On lexicographic goal programming method for generating weights from inconsistent interval comparison matrices

In a recent paper by [European Journal of Operational Research 97 (1997) 53-62] the lexicographic goal programming (LGP) method was developed to generate weights from inconsistent interval comparison matrices and a number of its properties and advantages as a weight determination technique were explored. It is shown in this paper that LGP is in fact defective in theory. Although the upper and lower triangular judgments of an inconsistent interval comparison matrix provide exactly the same information on the preferences of weights, in general they lead to distinctive priorities and rankings if LGP is used.