Neutrosophic Superhyperalgebra And New Types Of Topologies

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Neutrosophic SuperHyperAlgebra and New Types of Topologies

Florentin Smarandache,Memet Şahin,Derya Bakbak,Vakkas Uluçay,Abdullah Kargın
Neutrosophic SuperHyperAlgebra and New Types of Topologies Book PDF

Author : Florentin Smarandache,Memet Şahin,Derya Bakbak,Vakkas Uluçay,Abdullah Kargın
Publisher : Infinite Study
Page : 254 pages
File Size : 44,5 Mb
Release : 2023-09-01
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic SuperHyperAlgebra and New Types of Topologies by Florentin Smarandache,Memet Şahin,Derya Bakbak,Vakkas Uluçay,Abdullah Kargın Pdf

In general, a system S (that may be a company, association, institution, society, country, etc.) is formed by sub-systems Si { or P(S), the powerset of S }, and each sub-system Si is formed by sub-sub-systems Sij { or P(P(S)) = P2(S) } and so on. That’s why the n-th PowerSet of a Set S { defined recursively and denoted by Pn(S) = P(Pn-1(S) } was introduced, to better describes the organization of people, beings, objects etc. in our real world. The n-th PowerSet was used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order to build the SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one in fact encounters SuperHyperStructures. Also, six new types of topologies have been introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology.

New Type Hyper Groups, New Type SuperHyper Groups and Neutro-New Type SuperHyper Groups

Abdullah Kargın,Florentin Smarandache,Memet Şahin
New Type Hyper Groups New Type SuperHyper Groups and Neutro New Type SuperHyper Groups Book PDF

Author : Abdullah Kargın,Florentin Smarandache,Memet Şahin
Publisher : Infinite Study
Page : 15 pages
File Size : 43,8 Mb
Release : 2023-01-01
Category : Mathematics
ISBN : 8210379456XXX

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New Type Hyper Groups, New Type SuperHyper Groups and Neutro-New Type SuperHyper Groups by Abdullah Kargın,Florentin Smarandache,Memet Şahin Pdf

In this chapter, a new type Hyper groups are defined, corresponding basic properties and examples for new type Hyper groups are given and proved. Moreover, new type Hypergroups groups and are compared to hyper groups and groups. New type Hyper groups are shown to have a more general structure according to Hyper groups and groups. Also, new type SuperHyper groups are defined, corresponding basic properties and examples for new type SuperHyper are given and proved. Furthermore, we defined neutro-new type SuperHyper groups.

New Single-Valued Neutrosophic Rough Sets and Related Topology

Qiu Jin,Kai Hu, Chunxin Bo,Lingqiang Li
New Single Valued Neutrosophic Rough Sets and Related Topology Book PDF

Author : Qiu Jin,Kai Hu, Chunxin Bo,Lingqiang Li
Publisher : Infinite Study
Page : 14 pages
File Size : 43,9 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 8210379456XXX

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New Single-Valued Neutrosophic Rough Sets and Related Topology by Qiu Jin,Kai Hu, Chunxin Bo,Lingqiang Li Pdf

(Fuzzy) rough sets are closely related to (fuzzy) topologies. Neutrosophic rough sets and neutrosophic topologies are extensions of (fuzzy) rough sets and (fuzzy) topologies, respectively. In this paper, a new type of neutrosophic rough sets is presented, and the basic properties and the relationships to neutrosophic topology are discussed.

Data-Driven Modelling with Fuzzy Sets

Said Broumi,D. Nagarajan,Michael Gr. Voskoglou,S. A. Edalatpanah
Data Driven Modelling with Fuzzy Sets Book PDF

Author : Said Broumi,D. Nagarajan,Michael Gr. Voskoglou,S. A. Edalatpanah
Publisher : CRC Press
Page : 348 pages
File Size : 45,7 Mb
Release : 2024-07-17
Category : Computers
ISBN : 9781040043066

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Data-Driven Modelling with Fuzzy Sets by Said Broumi,D. Nagarajan,Michael Gr. Voskoglou,S. A. Edalatpanah Pdf

Zadeh introduced in 1965 the theory of fuzzy sets, in which truth values are modelled by numbers in the unit interval [0, 1], for tackling mathematically the frequently appearing in everyday life partial truths. In a second stage, when membership functions were reinterpreted as possibility distributions, fuzzy sets were extensively used to embrace uncertainty modelling. Uncertainty is defined as the shortage of precise knowledge or complete information and possibility theory is devoted to the handling of incomplete information. Zadeh articulated the relationship between possibility and probability, noticing that what is probable must preliminarily be possible. Following the Zadeh’s fuzzy set, various generalizations (intuitionistic, neutrosophic, rough, soft sets, etc.) have been introduced enabling a more effective management of all types of the existing in real world uncertainty. This book presents recent theoretical advances and applications of fuzzy sets and their extensions to Science, Humanities and Education. This book: Presents a qualitative assessment of big data in the education sector using linguistic Quadri partitioned single valued neutrosophic soft sets. Showcases application of n-cylindrical fuzzy neutrosophic sets in education using neutrosophic affinity degree and neutrosophic similarity Index. Covers scientific evaluation of student academic performance using single value neutrosophic Markov chain. Illustrates multi-granulation single-valued neutrosophic probabilistic rough sets for teamwork assessment. Examines estimation of distribution algorithm based on multiple attribute group decision-making to evaluate teaching quality. It is primarily written for Senior undergraduate and graduate students and academic researchers in the fields of electrical engineering, electronics and communication engineering, computer science and engineering.

