Connectedness on Hypersoft Topological Spaces PDF Download

Author: Sagvan Y. Musa
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 15

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Book Description
Connectedness (resp. disconnectedness), which reflects the key characteristic of topological spaces and helps in the differentiation of two topologies, is one of the most significant and fundamental concept in topological spaces. In light of this, we introduce hypersoft connectedness (resp. hypersoft disconnectedness) in hypersoft topological spaces and investigate its properties in details.

Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 970

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Book Description
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation and with their spectrum of neutralities in between them (i.e. notions or ideas supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic).

Author: D. Ajay
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 16

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Book Description
Hypersoft set is a generalization of soft sets, which takes into account a multiargument function. The main objective of this work is to introduce fuzzy semiopen and closed hypersoft sets and study some of their characterizations and also to present neutrosophic semiopen and closed hypersoft sets, an extension of fuzzy hypersoft sets, along with few basic properties. We propose two algorithms based on neutrosophic hypersoft open sets and topology to obtain optimal decisions in MAGDM. The efficiency of the algorithms proposed is demonstrated by applying them to the current COVID-19 scenario.

Author: Sagvan Y. Musa
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 16

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Book Description
According to its definition, a topological space could be a highly unexpected object. There are spaces (indiscrete space) which have only two open sets: the empty set and the entire space. In a discrete space, on the other hand, each set is open. These two artificial extremes are very rarely seen in actual practice. Most spaces in geometry and analysis fall somewhere between these two types of spaces. Accordingly, the separation axioms allow us to say with confidence whether a topological space contains a sufficient number of open sets to meet our needs. To this end, we use bipolar hypersoft (BHS) sets (one of the efficient tools to deal with ambiguity and vagueness) to define a new kind of separation axioms called BHS e Ti-space (i = 0, 1, 2, 3, 4).

Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 246

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Book Description
Florentin Smarandache generalize the soft set to the hypersoft set by transforming the function 𝐹 into a multi-argument function. This extension reveals that the hypersoft set with neutrosophic, intuitionistic, and fuzzy set theory will be very helpful to construct a connection between alternatives and attributes. Also, the hypersoft set will reduce the complexity of the case study. The Book “Theory and Application of Hypersoft Set” focuses on theories, methods, algorithms for decision making and also applications involving neutrosophic, intuitionistic, and fuzzy information. Our goal is to develop a strong relationship with the MCDM solving techniques and to reduce the complexion in the methodologies. It is interesting that the hypersoft theory can be applied on any decision-making problem without the limitations of the selection of the values by the decision-makers. Some topics having applications in the area: Multi-criteria decision making (MCDM), Multi-criteria group decision making (MCGDM), shortest path selection, employee selection, e-learning, graph theory, medical diagnosis, probability theory, topology, and some more.

Author: Adem Yolcu
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 14

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Book Description
The aim of this paper is to introduce the concept of intuitionistic fuzzy hypersoft topology. Certain properties of intuitionistic fuzzy hypersoft (IFH) topology like IFH b asis, IFH subspace, IFH interior and IFH cloure are investigated. Furthermore, the multicriteria decision making (MCDM) algorithms with aggregation operators based on IFH topology are developed. In Algorithm 1 and Algorithm 2, MCDM problem is applied for IFH sets and IFH topology, respectively. Any real-life implementations of the proposed MCDM algorithms are demonstrated by numerical illustrations.

Author: S. C. Sharma
Publisher: Discovery Publishing House
ISBN: 9788183561211
Category : Topology
Languages : en
Pages : 336

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Book Description
Contents: Connectedness, Topology Space, Continuity and Homeomorphism, Algebraic Systems, Separation Axioms.

Author: Victor Christianto
Publisher: Infinite Study
ISBN:
Category : Science
Languages : en
Pages : 10

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Book Description
Following our preceding article, where we discussed alternative interpretations of the advanced perihelion of Mercury, the present article revisits the 1919 solar eclipse expedition led by Arthur Eddington, which famously provided the first observational confirmation of Einstein's theory of general relativity. We focus on the deflection of starlight data obtained during the eclipse, a cornerstone of this validation. Here, we explore three alternative explanations for the observed light bending that challenge the sole attribution to general relativity. Firstly, the paper begins by arguing based on criticisms raised by Tullio Levi-Civita, a contemporary mathematician, regarding Einstein's use of pseudo-tensors in his calculations. Levi-Civita argued that this approach introduced unnecessary complexity and obscured alternative interpretations of the data. Secondly, we delve into astrophysical phenomena that could mimic the observed light deflection, based on the varying speed of light, by assuming a photon has mass. (cf. ‘t Hooft et al., Light is Heavy). Moreover, in the literature, Molodtsov initiated soft set theory as an extension of fuzzy set theory to deal with uncertainties occurring in the natural and social sciences. It attracted the attention of mathematicians as well as social scientists due to its potential to unify certain mathematical aspects and applications in decision making processes; therefore, we shall discuss a bit how to model the photon as an extended massive particle of light, possibly related to such a soft set point [15, 16]. For further exploration, it is possible to assume the crystalline lattice of subvacuum structure (cf. Gremaud) as part of hypersoft topological spaces [16, 16a]. We strongly believe that the true strength of science lies in its continuous search for evidence and refinement of existing models. Therefore, it can be expected that new data can be helpful to reevaluate these matters, for instance, in the upcoming eclipse in the next month of 2024.

Author: Ahu Acikgoz
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 5

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Book Description
In this study, we introduce the concept of neutrosophic connectedness and give some of its characterizations. Additionally, we present neutrosophic product space and show that this type of connectedness is not preserved under neutrosophic product spaces. We also introduce the notions of neutrosophic super-connected spaces, neutrosophic strongly connected spaces and study their properties.

Author: Sagvan Y. Musa
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 14

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Book Description
In this article, we introduce bipolar hypersoft topological spaces over the collection of bipolar hypersoft sets. It is proven that a bipolar hypersoft topological space gives a parametrized family of hypersoft topological spaces, but the converse does not hold in general, and this is shown with the help of an example. Furthermore, we give a condition on a given parametrized family of hypersoft topologies, which assure that there is a bipolar hypersoft topology whose induced family of hypersoft topologies is the given family. The notions of bipolar hypersoft neighborhood, bipolar hypersoft subspace, and bipolar hypersoft limit points are introduced. Finally, we define bipolar hypersoft interior, bipolar hypersoft closure, bipolar hypersoft exterior, and bipolar hypersoft boundary, and the relations between them, differing from the relations on hypersoft topology, are investigated.