In real-world recognition/classification tasks, limited by various objective factors, it is usually difficult to collect training samples exhaust all classes when a recognizer or classifier. A more realistic scenario open set recognition (OSR), where incomplete knowledge of the world exists at time, and unknown can be submitted an algorithm during testing, requiring classifiers not only accurat...

Open Set Recognition (OSR) has been an emerging topic. Besides recognizing predefined classes, the system needs to reject unknowns. Prototype learning is a potential manner handle problem, as its ability improve intra-class compactness of representations much needed in discrimination between known and In this work, we propose novel Mining And Learning (PMAL) framework. It prototype mining mecha...

In inference, open-set classification is to either classify a sample into known class from training or reject it as an unknown class. Existing deep classifiers train explicit closed-set classifiers, in some cases disjointly utilizing reconstruction, which we find dilutes the latent representation's ability distinguish classes. contrast, our model cooperatively learn reconstruction and perform c...

In this paper, we introduce fuzzy Banach algebra and study the properties of invertible elements and its relation with opensets. We obtain some interesting results.

For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a suffici...

The aim of this paper is to introduce and obtain some characterizations of weakly $e$-irresolute functions by means of $e$-open sets defined by Ekici [6]. Also, we look into further properties relationships between weak $e$-irresoluteness and separation axioms and completely $e$-closed graphs.

ABSTRACT Let ‎G=(V,E) ‎be a‎ ‎simple ‎connected ‎graph ‎with ‎vertex ‎set ‎V‎‎‎ ‎and ‎edge ‎set ‎‎‎E. ‎The Szeged index ‎of ‎‎G is defined by ‎ where ‎ respectively ‎ ‎ is the number of vertices of ‎G ‎closer to ‎u‎ (‎‎respectively v)‎ ‎‎than ‎‎‎v (‎‎respectively u‎).‎ ‎‎If ‎‎‎‎S ‎is a‎ ‎set ‎of ‎size‎ ‎ ‎ ‎let ‎‎V ‎be ‎the ‎set ‎of ‎all ‎subsets ‎of ‎‎S ‎of ‎size ‎3. ‎Then ‎we ‎define ‎t...