An Extension of Regret Theory Based on Probabilistic Linguistic Cloud Sets Considering Dual Expectations: An Application for the Stock Market

The decision of stock selection relies on experts' cognition and investors' behavioral characteristics. This requires the consideration of several conflicting, often fuzzy criteria with uncertainty conditions, which can benefit from multiple attribute decision-making (MADM). Accordingly, an extended regret theory (RT) decision-making method is developed in this study to identify and rank-order superior stocks. First, by extracting the strengths of probabilistic linguistic term sets and cloud models, a novel concept of probabilistic linguistic cloud sets (PLCSs) is proposed to effectively express and handle uncertain preference information. Second, RT is extended to the PLCSs environment. Considering the behavior characteristics of expectation dependence, dual (target and growth) expectations are shown. Third, a distance measure algorithm of PLCSs is defined to calculate the distance between the attribute value and dual expectations, which serves as the basis for the construction of a fuzzy pattern recognition model to determine the optimal membership and attribute weights. Membership is used to modify the RT-based perceived utility, the ranking of alternatives is determined by the modified comprehensive perceived utility. A case study is conducted to demonstrate the proposed method, and its reliability and effectiveness are further verified by comparing it with other methods.