A taifa ( from á Ä ` ifa , plural Ø Ù Ø Ø Ù á awÄ ` if ) was an independent Muslim-ruled principality . In the history of the Iberian Peninsula , a taifa ( from á Ä ` ifa , plural Ø Ù Ø Ø Ù á awÄ ` if ) was an independent Muslim-ruled principality , usually an emirate or petty kingdom , though there was one oligarchy , of which a number formed in the Al-Andalus ( Moorish Iberia ) after the final collapse of the Umayyad Caliphate of CÃ rdoba in 1031 .