Consistency based estimation of fuzzy linguistic preferences. The case of reciprocal intuitionistic fuzzy preference relations

The decision-making assumption of all experts being able to express their preferences on all available alternatives of a decision-making problem might be considered unrealistic. This is specially true when the number of alternatives is considerable high and/or when sources of information are conflicting and dynamic. Thus, the presence of incomplete information, which is not equivalent to low quality information, is worth investigation and its processing within decision-making processes desirable. A consistency based approach to deal with incomplete fuzzy linguistic preferences is the focus of this contribution. Consistency is considered here as linked to the transitivity of preferences, and in particular to Tanino’s multiplicative transitivity property of reciprocal fuzzy preference relations. The first result presented is the formal modelling and representation of Tanino’s multiplicative transitivity property to the case of fuzzy linguistic preference relations. This is done via Zadeh’s extension principle and the representation theorem of fuzzy sets. The second result derives the multiplicative transitivity property of reciprocal intuitionistic fuzzy preference relations, which can be isomorphically mapped to a particular type of linguistic preference relation: reciprocal interval-valued fuzzy preference relations. The third result is the computation of the consistency based estimated reciprocal intuitionistic fuzzy preference values using an indirect chain of alternatives, which can be used to address incomplete information in decision-making problems with this type of preference relations.