A distance-based framework to deal with ordinal and additive inconsistencies for fuzzy reciprocal preference relations

Consistency of preference relations is related to rationality, the lack of consistency in decision making often leads to misleading solutions. This paper studies the ordinal and cardinal consistency problems of fuzzy reciprocal preference relations. First, the concept of ordinal consistency of fuzzy reciprocal preference relations is introduced and analyzed. A lp distance-based method is proposed to formulate the underlying optimization problems as goal programming (GP) models for ordinal and additive consistency problems respectively. By setting different p, three GP models are obtained: (a) a linear GP model where p = 1; (b) a MINMAX GP model, where p = ∞; and (c) an extended GP model, which integrates the two previous models in particular cases. Utilizing these models, we can solve the ordinal and additive consistency problems for fuzzy reciprocal preference relations. The proposed model can preserve the initial preference information as much as possible. Finally, a numerical example and comparative analysis are provided to show effectiveness and validity of the proposed method.