Generating HFLTS possibility distribution with an embedded assessing attitude

Possibility distribution provides an alternative explanation of linguistic terms in an hesitant fuzzy linguistic term set (HFLTS). It is generated from a given HFLTS based on the assumption that all linguistic terms in an HFLTS follow a uniform distribution. In decision making contexts, linguistic terms in each HFLTS are assumed to exhibit the same possibility to represent the decision-maker(DM)'s assessment rating. However, DMs may give ratings based on different assessing attitudes because of individual differences in cognitive styles. In practice, comparative linguistic expressions are generally converted into HFLTSs through the transformation process as DMs usually use comparative linguistic expressions instead of HFLTSs when giving ratings. The transformed HFLTSs likewise exclude the DMs' assessing attitudes. To enhance the interpretability of generated possibility distributions, this paper relaxes the original assumption of uniform distribution and incorporates an attitudinal dimension into the transformation process that converts comparative linguistic expressions to HFLTSs. With these modified conditions for possibility distribution generation, an assessing attitude-driven approach is proposed based on probability density functions (PDFs) to generate HFLTS possibility distributions. The proposed PDF-based HFLTS possibility distributions personalize individual semantics and further facilitate the process of computing with words to obtain assessing attitude-embedded accurate linguistic results that are easy for individuals to interpret and understand.