Foundation of Revolutionary Topologies: An Overview, Examples, Trend Analysis, Research Issues, Challenges, and Future Directions

Florentin Smarandache
Foundation of Revolutionary Topologies An Overview Examples Trend Analysis Research Issues Challenges and Future Directions Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 22 pages
File Size : 44,5 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 8210379456XXX

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Foundation of Revolutionary Topologies: An Overview, Examples, Trend Analysis, Research Issues, Challenges, and Future Directions by Florentin Smarandache Pdf

We now found nine new topologies, such as: NonStandard Topology, Largest Extended NonStandard Real Topology, Neutrosophic Triplet Weak/Strong Topologies, Neutrosophic Extended Triplet Weak/Strong Topologies, Neutrosophic Duplet Topology, Neutrosophic Extended Duplet Topology, Neutrosophic MultiSet Topology, and recall and improve the seven previously founded topologies in the years (2019-2023), namely: NonStandard Neutrosophic Topology, NeutroTopology, AntiTopology, Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, SuperHyperTopology, and Neutrosophic SuperHyperTopology. They are called avantgarde topologies because of their innovative forms.

Introduction to SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra

Florentin Smarandache
Introduction to SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 8 pages
File Size : 47,9 Mb
Release : 2022-04-01
Category : Mathematics
ISBN : 8210379456XXX

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Introduction to SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra by Florentin Smarandache Pdf

In this paper we recall our concepts of n th-Power Set of a Set, SuperHyperOperation, SuperHyperAxiom, SuperHyperAlgebra, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one actually encounters SuperHyperStructures (or more accurately (m, n)- SuperHyperStructures).

The SuperHyperFunction and the Neutrosophic SuperHyperFunction

Florentin Smarandache
The SuperHyperFunction and the Neutrosophic SuperHyperFunction Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 7 pages
File Size : 47,6 Mb
Release : 2022-04-27
Category : Antiques & Collectibles
ISBN : 8210379456XXX

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The SuperHyperFunction and the Neutrosophic SuperHyperFunction by Florentin Smarandache Pdf

In this paper, one recalls the general definition of the SuperHyperAlgebra with its SuperHyperOperations and SuperHyperAxioms. Then one introduces for the first time the SuperHyperTopology and especially the SuperHyperFunction and Neutrosophic SuperHyperFunction. One gives a numerical example of a SuperHyperGroup.

Introduction to Non-Standard Neutrosophic Topology

Mohammed A. Al Shumrani ,Florentin Smarandache
Introduction to Non Standard Neutrosophic Topology Book PDF

Author : Mohammed A. Al Shumrani ,Florentin Smarandache
Publisher : Infinite Study
Page : 14 pages
File Size : 40,8 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 8210379456XXX

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Introduction to Non-Standard Neutrosophic Topology by Mohammed A. Al Shumrani ,Florentin Smarandache Pdf

For the first time we introduce non-standard neutrosophic topology on the extended non-standard analysis space, called non-standard real monad space, which is closed under neutrosophic non-standard infimum and supremum. Many classical topological concepts are extended to the non-standard neutrosophic topology, several theorems and properties about them are proven, and many examples are presented.

Neutrosophic Vague Binary Sets

Remya.P.B.,Francina Shalini
Neutrosophic Vague Binary Sets Book PDF

Author : Remya.P.B.,Francina Shalini
Publisher : Infinite Study
Page : 15 pages
File Size : 50,6 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic Vague Binary Sets by Remya.P.B.,Francina Shalini Pdf

Vague sets and neutrosophic sets play an inevitable role in the developing scenario of mathematical world. In this modern era of artificial intelligence most of the real life situations are found to be immersed with unclear data. Even the newly developed concepts are found to fail with such problems. So new sets like Plithogenic and new combinations like neutrosophic vague arose. Classical set theory dealt with single universe and can be studied by taking it’s subsets.

The SuperHyperFunction and the Neutrosophic SuperHyperFunction (revisited again)

Florentin Smarandache
The SuperHyperFunction and the Neutrosophic SuperHyperFunction revisited again Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 7 pages
File Size : 52,6 Mb
Release : 2022-12-01
Category : Mathematics
ISBN : 8210379456XXX

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The SuperHyperFunction and the Neutrosophic SuperHyperFunction (revisited again) by Florentin Smarandache Pdf

In this paper, one recalls the general definition of the SuperHyperAlgebra with its SuperHyperOperations and SuperHyperAxioms [2, 6]. Then one introduces for the first time the SuperHyperTopology and especially the SuperHyperFunction and Neutrosophic SuperHyperFunction. One gives a numerical example of a Neutro-SuperHyperGroup.

