Neutrosophic SuperHyperAlgebra and New Types of Topologies
Neutrosophic SuperHyperAlgebra and New Types of Topologies

Author: Florentin Smarandache

Publisher: Infinite Study

Published: 2023-09-01

Total Pages: 254

ISBN-13:

DOWNLOAD EBOOK

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

Author: Abdullah Kargın

Publisher: Infinite Study

Published: 2023-01-01

Total Pages: 15

ISBN-13:

DOWNLOAD EBOOK

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.

Data-Driven Modelling with Fuzzy Sets
Data-Driven Modelling with Fuzzy Sets

Author: Said Broumi

Publisher: CRC Press

Published: 2024-07-17

Total Pages: 348

ISBN-13: 1040043062

DOWNLOAD EBOOK

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

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 22

ISBN-13:

DOWNLOAD EBOOK

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.

Carvings and Commerce
Carvings and Commerce

Author: Michael D. Hall

Publisher:

Published: 2011

Total Pages: 223

ISBN-13: 9780295991498

DOWNLOAD EBOOK

Carvings and Commerce celebrates the model totem pole in all its myriad forms. Native American carvers supplying curios for the Pacific Northwest souvenir trade in the late 1800s created the first model totem poles. Over time, totem poles came to be perceived as generalized icons of "Indian life" and Native groups all across North America began making model totems for the ever-expanding tourism industry that attended the popularization of automobile travel. By the middle of the 20th century, totems were being produced by a variety of non-Native groups, including Boy Scouts and hobby crafters. Native artists in the 21st century, in both the United States and Canada, have revitalized the model totem pole tradition, sharing it with a growing fine-art audience. Carvings and Commerce traces the history of model totem poles from the end of the 19th century to the present time. Internationally recognized scholars and artists examine the issues of politics, economics, cultural identity, tradition, and aesthetics that have shaped the evolution of the model totem pole for over a hundred and thirty years. Michael D. Hall and Pat Glascock are artists and collectors. Other contributors include Robert Davidson, Kate Duncan, Charlotte Townsend-Gault, Aaron Glass, Aldona Jonaitis, and Christopher W. Smith.

Neutrosophic Sets: An Overview
Neutrosophic Sets: An Overview

Author: Said Broumi

Publisher: Infinite Study

Published:

Total Pages: 32

ISBN-13:

DOWNLOAD EBOOK

In this study, we give some concepts concerning the neutrosophic sets, single valued neutrosophic sets, interval-valued neutrosophic sets, bipolar neutrosophic sets, neutrosophic hesitant fuzzy sets, inter-valued neutrosophic hesitant fuzzy sets, refined neutrosophic sets, bipolar neutrosophic refined sets, multi-valued neutrosophic sets, simplified neutrosophic linguistic sets, neutrosophic over/off/under sets, rough neutrosophic sets, rough bipolar neutrosophic sets, rough neutrosophic hyper-complex set, and their basic operations.

Research on Novel Correlation Coefficient of Neutrosophic Cubic Sets and Its Applications
Research on Novel Correlation Coefficient of Neutrosophic Cubic Sets and Its Applications

Author: Huiling Xue

Publisher: Infinite Study

Published:

Total Pages: 11

ISBN-13:

DOWNLOAD EBOOK

Single-valued neutrosophic cubic set is a good tool to solve the vague and uncertain problems because it containsmore information. The article first gives the correlation coefficient of single-valued neutrosophic cubic sets. Then, a decision method is proposed, and an application in pattern recognition is considered. Finally, examples are given to explain the feasibility of thismethod. At the same time, the comparative analysis shows the superiority of this method.

Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications
Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications

Author: Avishek Chakraborty

Publisher: Infinite Study

Published:

Total Pages: 27

ISBN-13:

DOWNLOAD EBOOK

In this paper, we introduce the concept of neutrosophic number from different viewpoints. We define different types of linear and non-linear generalized triangular neutrosophic numbers which are very important for uncertainty theory. We introduced the de-neutrosophication concept for neutrosophic number for triangular neutrosophic numbers. This concept helps us to convert a neutrosophic number into a crisp number. The concepts are followed by two application, namely in imprecise project evaluation review technique and route selection problem.