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

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سال انتشار : ۲۰۱۳

تعداد صفحات :۲۷

Intuitionistic Fuzzy Modal Operator was defined by Atanassov in cite{at3}in 1999. In 2001, cite{at4}, he introduced the generalization of thesemodal operators. After this study, in 2004, Dencheva cite{dencheva} definedsecond extension of these operators. In 2006, the third extension of thesewas defined in cite{at6} by Atanassov. In 2007,cite{gc1}, the authorintroduced a new operator over Intuitionistic Fuzzy Sets which is ageneralization of Atanassov”s and Dencheva”s operators. At the same year,Atanassov defined an operator which is an extension of all the operatorsdefined until 2007. The diagram of One Type Modal Operators onIntuitionistic Fuzzy Sets was introduced first in 2007 by Atanassovcite{at10}. In 2008, Atanassov defined the most general operator and in2010 the author expanded the diagram of One Type Modal Operators onIntuitionistic 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 operatorsover intuitionistic fuzzy sets . For this purpose, we defined a new modaloparator $Z_{alpha ,beta }^{omega ,theta }$ over intuitionistic fuzzysets. It is shown that this oparator is the generalization of the operators$Z_{alpha ,beta }^{omega },E_{alpha ,beta },boxplus _{alpha ,beta},boxtimes _{alpha ,beta }.$