of One Type Modal Operators on Intuitionistic Fuzzy Sets was introduced first in 2007 by Atanassov cite{at10}. In 2008, Atanassov defined the most general operator and in 2010 the author expanded the diagram of One Type Modal Operators on Intuitionistic Fuzzy Sets with the operator $Z_{alpha ,beta }^{omega }$. Some relationships among these operators were studied by several researchers% cite{at5}-cite{at8} cite{gc1}, cite{gc3}, cite{dencheva}- cite% {narayanan}. The aim of this paper is to expand the diagram of one type modal operators over intuitionistic fuzzy sets . For this purpose, we defined a new modal oparator $Z_{alpha ,beta }^{omega ,theta }$ over intuitionistic fuzzy sets. It is shown that this oparator is the generalization of the operators $Z_{alpha ,beta }^{omega },E_{alpha ,beta },boxplus _{alpha ,beta },boxtimes _{alpha ,beta }.$

bibitem{at1} K. T. Atanassov, emph{Intuitionistic fuzzy sets}, VII ITKR's Session, Sofia, June 1983.

bibitem{at2} K. T. Atanassov, emph{Intuitionistic fuzzy sets}, Fuzzy Sets and Systems, textbf{20} (1986), 87-96.

bibitem{at3} K. T. Atanassov, emph{Intuitionistic fuzzy sets}, Phiysica-Verlag, Heidelberg, NewYork, 1999.

bibitem{at4} K. T. Atanassov, emph{Remark on two operations over intuitionistic fuzzy sets,} Int. J. of Unceratanity, Fuzzyness and Knowledge Syst., textbf{9(1)} (2001), 71-75.

bibitem{at5} K. T. Atanassov, emph{On the type of intuitionistic fuzzy modal operators}, NIFS, textbf{11(5)} (2005), 24-28.

bibitem{at6} K. T. Atanassov, emph{The most general form of one type of intuitionistic fuzzy modal operators}, NIFS, textbf{12(2)} (2006), 36-38.

bibitem{at7} K. T. Atanassov, emph{Some properties of the operators from one type of intuitionistic fuzzy modal operators}, Advanced Studies on Contemporary Mathematics, textbf{15(1)} (2007), 13-20.

bibitem{at8} K. T. Atanassov, emph{The most general form of one type of intuitionistic fuzzy modal operators, part 2}, NIFS, textbf{14(1)} (2008), 27-32.

bibitem{at9} K.T. Atanassov, emph{Theorem for equivalence of the two most general intuitionistic fuzzy modal operators}, NIFS, textbf{15(1)}(2008), 26-31.

bibitem{at10} K. T. Atanassov, emph{25 years of intuitionistic fuzzy sets, or: the most important results and mistakes of mine}, 7 th Int. workshop on IFSs and gen. nets. , Poland, 2008.

bibitem{gc1} G. c{C}uvalci ou{g}lu, emph{Some properties of $E_{alpha ,beta }$ operator}, Advanced Studies on Contemporary Mathematics, textbf{14(2)} (2007), 305-310.

bibitem{gc2} G. c{C}uvalci ou{g}lu, emph{Expand the modal operator diagram with $Z_{alpha ,beta }^{omega },$}, Proc. Jangjeon Math. Soc., textbf{13(3)} (2010), 403-412

bibitem{gc3} G. c{C}uvalci ou{g}lu, S. Yi lmaz, emph{Some properties of OTMOs on IFSs, Advanced Studies on Contemporary Mathematics}, textbf{14(2)} (2010), 305-310.

bibitem{dencheva} K. Dencheva, emph{Extension of intuitionistic fuzzy modal operators $boxplus $ and $boxtimes ,$}, Proc.of the Second Int. IEEE Symp. Intelligent systems, Varna, June 22-24, textbf{3} (2004), 21-22.

bibitem{doycheva} B. Doycheva, emph{Inequalities with intuitionistic fuzzy topological and G"{o}khan c{C}uvalci ou{g}lu's operators}, NIFS, textbf{14(1)} (2008), 20-22.

bibitem{hasan} A. Hasankhani, A. Nazari and M. Saheli, emph{Some properties of fuzzy Hilbert spaces and norm of operators}, Iranian Journal of Fuzzy Systems, textbf{7(3)} (2010), 129-157.

bibitem{li} D. Li, F. Shan and C. Cheng, emph{On properties of four IFS operators}, Fuzzy Sets and Systems, textbf{154} (2005), 151-155.

bibitem{luo} X. Luo and J. Fang, emph{Fuzzifying closure systems and closure operators}, Iranian Journal of Fuzzy Systems, textbf{8(1)} (2011), 77-94.

bibitem{narayanan} A. Narayanan, S. Vijayabalaji and N. Thillaigovindan, emph{Intuitionistic fuzzy bounded linear operators}, Iranian Journal of Fuzzy Systems, textbf{4(1)} (2007), 89-101.

bibitem{zadeh} L. A. Zadeh, emph{Fuzzy sets}, Information and Control, textbf{8} (1965) , 338-353.