The categorical treatment of fuzzy modules presents some problems, due to the well known fact that category is not abelian, and even normal. Our aim give a representation inside generalized modules, in fact, functor category, Mod−P, which Grothendieck category. To do that, first we consider preadditive P, defined by interval P=(0,1], build torsionfree class J hereditary torsion theory finally i...

Impossibility results show that important fairness measures (independence, separation, sufficiency) cannot be satisfied at the same time under reasonable assumptions. This paper explores whether we can satisfy and/or improve these simultaneously to a certain degree. We introduce information-theoretic formulations of and define degrees based on formulations. The suggest unexplored theoretical re...

Gradual semantics are now well-studied in the computational argumentation literature. In this paper, we argue that gradual can handle both bipolarity (e.g. attacks and supports) sets of attacking arguments (i.e. several together an argument) might be useful some contexts. We define formal framework properties for such semantics. proceed by adapting, studying implementing three well-known from b...

Federated averaging (FedAvg) is a popular federated learning (FL) technique that updates the global model by local models and then transmits updated to devices for their update. One main limitation of FedAvg average-based not necessarily better than in early stage training process so might diverge realistic scenarios, especially when data non-identically distributed across number samples varies...

Search for an improved gear tooth flank shape arose from heavy industry problems rolling mills. Original involute gears suffered severe damages. So, better teeth flanks should improve contact circumstances, decrease the pressure, and enhance a lubrication film. This was achieved by curved, pole symmetric path of purely graphical methods. And developed gears, proven in applications, showed highl...