The purpose of this study was to develop a computing system (CS) with fuzzy membership and graph connectivity approach to estimate the predictability of thunderstorms during the pre-monsoon season (April–May) over Kolkata (22°32′N, 88°20′E), India. The stability indices are taken to form the inputs of the CS. Ten important stability indices are selected to prepare the input of the fuzzy set. The data analysis during the period from 1997 to 2006 led to identify the ranges of the stability indices through membership function for preparing the fuzzy inputs. The possibility of thunderstorms with the given ranges of the stability indices is validated with the bipartite graph connectivity method. The bipartite graphs are prepared with two sets of vertices, one set for three membership functions (strong, moderate and weak) with the stability indices and the other set includes the three membership functions for the probability of thunderstorms (high, medium and low). The percentages of degree of vertex (ΔG) are computed from a sample set of bipartite graph on thunderstorm days and are assigned as the measure of the likelihood of thunderstorms. The results obtained from graph connectivity analysis are found to be in conformity with the output of fuzzy interface system (FIS). The result reveals that the skill of graph connectivity is better and supports the FIS in estimating the predictability of thunderstorms over Kolkata during the pre-monsoon season. The result further reveals from the minimum degree of vertex connectivity that among the ten selected stability indices, only four indices: lifted index, bulk Richardson number, Boyden index and convective available potential energy, are most relevant for estimating the predictability of thunderstorms over Kolkata, India. © 2014, Springer Science+Business Media Dordrecht.