Consistency measures of linguistic preference relations with hedges

Modeling linguistic information is vital for qualitative decision making (QDM). Compared with single linguistic terms, the complex linguistic expressions (CLEs) are more powerful and flexible to express linguistic opinions under uncertainties. Among the existing types of CLEs, the linguistic terms with weakened hedges (LTWHs), which focus on the uncertainty of using single terms, can be used to model the linguistic expressions in natural languages. This paper concentrates on the application of LTWHs in the framework of QDM with preference relations. The concept of linguistic preference relations with hedges (LHPRs) are presented after a new computational model of LTWHs is formed. Some consistency concepts, such as weak consistency and additive consistency, are then defined and their properties are studied. Especially, the theories and algorithms for consistency checking and improving are proposed. Different from many studies related to consistency measure, we make use of fuzzy weighted digraphs to develop the theories and algorithms in a visible manner. Moreover, for consistency improving, the degree of consistency are measured by linguistic terms rather than numerical values so that the threshold of satisfactory consistency is interpretable and can be easily determined.