Abstract:
This research work focuses on T-transitive fuzzy orderings, their mathematical
structures and representation results on these orderings. We have shown that the
consistent nature of a fuzzy preference relation has direct relationship with its being
more or less T-transitive. After handling this task, some work is done on applications
of T-transitivity in the area of preference modeling. Here we have presented some
new algorithms to complete an incomplete fuzzy preference relation. These
algorithms are based on T-transitivity of a given fuzzy relation. This work has its
roots in multi criteria and multi agent decision making. The target is to achieve a
ranking among alternatives while incomplete information is provided by the judges
about criteria of selection and pair wise preferences amongst alternatives. We have
further extended these results to their interval valued versions where the consistent
and consensus degrees are also accommodated. The theory and algorithms provided
so far are then used to solve real life problems of industry i.e., the problem of supplier
selection in the supply chain management where the successful implementation of the
results is demonstrated.
