This paper introduces an extension to the Python Neutrosophic Sets (PYNS) framework, originally d... more This paper introduces an extension to the Python Neutrosophic Sets (PYNS) framework, originally detailed in [13], 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.
In this paper, we introduce and study the concept of neutrosophic homotopic functions using topol... more In this paper, we introduce and study the concept of neutrosophic homotopic functions using topological properties. Also, we obtain some properties of neutrosophic homotopic functions and concept of neutrosophic homotopy.
The aim of this paper is to introduce the notion of neutrosophic singletons and the induced neutr... more The aim of this paper is to introduce the notion of neutrosophic singletons and the induced neutrosophic topology. We also study some of its basic properties.
In this paper we present an open source framework developed in Python and consisting of three dis... more 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. [21], Saranya et al. [23], El-Ghareeb [7], Topal et al. [29] and Sleem [26]. The code is described in detail and many examples and use cases are also provided.
The notion of fuzzy graph (FG) is widely used in many problems arising from partial or incomplete... more The notion of fuzzy graph (FG) is widely used in many problems arising from partial or incomplete descriptions of the real world and in particular from fields such as engineering, economics, computer science, social disciplines, or medical diagnostics, and has been used in many fields of pure mathematics as well as in several areas of applied sciences such as decision making, statistics and networking. In this paper we will deal with the graph of the picture fuzzy(symmetric) set using the notion of domination in picture fuzzy graph (PFG) as a generalization of both the concept of fuzzy graph domination and intuitionistic fuzzy graph (IFG) domination. The concepts of domination theory (DT) and double domination theory (DDT) of a PFG are introduced, studied and concretely applied to the real case of an election competition to determine the minimum number of citizens a politician should meet in person in order to win the election. The choice of fuzzification (symmetric) and defuzzifica...
The research for treatments and vaccines for novel coronavirus disease (Covid-19) is still going ... more The research for treatments and vaccines for novel coronavirus disease (Covid-19) is still going on. Desperation in the community, particularly among middle and low-income groups who have been hit hard by the economic effects of forced lockdowns, has sparked a surge in interest in alternative medical plant-based therapies. This article attempts to provide evidence summaries examining the potential of complementary therapies in Covid-19 management by studying the findings of some wild medicinal edible plants that have been reported to have antiviral, anti-inflammatory, and immunomodulatory activities. We examine and compare the current growth pattern of covid-19 between tribal and nontribal people in different regions of Kokrajhar, Assam, India where during the Covid-19 pandemic, tribes have increased their use of wild medicinal edible herbs and the recovery rate by Covid-19 is high in comparison to non-tribal people of the same area in order to describe the current state of wild medicinal edible plant use and provide critical recommendations to the relevant authorities. In addition, this study presents a multi-criteria decision making (MCDM) procedure based on the Neutrosophic VIKOR method to survey the region where most wild medicinal edible plants are used and found. Also, with the help of the Neutrosophic VIKOR method, we can identify the regions where most people of the Kokrajhar district is affected and recovered.
In this paper, the notion of generalized neutrosophic soft open set (GNSOS) in neutrosophic soft ... more In this paper, the notion of generalized neutrosophic soft open set (GNSOS) in neutrosophic soft open set (GNSOS) in neutrosophic soft topological structures relative to neutrosophic soft points is introduced.The concept of generalized neutrosophic soft separation axioms in neutrosophic soft topological spaces with respect to soft points. Several related properties, structural characteristics have been investigated. Then the convergence of sequence in neutrosophic soft topological space is defined and its uniqueness in generalized neutrosophic soft Hausdorff space (GNSHS) relative to soft points is examined. Neutrosophic monotonous soft function and its characteristics are switched over to different results. Lastly, generalized neutrosophic soft product spaces with respect to crisp points have been addressed.
It is shown that the P-functions for the topological properties P=T(0 pedice), T (1 pedice), Haus... more It is shown that the P-functions for the topological properties P=T(0 pedice), T (1 pedice), Hausdorff, regular, introduced by Pasynkov in [P(2 pedice)] and P=Urysohn, almost regular, semiregular, introduced by author and Cammaroto in [CN], are productive.
The objective of this paper is to study the algebraic properties of weak fuzzy complex matrices, ... more The objective of this paper is to study the algebraic properties of weak fuzzy complex matrices, where many elementary properties will be obtained such as the invertibility, the determinants, and the eigen values and vectors. In addition, a full solution of linear systems of weak fuzzy complex equations will be provided as an effective and easy algorithm. Also, many examples to clarify the validity of our approach.
In our work, we defined new operations in a new way in connection with vague hyper soft sets. The... more In our work, we defined new operations in a new way in connection with vague hyper soft sets. These operations are vague hyper soft sets, vague hyper soft subsets, vague hyper soft complements, vague hyper soft null sets, vague hyper soft absolute sets, vague hyper soft union and vague hyper soft intersection. On the basis of these new operations vague hyper soft topology is defined. In addition, the concept of some generalized vague hyper soft open sets are reflected in vague hyper soft topology. Among these generalized vague hyper soft open sets vague hyper soft α-open set is selected to produce different structures. Finally, on the basis of this vague hyper soft α-open set some more results are addressed. Non-validity of some results are diffused with appropriate examples.
