The aim of this paper is to introduce fuzzy ($e$, almost) $e^{*}$-regular spaces in $check{S}$ostak's fuzzy topological spaces. Using the $r$-fuzzy $e$-closed sets, we define $r$-($r$-$theta$-, $r$-$etheta$-) $e$-cluster points and their properties. Moreover, we investigate the relations among $r$-($r$-$theta$-, $r$-$etheta$-) $e$-cluster points, $r$-fuzzy ($e$, almost) $e^{*}$-regular spaces a...

We show that if a real x ∈ 2 is Hausdorff H-random, where h is an order function, then it is also random for a continuous probability measure μ such that the μ-measure of the basic open cylinders shrinks according to h. We use this result to derive a characterization of effective Hausdorff dimension similar to Frostman’s Theorem.

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Let G be a nonempty closed (resp. bounded closed) subset in a strongly convex Banach space X. Let BðXÞ denote the space of all nonempty bounded closed subsets of X endowed with the Hausdorff distance and let BGðXÞ denote the closure of the set fA 2 BðXÞ : A \ G 1⁄4 ;g. We prove that E(G) (resp. Eo(G)), the set of all A 2 BGðXÞ (resp. A 2 BðXÞ) such that the minimization (resp. maximization) pro...

We propose a new approach for semi-supervised learning using closed set lattices, which have been recently used for frequent pattern mining within the framework of the data analysis technique of Formal Concept Analysis (FCA). We present a learning algorithm, called SELF (SEmi-supervised Learning via FCA), which performs as a multiclass classifier and a label ranker for mixed-type data containin...

For a given transitive binary relation e on a set E, the transitive closures of open (i.e., co-transitive in e) sets, called the regular closed subsets, form an ortholattice Reg(e), the extended permutohedron on e. This construction, which contains the poset Clop(e) of all clopen sets, is a common generalization of known notions such as the generalized permutohedron on a partially ordered set o...

Digital signatures have been a hot topic in the e-government era as a key enabler for e-services provided to business and citizens, and secure exchange of e-documents. When this exchange crosses the borders of closed systems or EU’s Member States several interoperability issues arise. In EU many schemes and solutions have been proposed to overcome some problems, yet there is still more to be do...

in this paper, the dual area vector of a closed dual spherical curve is kinematically generatedand the dual steineer vector of a motion are extensively studied by the methods of differential geometry.jacobi’s theorems, known for real curves, are investigated for closed dual curves. the closed trajectorysurfaces generated by an oriented line are fixed in a moving rigid body in ir3 , in which the...