Intuitionistic fuzzy set theory was introduced by Atanassov as an extension of fuzzy sets [1]. The algebraic structures like groups, rings, modules, etc. were generalized to intuitionistic fuzzy sets by different authors. Some properties of them were studied [4, 9, 11, 14, 15]. In this study, we generalized the action of a group on a set to intuitionistic fuzzy action. We obtained some basic results.
In this study, the representation theorem and a partition for intuitionistic fuzzy sets were given. For those properties, intuitionistic fuzzy sheet t-level set, intuitionistic fuzzy α-t block level set and intuitionistic fuzzy t-subset were used.
The concept of abstract algebra on intuitionistic fuzzy sets were introduced and some basic theorems were proved by authors in 2017. In this study, homomorphism between intuitionistic fuzzy abstract algebras is defined, intuitionistic fuzzy function is examined and then intuitionistic fuzzy congruence relations are defined on intuitionistic fuzzy abstract algebra. First and third isomorphism theorems on intuitionistic abstract algebras are introduced.
In this study, it is purposed to introduced the concept of quasi-interior ideal on intuitionistic fuzzy semigroups. The concept introduced is supported with examples and its basic algebraic properties are examined.
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