^{}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 $Z_{alpha ,beta }^{omega },E_{alpha ,beta },boxplus _{alpha ,beta },boxtimes _{alpha ,beta }.$

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