This paper introduces an extension to the Python Neutrosophic Sets (PYNS) framework, originally d... more This paper introduces an extension to the Python Neutrosophic Sets (PYNS) framework, originally detailed in [13], 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.
In this paper, we introduce and study the concept of neutrosophic homotopic functions using topol... more In this paper, we introduce and study the concept of neutrosophic homotopic functions using topological properties. Also, we obtain some properties of neutrosophic homotopic functions and concept of neutrosophic homotopy.
The aim of this paper is to introduce the notion of neutrosophic singletons and the induced neutr... more The aim of this paper is to introduce the notion of neutrosophic singletons and the induced neutrosophic topology. We also study some of its basic properties.
In this paper we present an open source framework developed in Python and consisting of three dis... more 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. [21], Saranya et al. [23], El-Ghareeb [7], Topal et al. [29] and Sleem [26]. The code is described in detail and many examples and use cases are also provided.
The notion of fuzzy graph (FG) is widely used in many problems arising from partial or incomplete... more The notion of fuzzy graph (FG) is widely used in many problems arising from partial or incomplete descriptions of the real world and in particular from fields such as engineering, economics, computer science, social disciplines, or medical diagnostics, and has been used in many fields of pure mathematics as well as in several areas of applied sciences such as decision making, statistics and networking. In this paper we will deal with the graph of the picture fuzzy(symmetric) set using the notion of domination in picture fuzzy graph (PFG) as a generalization of both the concept of fuzzy graph domination and intuitionistic fuzzy graph (IFG) domination. The concepts of domination theory (DT) and double domination theory (DDT) of a PFG are introduced, studied and concretely applied to the real case of an election competition to determine the minimum number of citizens a politician should meet in person in order to win the election. The choice of fuzzification (symmetric) and defuzzifica...
The research for treatments and vaccines for novel coronavirus disease (Covid-19) is still going ... more The research for treatments and vaccines for novel coronavirus disease (Covid-19) is still going on. Desperation in the community, particularly among middle and low-income groups who have been hit hard by the economic effects of forced lockdowns, has sparked a surge in interest in alternative medical plant-based therapies. This article attempts to provide evidence summaries examining the potential of complementary therapies in Covid-19 management by studying the findings of some wild medicinal edible plants that have been reported to have antiviral, anti-inflammatory, and immunomodulatory activities. We examine and compare the current growth pattern of covid-19 between tribal and nontribal people in different regions of Kokrajhar, Assam, India where during the Covid-19 pandemic, tribes have increased their use of wild medicinal edible herbs and the recovery rate by Covid-19 is high in comparison to non-tribal people of the same area in order to describe the current state of wild medicinal edible plant use and provide critical recommendations to the relevant authorities. In addition, this study presents a multi-criteria decision making (MCDM) procedure based on the Neutrosophic VIKOR method to survey the region where most wild medicinal edible plants are used and found. Also, with the help of the Neutrosophic VIKOR method, we can identify the regions where most people of the Kokrajhar district is affected and recovered.
In this paper, the notion of generalized neutrosophic soft open set (GNSOS) in neutrosophic soft ... more In this paper, the notion of generalized neutrosophic soft open set (GNSOS) in neutrosophic soft open set (GNSOS) in neutrosophic soft topological structures relative to neutrosophic soft points is introduced.The concept of generalized neutrosophic soft separation axioms in neutrosophic soft topological spaces with respect to soft points. Several related properties, structural characteristics have been investigated. Then the convergence of sequence in neutrosophic soft topological space is defined and its uniqueness in generalized neutrosophic soft Hausdorff space (GNSHS) relative to soft points is examined. Neutrosophic monotonous soft function and its characteristics are switched over to different results. Lastly, generalized neutrosophic soft product spaces with respect to crisp points have been addressed.
It is shown that the P-functions for the topological properties P=T(0 pedice), T (1 pedice), Haus... more It is shown that the P-functions for the topological properties P=T(0 pedice), T (1 pedice), Hausdorff, regular, introduced by Pasynkov in [P(2 pedice)] and P=Urysohn, almost regular, semiregular, introduced by author and Cammaroto in [CN], are productive.
The objective of this paper is to study the algebraic properties of weak fuzzy complex matrices, ... more The objective of this paper is to study the algebraic properties of weak fuzzy complex matrices, where many elementary properties will be obtained such as the invertibility, the determinants, and the eigen values and vectors. In addition, a full solution of linear systems of weak fuzzy complex equations will be provided as an effective and easy algorithm. Also, many examples to clarify the validity of our approach.
In our work, we defined new operations in a new way in connection with vague hyper soft sets. The... more In our work, we defined new operations in a new way in connection with vague hyper soft sets. These operations are vague hyper soft sets, vague hyper soft subsets, vague hyper soft complements, vague hyper soft null sets, vague hyper soft absolute sets, vague hyper soft union and vague hyper soft intersection. On the basis of these new operations vague hyper soft topology is defined. In addition, the concept of some generalized vague hyper soft open sets are reflected in vague hyper soft topology. Among these generalized vague hyper soft open sets vague hyper soft α-open set is selected to produce different structures. Finally, on the basis of this vague hyper soft α-open set some more results are addressed. Non-validity of some results are diffused with appropriate examples.
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Papers by Giorgio NORDO