The use of hesitant fuzzy linguistic term sets (HFLTS) contributes to the elicitation of comparative linguistic expressions (CLEs) in decision contexts when experts hesitate among different linguistic terms to provide their assessments. Since the existing representation models for linguistic expressions based on HFLTS do not properly consider the uncertainty caused by the inherent vagueness of such linguistic expressions, it is necessary to improve their modeling to cope with such vagueness. In this paper, we propose a new fuzzy envelope for the HFLTS in form of type-2 fuzzy sets for representing CLEs. Such an envelope overcomes the limitation of existing representations in coping with inherent uncertainties and facilitates the processes of computing with words for linguistic decision making problems dealing with CLEs.

The research on incomplete fuzzy soft sets is an integral part of the research on fuzzy soft sets and has been initiated recently. In this work, we first point out that an existing approach to predicting unknown data in an incomplete fuzzy soft set suffers from some limitations and then we propose an improved method. The hidden information between both objects and parameters revealed in our approach is more comprehensive. Furthermore, based on the similarity measures of fuzzy sets, a new adjustable object-parameter approach is proposed to predict unknown data in incomplete fuzzy soft sets. Data predicting converts an incomplete fuzzy soft set into a complete one, which makes the fuzzy soft set applicable not only to decision making but also to other areas. The compared results elaborated through rate exchange data sets illustrate that both our improved approach and the new adjustable object-parameter one outperform the existing method with respect to forecasting accuracy.

In most real-life decision-making situations, experts tend to utilize linguistic information rather than numerical values to express their preferences or evaluations on alternatives. Considering the complexity of the decision-making problems, it is usually difficult to use single linguistic terms to elicit experts' preferences. Linguistic expressions that are close to cognition of human-being, such as comparative linguistic expression (CLE), are suggested to be applied in such cases. Three-way decision (3WD) has been proved an effective manner to handle multi-attribute decision-making (MADM) problems, however there is a lack of 3WD methods dealing with linguistic expressions. By combining CLE and 3WD, a new multi-attribute three-way group decision-making (3WGDM) method incorporating CLE (called CLE-3WGDM method) is proposed. A novel personalized numerical scale (PNS) computation method, based on pre-decision in 3WGDM, is introduced to manage diverse interpretations of CLE for different individuals. Afterwards, the attribute weights are calculated through a novel optimization model, which applies the principle of deviation maximization and minimum entropy of CLE. A novel 3WD-social network method is presented to compute the weights of experts. Comparative analysis with other existing methods have been carried out to verify the feasibility of the proposed one. Finally, the CLE-3WGDM method is applied to a traditional Chinese medicine (TCM) decision problem.