In financial markets, investors attempt to maximize their profits within a constructed portfolio with the aim of optimizing the tradeoffs between risk and return across the many stocks. This requires proper handling of conflicting factors, which can benefit from the domain of multiple criteria decision making (MCDM). However, the indexes and factors representing the stock performance are often imprecise or vague and this should be represented by linguistic terms characterized by fuzzy numbers. The aim of this research is to first develop three group MCDM methods, then use them for selecting undervalued stocks by dint of financial ratios and subjective judgments of experts. This study proposes three versions of fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution): conventional TOPSIS (C-TOPSIS), adjusted TOPSIS (A-TOPSIS) and modified TOPSIS (M-TOPSIS) where a new fuzzy distance measure, derived from the confidence level of the experts and fuzzy performance ratings have been included in the proposed methods. The practical aspects of the proposed methods are demonstrated through a case study in the Tehran stock exchange (TSE), which is timely given the need for investors to select undervalued stocks in untapped markets in the anticipation of easing economic sanctions from a change in recent government leadership.