k-pseudo similar intuitionistic fuzzy matrices
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In this paper, we shall define k-pseudo similarity (right k-pseudo similar or left k-pseudo similar) for intuitionistic fuzzy matrices and prove that, for a pair of intuitionistic fuzzy matrices $A,B\in\left(IF\right)_n,$ if $A$ is said to be right (left) k-pseudo similar to $B$ then $A^s$ is said to be right (left) k-pseudo similar to $B^s$ for any integer $s\geq1,$ but the converse is not true which is illustrated by an example. Also prove that, $A$ is said to be right (left) k-pseudo similar to $B$ if and only if $B^T$ is said to be left (right) k-pseudo similar to $A^T$. We exhibit that the k-pseudo similarity on $A$ and $B$ preserve k-regularity of the intuitionistic fuzzy matrices $A$ and $B$. As a special case, for $k=1$ it reduces to pseudo similar intuitionistic fuzzy matrices [3].
Abstract
In this paper, we shall define k-pseudo similarity (right k-pseudo similar or left k-pseudo similar) for intuitionistic fuzzy matrices and prove that, for a pair of intuitionistic fuzzy matrices $A,B\in\left(IF\right)_n,$ if $A$ is said to be right (left) k-pseudo similar to $B$ then $A^s$ is said to be right (left) k-pseudo similar to $B^s$ for any integer $s\geq1,$ but the converse is not true which is illustrated by an example. Also prove that, $A$ is said to be right (left) k-pseudo similar to $B$ if and only if $B^T$ is said to be left (right) k-pseudo similar to $A^T$. We exhibit that the k-pseudo similarity on $A$ and $B$ preserve k-regularity of the intuitionistic fuzzy matrices $A$ and $B$. As a special case, for $k=1$ it reduces to pseudo similar intuitionistic fuzzy matrices [3].
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