arXiv subjects

Giorgio Nordo

Publications and source records attributed to Giorgio Nordo.

11 recordsLinked to original sources

arXiv2024

A Python Framework Enhancement for Neutrosophic Topologies

This paper introduces an extension to the Python Neutrosophic Sets (PYNS) framework, originally detailed in Nordo et al. 2024, with the addition of the NSfamily class for constructing and manipulating neutrosophic topologies. Building on existing classes like NSuniverse and NSset, the NSfamily class enables the definition and testing of neutrosophic families as basis and sub-basis for neutrosophic topological spaces. This extension provides tools for verifying closure properties under union and intersection, and for determining whether a given family constitutes a neutrosophic topology. Through implemented algorithms, the framework automates the generation of topologies from families of neutrosophic sets, offering an efficient tool for advancing research in neutrosophic topology. Practical applications are demonstrated with detailed examples, showcasing how this class enhances the scope and flexibility of neutrosophic modeling within the PYNS framework.

math.GM↗

arXiv2024

A Python Framework for Neutrosophic Sets and Mappings

In this paper we present an open source framework developed in Python and consisting of three distinct classes designed to manipulate in a simple and intuitive way both symbolic representations of neutrosophic sets over universes of various types as well as mappings between them. The capabilities offered by this framework extend and generalize previous attempts to provide software solutions to the manipulation of neutrosophic sets such as those proposed by Salama et al., Saranya et al., El-Ghareeb, Topal et al. and Sleem. The code is described in detail and many examples and use cases are also provided.

cs.AI↗

arXiv2021

0-Gaps on 3D Digital Curves

In Digital Geometry, gaps are some basic portion of a digital object that a discrete ray can cross without intersecting any voxel of the object itself. Such a notion is quite important in combinatorial image analysis and it is strictly connected with some applications in fields as CAD and Computer graphics. In this paper we prove that the number of $0$-gaps of a $3$D digital curve can be expressed as a linear combination of the number of its $i$-cells (with $i = 0, \ldots, 3$).

cs.DM↗

arXiv2020

Single Valued Neutrosophic Filters

In this paper we give a comprehensive presentation of the notions of filter base, filter and ultrafilter on single valued neutrosophic set and we investigate some of their properties and relationships. More precisely, we discuss properties related to filter completion, the image of neutrosophic filter base by a neutrosophic induced mapping and the infimum and supremum of two neutrosophic filter bases.

math.GM↗

arXiv2020

On Completion of Metric Mappings

An internal characterization of complete metric mappings (by means of Cauchy nets tied at a point) is given and a construction of the completion of a metric mapping is presented.

math.GN↗

arXiv2020

A Brief Survey on Fibrewise General Topology

We present some recent results in Fibrewise General Topology with special regard to the theory of Tychonoff compactifications of mappings. Several open problems are also proposed.

math.GM↗

arXiv2019

Soft N-Topological Spaces

Very recently, the idea of studying structures equipped with two or more soft topologies has been considered by several researchers. Soft bitopological spaces were introduced and studied, in 2014, by Ittanagi as a soft counterpart of the notion of bitopological space and, independently, in 2015, by Naz, Shabir and Ali. In 2017, Hassan too introduced the concept of soft tritopological spaces and gave some first results. The notion of N-topological space related to ordinary topological spaces was instead introduced and studied, in 2011, by Tawfiq and Majeed. In this paper we introduce the concept of Soft N-Topological Space as generalization both of the concepts of Soft Topological Space and N-Topological Space and we investigate such class of spaces and their basic properties with particular regard to their subspaces, the parameterized families of crisp topologies generated by them and some new separation axioms called N-wise soft T0, N-wise soft T1, and N-wise soft T2.

math.GN↗

arXiv2019

A Soft Embedding Lemma for Soft Topological Spaces

In 1999, Molodtsov initiated the theory of soft sets as a new mathematical tool for dealing with uncertainties in many fields of applied sciences. In 2011, Shabir and Naz introduced and studied the notion of soft topological spaces, also defining and investigating many new soft properties as generalization of the classical ones. In this paper, we introduce the notions of soft separation between soft points and soft closed sets in order to obtain a generalization of the well-known Embedding Lemma to the class of soft topological spaces.

math.GN↗

arXiv2019

An Embedding Lemma in Soft Topological Spaces

In 1999, Molodtsov initiated the concept of Soft Sets Theory as a new mathematical tool and a completely different approach for dealing with uncertainties in many fields of applied sciences. In 2011, Shabir and Naz introduced and studied the theory of soft topological spaces, also defining and investigating many new soft properties as generalization of the classical ones. In this paper, we introduce the notions of soft separation between soft points and soft closed sets in order to obtain a generalization of the well-known Embedding Lemma for soft topological spaces.

math.GN↗

arXiv2012

A formula for the number of (n-2)-gap in digital n-objects

We provide a formula that expresses the number of (n-2)-gaps of a generic digital n-object. Such a formula has the advantage to involve only a few simple intrinsic parameters of the object and it is obtained by using a combinatorial technic based on incidence structure and on the notion of free cells. This approach seems suitable as a model for an automatic computation, and also allow us to find some expressions for the maximum number of i-cells that bound or are bounded by a fixed j-cell.

cs.DM↗

arXiv2005

An explicit formula for the number of tunnels in digital objects

An important concept in digital geometry for computer imagery is that of tunnel. In this paper we obtain a formula for the number of tunnels as a function of the number of the object vertices, pixels, holes, connected components, and 2x2 grid squares. It can be used to test for tunnel-freedom a digital object, in particular a digital curve.

cs.DM↗