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Cyclic Associative Groupoids (CA-Groupoids) and Cyclic Associative Neutrosophic Extended Triplet Groupoids (CA-NET-Groupoids)

Author: Xiaohong Zhang

Publisher: Infinite Study

Published:

Total Pages: 11

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Group is the basic algebraic structure describing symmetry based on associative law. In order to express more general symmetry (or variation symmetry), the concept of group is generalized in various ways, for examples, regular semigroups, generalized groups, neutrosophic extended triplet groups and AG-groupoids. In this paper, based on the law of cyclic association and the background of non-associative ring, left weakly Novikov algebra and CA-AG-groupoid, a new concept of cyclic associative groupoid (CA-groupoid) is firstly proposed, and some examples and basic properties are presented. Moreover, as a combination of neutrosophic extended triplet group (NETG) and CA-groupoid, the notion of cyclic associative neutrosophic extended triplet groupoid (CA-NET-groupoid) is introduced, some important results are obtained, particularly, a decomposition theorem of CA-NET-groupoid is proved.

Regular CA-Groupoids and Cyclic Associative Neutrosophic Extended Triplet Groupoids (CA-NETGroupoids) with Green Relations

Author: Wangtao Yuan

Publisher: Infinite Study

Published:

Total Pages: 15

ISBN-13:

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Based on the theories of AG-groupoid, neutrosophic extended triplet (NET) and semigroup, the characteristics of regular cyclic associative groupoids (CA-groupoids) and cyclic associative neutrosophic extended triplet groupoids (CA-NET-groupoids) are further studied, and some important results are obtained.

A Kind of Non-associative Groupoids and Quasi Neutrosophic Extended Triplet Groupoids (QNET-Groupoids)

Author: Xiaohong Zhang

Publisher: Infinite Study

Published:

Total Pages: 20

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The various generalized associative laws can be considered as generalizations of traditional symmetry. Based on the theories of CA-groupoid, TA-groupoid and neutrosophic extended triplet (NET), this paper first proposes a new concept, which is type-2 cyclic associative groupoid (shortly by T2CA-groupoid), and gives some examples and basic properties. Furthermore, as a combination of neutrosophic extended triplet group (NETG) and T2CAgroupoid, the notion of type-2 cyclic associative neutrosophic extended triplet groupoid (T2CANET-groupoid) is introduced, and a decomposition theorem of T2CA-NET-groupoid is proved. Finally, as a generalization of neutrosophic extended triplet group (NETG), the concept of quasi neutrosophic extended triplet groupoid (QNET-groupoid) is introduced, and the relationships among T2CA-QNET-groupoid, T2CA-NET-groupoid and CA-NET-groupoid are discussed.

Neutrosophic Sets and Systems, Vol. 29, 2019

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 264

ISBN-13:

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Neutrosophic Sets and Systems, Book Series, Vol. 29, 2019

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 262

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Neutrosophic Sets and Systems, Vol. 36, 2020

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 410

ISBN-13:

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“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. Some articles in this issue: n-Refined Neutrosophic Modules, A Neutrosophic Approach to Digital Images, A Novel Method for Neutrosophic Assignment Problem by using Interval-Valued Trapezoidal Neutrosophic Number.

Neutrosophic Sets and Systems. An International Journal in Information Science and Engineering, Vol. 36, 2020

Author: Florentin Smarandache

Publisher: Infinite Study

Published: 2020-10-01

Total Pages: 410

ISBN-13:

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Neutrosophic Sets and Systems (NSS) is an academic journal, published quarterly online and on paper, that has been created for publications of advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics etc. and their applications in any field.

Some Results on Various Cancellative CA-Groupoids and Variant CA-Groupoids

Author: Zhirou Ma

Publisher: Infinite Study

Published:

Total Pages: 21

ISBN-13:

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Cyclic associativity can be regarded as a kind of variation symmetry, and cyclic associative groupoid (CA-groupoid) is a generalization of commutative semigroup. In this paper, the various cancellation properties of CA-groupoids, including cancellation, quasi-cancellation and power cancellation, are studied. The relationships among cancellative CA-groupoids, quasi-cancellative CA-groupoids and power cancellative CA-groupoids are found out. Moreover, the concept of variant CA-groupoid is proposed firstly, some examples are presented. It is shown that the structure of variant CA-groupoid is very interesting, and the construction methods and decomposition theorem of variant CA-groupoids are established.

A Kind of Variation Symmetry: Tarski Associative Groupoids (TA-Groupoids) and Tarski Associative Neutrosophic Extended Triplet Groupoids (TA-NETGroupoids)

Author: Xiaohong Zhang

Publisher: Infinite Study

Published:

Total Pages: 20

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The associative law reflects symmetry of operation, and other various variation associative laws reflect some generalized symmetries. In this paper, based on numerous literature and related topics such as function equation, non-associative groupoid and non-associative ring, we have introduced a new concept of Tarski associative groupoid (or transposition associative groupoid (TAgroupoid)), presented extensive examples, obtained basic properties and structural characteristics, and discussed the relationships among few non-associative groupoids. Moreover, we proposed a new concept of Tarski associative neutrosophic extended triplet groupoid (TA-NET-groupoid) and analyzed related properties. Finally, the following important result is proved: every TA-NETgroupoid is a disjoint union of some groups which are its subgroups.

New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic Plithogenic Optimizations

Author: Florentin Smarandache

Publisher: Infinite Study

Published: 2022-09-01

Total Pages: 411

ISBN-13:

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This volume presents state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, and neutrosophic symmetry, as well as their applications in the real world.