E. Wajch | Searcharxiv

arXiv2017

Inconsistency indicator maps on groups for pairwise comparisons

This study presents an abelian group approach to analyzing inconsistency in pairwise comparisons. However, it wrongly assumes that an inconsistency indicator can take values in any abelian linearly ordered group. The followup publication (On normalization of inconsistency indicators in pairwise comparisons, a collaboration which includes two of three authors of this publication) shows that any inconsistency indicator should be normalized for a number of practical and theoretical reasons. The publication below fails to demonstrate even one example of a non trivial group (other than a group consisting of real numbers. However, some obtained results (under erroneous assumptions) are still valid.

cs.DM↗

arXiv2014

Quasi-Metrizability of Bornological Biuniverses in ZF

Hu's metrization theorem for bornological universes is shown to hold in ZF and it is adapted to a quasi-metrization theorem for bornologies in bitopological spaces. The problem of uniform quasi-metrization of quasi-metric bornological universes is investigated. Several consequences for natural bornologies in generalized topological spaces in the sense of Delfs and Knebusch are deduced. Some statements concerning (uniform)-(quasi)-metrization of bornologies are shown to be relatively independent of ZF.

math.GN↗