Principally, traditional process capability indices (PCIs) based on normality are not convenient for non-normal industrial processes to reflect their performances. For non-normal processes, Clements' method modifies the traditional PCIs by assessing percentiles and median of the process distribution to define percentile based PCIs. The elementary idea of using the fuzzy set theory for PCIs can simply be expressed as to overcome infirmity of PCIs arisen from the sharp crisp nature that restricts the applicability, flexibility, and sensitivity. The proposition of the fuzzy sets is motivated by the need to capture and represent real life case data with uncertainty due to imprecise measurement. In this study, the percentile based basic PCIs for non-normal data are examined and fuzzy formulations for them are developed using Clements' method. These percentile based basic PCIs along with their fuzzy formulations are then applied and compared for the data generated from Weibull(1,1) and Weibull(1,2).