Reciprocal transitive matrices over abelian linearly ordered groups: Characterizations and application to multi-criteria decision problems

We consider reciprocal matrices over an abelian linearly ordered group; in this way we provide a general framework including multiplicative, additive and fuzzy matrices. In a multi-criteria decision making context, a pairwise comparison matrix A=(aij) is a reciprocal matrix that represents a useful tool for determining a weighting vector w for a set X of decision elements; but, when A is inconsistent, the weighting vector, usually proposed in...