On Neutrosophic Crisp Topology via N-Topology

Riad K. Al-Hamido,T. Gharibah,S. Jafari,F. Smarandache
On Neutrosophic Crisp Topology via N Topology Book PDF

Author : Riad K. Al-Hamido,T. Gharibah,S. Jafari,F. Smarandache
Publisher : Infinite Study
Page : 14 pages
File Size : 41,9 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 8210379456XXX

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On Neutrosophic Crisp Topology via N-Topology by Riad K. Al-Hamido,T. Gharibah,S. Jafari,F. Smarandache Pdf

In this paper, we extend the neutrosophic crisp topological spaces into N–neutrosophic crisp topological spaces (Nnc-topological space). Moreover, we introduced new types of open and closed sets in N–neutrosophic crisp topological spaces. We also present Nncsemi (open) closed sets, Nnc-preopen (closed) sets and Nnc-α-open (closed) sets and investigate their basic properties.

Further Theory of Neutrosophic Triplet Topology and Applications

Mohammed A. Al Shumrani,Muhammad Gulistan,Florentin Smarandache
Further Theory of Neutrosophic Triplet Topology and Applications Book PDF

Author : Mohammed A. Al Shumrani,Muhammad Gulistan,Florentin Smarandache
Publisher : Infinite Study
Page : 12 pages
File Size : 46,5 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 8210379456XXX

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Further Theory of Neutrosophic Triplet Topology and Applications by Mohammed A. Al Shumrani,Muhammad Gulistan,Florentin Smarandache Pdf

In this paper we study and develop the Neutrosophic Triplet Topology (NTT) that was recently introduced by Sahin et al. Like classical topology, the NTT tells how the elements of a set relate spatially to each other in a more comprehensive way using the idea of Neutrosophic Triplet Sets.

Neutrosophic Topological Spaces

Murad Arar,Saeid Jafari
Neutrosophic Topological Spaces Book PDF

Author : Murad Arar,Saeid Jafari
Publisher : Infinite Study
Page : 16 pages
File Size : 44,8 Mb
Release : 2020-12-01
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic Topological Spaces by Murad Arar,Saeid Jafari Pdf

In this paper, the concept of neutrosophic topological spaces is introduced. We define and study the properties of neutrosophic open sets, closed sets, interior and closure. The set of all generalize neutrosophic pre-closed sets GNPC and the set of all neutrosophic open sets in a neutrosophic topological space can be considered as examples of generalized neutrosophic topological spaces.

Topological Structures via Interval-Valued Neutrosophic Crisp Sets

Dongsik Jo, S. Saleh,Jeong-Gon Lee, Kul Hur, Chen Xueyou
Topological Structures via Interval Valued Neutrosophic Crisp Sets Book PDF

Author : Dongsik Jo, S. Saleh,Jeong-Gon Lee, Kul Hur, Chen Xueyou
Publisher : Infinite Study
Page : 29 pages
File Size : 45,7 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 8210379456XXX

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Topological Structures via Interval-Valued Neutrosophic Crisp Sets by Dongsik Jo, S. Saleh,Jeong-Gon Lee, Kul Hur, Chen Xueyou Pdf

In this paper, we introduce the new notion of interval-valued neutrosophic crisp sets providing a tool for approximating undefinable or complex concepts in real world. First, we deal with some of its algebraic structures. We also define an interval-valued neutrosophic crisp (vanishing) point and obtain some of its properties. Next, we define an interval-valued neutrosophic crisp topology, base (subbase), neighborhood, and interior (closure), respectively and investigate some of each property, and give some examples. Finally, we define an interval-valued neutrosophic crisp continuity and quotient topology and study some of each property.

SuperHyperFunction, SuperHyperStructure, Neutrosophic SuperHyperFunction and Neutrosophic SuperHyperStructure: Current understanding and future directions

Florentin Smarandache
SuperHyperFunction SuperHyperStructure Neutrosophic SuperHyperFunction and Neutrosophic SuperHyperStructure Current understanding and future directions Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 9 pages
File Size : 46,9 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 8210379456XXX

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SuperHyperFunction, SuperHyperStructure, Neutrosophic SuperHyperFunction and Neutrosophic SuperHyperStructure: Current understanding and future directions by Florentin Smarandache Pdf

The n-th PowerSet of a Set {or Pn(S)} better describes our real world, because a system S (which may be a company, institution, association, country, society, set of objects/plants/animals/beings, set of concepts/ideas/propositions, etc.) is formed by sub-systems, which in their turn by sub-sub-systems, and so on. We prove that the SuperHyperFunction is a generalization of classical Function, SuperFunction, and HyperFunction. And the SuperHyperAlgebra, SuperHyperGraph are part of the SuperHyperStructure. Almost all structures in our real world are Neutrosophic SuperHyperStructures since they have indeterminate/incomplete/uncertain/conflicting data.