What is the ruling on one who made the intention to fast a supererogatory fast and then broke it, and is it obligatory for him to make up for it?

One who begins a voluntary fast and then breaks it is not obligated to complete it or make up for it, due to the saying of Aisha (may Allah be pleased with her): "Some 'Hais' (a dish made of dates, clarified butter, and cheese) was presented to us, and he (the Prophet) said: 'Show it to me, for I started the day fasting.' Then he ate." And due to the saying of the Prophet (peace be upon him): "The one observing a voluntary fast is the master of himself; if he wishes, he fasts, and if he wishes, he breaks his fast." However, it is recommended for one who has started a voluntary fast to complete it, due to the saying of Allah the Almighty: "And do not invalidate your deeds."