One, Two and Uni-type Operators on IFSs

Abstract

Intuitionistic Fuzzy Modal Operator was defined by Atanassov in (Intuitionistic Fuzzy Sets. Phiysica-Verlag, Heidelberg, 1999, [2], Int J Uncertain Fuzzyness Knowl Syst 9(1):71–75, 2001, [3]). He introduced the generalization of these modal operators. After this study, Dencheva (Proceedings of the Second International. IEEE Symposium: Intelligent Systems, vol 3, pp 21–22. Varna, 2004, [10]) defined second extension of these operators. The third extension of these was defined by Atanassov in (Adv Stud Contemp Math 15(1):13–20, 2007, [5]). In (Atanassov, NIFS 14(1):27–32 2008, [6]), the author introduced a new operator over Intuitionistic Fuzzy Sets which is generalization of Atanassov’s and Dencheva’s operators. At the same year, Atanassov defined an operator which is an extension of all the operators. The diagram of One Type Modal Operators on Intuitionistic Fuzzy Sets was introduced first time by Atanassov (Int J Uncertain Fuzzyness Knowl Syst 9(1):71–75, 2001, [3]). The author expanded the diagram of One Type Modal Operators on Intuitionistic Fuzzy Sets with the operator Z (alpha beta gamma). In 2013, the last operators were defined. These operators have properties which are belong to both first and second type modal operators. So, they called uni-type operators. After these operators the diagram of modal operators on intuitionistic fuzzy sets is expanded.