Feminism is defined as...
...the theory of the political, economic, and social equality of the sexes.
We might infer that in a "feminist's way of thinking" the tale offers reasoning within the plot to promote proof of a woman's intelligence, wit, etc., presenting her as the Sultan's equal.
There are many versions of in The Arabian Knights, also called A Thousand and One Nights. The begin with the Sultan, Schahriar (or Shahryar), who is betrayed by his wife and has her killed. He has lost trust in all women, so each day—to prevent further exploitation of his person— he marries a young girl, spends the night with her, and has her killed the next day.
The effect on this kingdom that had prospered for hundreds of years is deeply tragic. A new family mourns each day for the loss of a daughter, and other parents live in constant fear that their daughter will be chosen next. Instead of praising the sultan, the people curse him.
The job of finding a new wife falls to the grand-vizir. He is greatly troubled by the Sultan's actions and his own part in the process. He also has two daughters, and one day his daughter, Scheherazade, speaks to her father:
"I am determined to stop this barbarous practice of the Sultan's, and to deliver the girls and mothers from the awful fate that hangs over them....My father...it is you who have to provide the Sultan daily with a fresh wife, and I implore you, by all the affection you bear me, to allow the honour to fall upon me...If I fail, my death will be a glorious one, and if I succeed I shall have done a great service to my country."
It is significant that Scheherazade approaches her father. She is a strong female figure who sets out to solve the problem on her own. She also has a sense of honor. Scheherazade is concerned for others, willing to risk losing her life to save other women and improve the conditions in her country. Even in the face of her father's resistance (or the resistance of the "man/the authority figure"), she does not falter. When the grand-vizir can no longer resist his daughter's endless entreaties, he tells the Sultan who...
...received this news with the greatest astonishment.
"How have you made up your mind," he asked, "to sacrifice your own daughter to me?"
Schahriar is certain this decision was made by his grand-vizir (a man), but learns that it comes from a "lowly" woman—a strong and courageous female.
Scheherazade arranges that her sister Dinarzade (or Dunyazade) spend the night with her, to awaken her before sunrise and ask her for a story. This shows how intelligent and wise Scheherazade is, and her ability to understand human nature. She begins to tell her story, stopping in the middle as the sun rises.
Schahriar...had been listening to Scheherazade with pleasure...
Captivated, the Sultan allows her to live another day so he can hear the end. Scheherazade is a gifted storyteller, a valuable talent in cultures where stories were passed for many years by word of mouth. This would also show her worth in a man's world.
As Scheherazade begins the end of her tale, "a series of interlocking stories" emerge. Scheherazade continues for so many nights that the Sultan falls in love with her and makes her his "sultana."
The story shows "a more progressive feminist way of thinking" in giving Scheherazade many gifts generally associated with men, including wisdom and a talent for telling stories; in saving herself, we could say she proves she is the Sultan's equal.