Fuzzy Relations and Monometrics: Some Correspondences
Megha Gupta, Balasubramaniam Jayaram · Atlantis studies in uncertainty modelling/Atlantis Studies in Uncertainty Modelling · 2021
Fuzzy relations that are not T -transitive have not merited as much scrutiny as their Ttransitive counterparts.Recently monometrics on a given betweenness set, or a B-set, has garnered a lot of attention, especially for their role in decision making and penalty based data aggregation.In this work, we show that from non strict T -transitive relations one can obtain both betweenness relations, satisfying various types of transitivities, and monometrics on them.In fact, it can be shown that the natural or canonical betweenness obtained from a given distance function can be seen as being obtained from an appropriate non strict T -transitive similarity relation.Further, a typical practical problem in this context is that of obtaining a monometric on a given B-set.Our investigations show that there exists a oneone correspondence between non strict Ttransitive similarity relations and monometrics defined on the given B-set.This study, thus, shows the usefulness of non strict Ttransitive fuzzy relations as much as their Ttransitive counterparts.