Abstract
In this paper, we propose the concept of ρ anti-intuitionistic fuzzy sets, ρ anti - intuitionistic fuzzy subgroups and prove some of their algebraic properties. We investigate a necessary and sufficient condition for a ρ-anti intuitionistic fuzzy set to be a ρ-anti intuitionistic fuzzy subgroup. We extend this ideology by defining the notions of ρ anti-intuitionistic fuzzy coset, ρ anti-intuitionistic fuzzy normal subgroup and derive some of their key algebraic characteristics. In addition, we study the quotient group of a group induced by ρ-anti intuitionistic fuzzy normal subgroup and establish a group isomorphism between this newly defined quotient group and the quotient group of group G relative to its particular normal subgroup G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Sρ</sub> .
Highlights
Crisp set theory deals with the situations which are inevitable and precise and the elements have a Boolean state of nature
We explore the ideas of ρ-antiintuitionistic fuzzy coset and ρ-anti-intuitionistic fuzzy normal subgroup (AIFNSG) together with some of their important properties
We prove the condition for a ρ-anti intuitionistic fuzzy subgroup (ρ-anti intuitionistic fuzzy subgroup (AIFSG)) of a group G to be a ρ-AIFNSG
Summary
Crisp set theory deals with the situations which are inevitable and precise and the elements have a Boolean state of nature. Owing to the complicated pattern of executive surroundings and judgmental obstacles themselves, judgment composers can present evaluations or judgments to a few specific extent there may occur an element of mistake, because sometimes they are not sure regarding to the decisions namely, there may exist some reluctancy degree, such kind of reluctancy is perfectly expressed in the framework of anti-intuitionistic fuzzy sets This particular theory deals with the arrangement of instructions and processing in human brains and such crucial traits as it has the capability to deal with inconclusiveness and vagueness. Atanassov [7] characterized the concept of IFSs and described its essential features in 1986 This specific theory has effectively been used in the formulation of IFS iterated function system to image analysis [8], topological spaces [9], medical sciences [10], fractal image construction [11], matrix theory [12] and graph theory [13].
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