Islanding is the most important prerequisite to integrated energy systems, significantly when they are operating with Distributed Generation (DG) or Microgrid (MG) units. In this paper, a novel Variable Fuzzy Membership Function (VFMF) islanding detection is proposed for an inverter based integrated renewable energy system that consists of a either DG or MG units. Passive Islanding Detection (IDT) with Deviations in Frequency (DIF) and Deviations in Voltage (DIV) are the main data sets for the proposed VFMF approach. Proposed method is based on updating of Fuzzy Membership Function (FMF); those are obtained for each Islanding Event (IE) and Non Islanding Event (NIE) of operation. Control vector of a fuzzy system i.e Fuzzy Control Vector (FCV) is used for a range of Misclassification Data of Event (MDOE) either in IE or NIE. VFMF supports for obtaining FCV to achieve proper assessment of IDT in the test system. Handling of DIV/DIF from MDOE, false tripping signal is avoided at every NIE. Effectiveness of proposed method is validated through many IE and NIE cases.