Ciències Matemàtiques i Informàtica http://hdl.handle.net/11201/256 2020-09-26T19:29:31Z A Duality Relationship Between Fuzzy Partial Metrics and Fuzzy Quasi-Metrics http://hdl.handle.net/11201/153431 A Duality Relationship Between Fuzzy Partial Metrics and Fuzzy Quasi-Metrics Gregori, Valentín; Miñana, Juan-José; Miravet, David [eng] In 1994, Matthews introduced the notion of partial metric and established a duality relationship between partial metrics and quasi-metrics defined on a set X. In this paper, we adapt such a relationship to the fuzzy context, in the sense of George and Veeramani, by establishing a duality relationship between fuzzy quasi-metrics and fuzzy partial metrics on a set X, defined using the residuum operator of a continuous t-norm . Concretely, we provide a method to construct a fuzzy quasi-metric from a fuzzy partial one. Subsequently, we introduce the notion of fuzzy weighted quasi-metric and obtain a way to construct a fuzzy partial metric from a fuzzy weighted quasi-metric. Such constructions are restricted to the case in which the continuous t-norm is Archimedean and we show that such a restriction cannot be deleted. Moreover, in both cases, the topology is preserved, i.e., the topology of the fuzzy quasi-metric obtained coincides with the topology of the fuzzy partial metric from which it is constructed and vice versa. Besides, different examples to illustrate the exposed theory are provided, which, in addition, show the consistence of our constructions comparing it with the classical duality relationship. On t-Conorm Based Fuzzy (Pseudo)metrics http://hdl.handle.net/11201/153430 On t-Conorm Based Fuzzy (Pseudo)metrics Grigorenko, O.; Miñana, J.J.; Sostak, A.; Valero, O. [eng] We present an alternative approach to the concept of a fuzzy (pseudo)metric using t-conorms instead of t-norms and call them t-conorm based fuzzy (pseudo)metrics or just CB-fuzzy (pseudo)metrics. We develop the basics of the theory of CB-fuzzy (pseudo)metrics and compare them with 'classic' fuzzy (pseudo)metrics. A method for construction CB-fuzzy (pseudo)metrics from ordinary metrics is elaborated and topology induced by CB-fuzzy (pseudo)metrics is studied. We establish interrelations between CB-fuzzy metrics and modulars, and in the process of this study, a particular role of Hamacher t-(co)norm in the theory of (CB)-fuzzy metrics is revealed. Finally, an intuitionistic version of a CB-fuzzy metric is introduced and applied in order to emphasize the roles of t-norms and a t-conorm in this context. Asymptotic dynamics of a difference equation with a parabolic equilibrium http://hdl.handle.net/11201/153249 Asymptotic dynamics of a difference equation with a parabolic equilibrium Coll, B.; Gasull, A.; Prohens, R. [eng] The aim of this work is the study of the asymptotic dynamical behaviour, of solutions that approach parabolic fixed points in difference equations. In one dimensional difference equations, we present the asymptotic development for positive solutions tending to the fixed point. For higher dimensions, through the study of two families of difference equations in the two and three-dimensional case, we take a look at the asymptotic dynamic behaviour. To show the existence of solutions we rely on the parametrization method. UIBVFED: Virtual facial expression dataset http://hdl.handle.net/11201/153181 UIBVFED: Virtual facial expression dataset Mascaró Oliver, Miquel; Amengual Alcover, Esperança [eng] Facial expression classification requires large amounts of data to reflect the diversity of conditions in the real world. Public databases support research tasks providing researchers an appropriate work framework. However, often these databases do not focus on artistic creation. We developed an innovative facial expression dataset that can help both artists and researchers in the field of affective computing. This dataset can be managed interactively by an intuitive and easy to use software application. The dataset is composed of 640 facial images from 20 virtual characters each creating 32 facial expressions. The avatars represent 10 men and 10 women, aged between 20 and 80, from different ethnicities. Expressions are classified by the six universal expressions according to Gary Faigin classification.