Type-2 Fuzzy Envelope of Hesitant Fuzzy Linguistic Term Set: A New Representation Model of Comparative Linguistic Expression

Abstract

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.