Multi-Criteria Decision Making (MCDM) methods are widely used to assist in decision making when there are different criteria and the best alternative is to be selected. Often one needs to make a best compromise choice from the available options, since finding the best alternative may not be practically feasible. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is one of the most widely used MCDM methods (Zyoud & Fuchs-Hanusch, 2017) in such situations. TOPSIS works on the principle of finding the best compromise solution when compared to an Ideal Solution. However, in contemporary business situations such as technology selection, decisions are often taken in uncertain environments, and evaluators may feel more confident in expressing the ratings of alternatives for given criteria in fuzzy sets or interval-values (Durbach & Stewart, 2012). To address this challenge, researchers have presented different versions of Fuzzy-TOPSIS method for specific decision-making environments (Behzadian, Khanmohammadi Otaghsara, Yazdani & Ignatius, 2012; Joshi & Kumar, 2016; Mardani, Jusoh & Zavadskas, 2015; Walczak & Rutkowska, 2017). Further, it is also possible that there could be different types of fuzzy or interval-valued numbers, with or without subjective weights of criteria by evaluators, and the current approaches do not incorporate these flexibilities and uncertainties in a single method. We therefore seek to enhance the decision making approach to incorporate all the above problem variants. Developing a generalised and flexible selection model is important, since an organisation or decision-maker may not be willing to invest unduly high time or money in the development of different types of selection models. Accordingly, in this paper we propose a Generalised-FuzzyTOPSIS (GFTOPSIS) method, a versatile evaluation model capable of incorporating different kinds of flexibilities and uncertainties in the decision making process. The proposed approach is a generalised, flexible and intelligent fuzzy MCDM method, using IntervalValued Intuitionistic Fuzzy Set (IVIFS) for preference rating, suitable for use in uncertain environments. TOPSIS method is modified to incorporate IVIFS preference rating along with Degree of Optimism (DOpt). The proposed GFTOPSIS method uses DOpt to derive the expected IFS matrix, and subsequent calculations are performed based on the expected IFS matrix and distance between two IFS. This method is different from the work of F. Ye (2010), who recommended TOPSIS based on distances between two IVIFS.