A Fuzzy Approach to Fleming-Harrington Estimator

Abstract

Apart from randomness and other characteristics which are embedded with survival data, impreciseness in the observations is a quite common phenomenon. Statistical methods deal with randomness, however, not with impreciseness. The theory of fuzzy helps to deal with the impreciseness in the data. In this paper, the Fleming-Harrington estimator (1984) which is developed for estimating the survival function of the survival data in the presence of censoring is modified through the implementation of the fuzzy concept in the observations. The survival times are normally measured as crisp observations, but in reality, they are “more or less fuzzy” (Viertl (2015)) and so in this article, the fuzziness is introduced to the survival times and related fuzzy survival curves and median survival time are obtained. As there is no specific article related to fuzzy orientation to the Fleming-Harrington estimator (1984), this method paves the way by proposing a new methodology by finding a fuzzy Fleming-Harrington estimator.The proposed methodology has been illustrated through an example. The suggested fuzzy technique brings out an enhancement in the estimation of the survival probabilities.