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.