A cosine similarity based QUALIFLEX approach with hesitant fuzzy linguistic term sets for financial performance evaluation

The financial performance evaluation is important for investors of listed companies to make investment decisions. It enables investors to avoid haphazard investment and make a better decision in the capital market with high risk. Financial performance evaluation can be formulated as a kind of multi-criteria decision making (MCDM) problems with hesitant fuzzy linguistic term sets (HFLTSs). Considering that the number of criteria markedly exceeds the number of alternatives in real-world financial performance evaluation, this paper aims to develop a cosine similarity based QUALIFLEX (QUALItative FLEXible multiple criteria method) approach for MCDM with HFLTSs to effectively solve such problems. Firstly, a new fuzzy envelope of HFLTS is proposed using a Bonferroni mean (BM) operator. A new cosine similarity measure for HFLTSs is defined on the basis of trapezoidal membership functions of the new fuzzy envelopes. By taking a hesitancy index of HFLTS into account, an adjusted cosine similarity measure is developed for HFLTSs. Subsequently, a linear programming model is constructed to objectively determine the criteria weights on the basis of the adjusted cosine similarity measure. Then a cosine similarity based QUALIFLEX approach is put forward for MCDM with HFLTSs. Finally, an example of financial performance evaluation is analyzed to illustrate the effectiveness and applicability of the proposed approach.