We obtain a principal topology and some related results. We also give some hints of possible applications. Some mathematical systems are both lattice and topological space. We show that a topology defined on the any bounded lattice is definable in terms of uninorms. Also, we see that these topologies satisfy the condition of the principal topology. These topologies can not be metrizable except for the discrete metric case. We show an equivalence relation on the class of uninorms on a bounded lattice based on equality of the topologies induced by uninorms.
In this survey we consider superlinear parabolic problems which possess both blowing-up and global solutions and we study a priori estimates of global solutions.
We present an approach for probabilistic contour prediction within the framework of an object tracking system. We combine level-set methods for image segmentation with optical flow estimations based on probability distribution functions (pdfs) calculated at each image position. Unlike most recent level-set methods that consider exclusively the sign of the level-set function to determine an object and its background, we introduce a novel interpretation of the value of the level-set function that reflects the confidence in the contour. To this end, in a sequence of consecutive images, the contour of an object is transformed according to the optical flow estimation and used as the initial object hypothesis in the following image. The values of the initial level-set function are set according to the optical flow pdfs and thus provide an opportunity to incorporate the uncertainties of the optical flow estimation in the object contour prediction.
The aim of this paper is to propose a new approach to probability density function (PDF) estimation which is based on the fuzzy transform (F-transform) introduced by Perfilieva in \cite{Perfilieva:FSS06}. Firstly, a smoothing filter based on the combination of the discrete direct and continuous inverse F-transform is introduced and some of the basic properties are investigated. Next, an alternative approach to PDF estimation based on the proposed smoothing filter is established and compared with the most used method of Parzen windows. Such an approach can be of a great value mainly when dealing with financial data, i. e. large samples of observations.
In [6] we proved that tlie monoidal t-norm logic MTL introduced by
Esteva and Godo in [4] is the logic of left-continuons t-norms and their residuals. Recently, the Ruinenian school, P. Hájek and others investigated in deep noncommutative t-norms. Tlins it is natural to look for the logic of left-continuons non-commutative t-norms. This is precisely what we do in this paper. The proof is a combination of the inethod used in [6] and of results by .J. Kühn in [13] and by P. Hájek in [9].