Incomplete fuzzy linguistic preference relations under uncertain environments

When addressing decision-making problems, decision-makers typically express their opinions using fuzzy preference relations. In some instances, decision-makers may have to deal with the problems in which only partial information is available. Consequently, decision-makers embody their preferences as incomplete fuzzy preference relations. The values of incomplete fuzzy preference relations have been considered crisp in recent studies. To allow decision-makers to provide vague or imprecise responses, this study proposes a novel method, called incomplete fuzzy linguistic preference relations, that uses fuzzy linguistic assessment variables instead of crisp values of incomplete fuzzy preference relations to ensure comparison consistency. The proposed method reflects an environment in which some uncertainty or vagueness exists. Examples are included that illustrate the effectiveness of the proposed method.