Semigroups On Mod Natural Neutrosophic Elements

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Semigroups on MOD Natural Neutrosophic Elements

W B Vasantha Kandasamy,Ilanthenral K,Florentin Smarandache
Semigroups on MOD Natural Neutrosophic Elements Book PDF

Author : W B Vasantha Kandasamy,Ilanthenral K,Florentin Smarandache
Publisher : Infinite Study
Page : 128 pages
File Size : 46,8 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9781599733807

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Semigroups on MOD Natural Neutrosophic Elements by W B Vasantha Kandasamy,Ilanthenral K,Florentin Smarandache Pdf

In this book the notion of semigroups under + is constructed using: the MOD natural neutrosophic integers, or MOD natural neutrosophic-neutrosophic numbers, or MOD natural neutrosophic finite complex modulo integer, or MOD natural neutrosophic dual number integers, or MOD natural neutrosophic special dual like number, or MOD natural neutrosophic special quasi dual numbers.

MOD Natural Neutrosophic Subset Semigroups

W. B. Vasantha Kandasamy ,Ilanthenral K,Florentin Smarandache
MOD Natural Neutrosophic Subset Semigroups Book PDF

Author : W. B. Vasantha Kandasamy ,Ilanthenral K,Florentin Smarandache
Publisher : Infinite Study
Page : 128 pages
File Size : 41,8 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9781599734859

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MOD Natural Neutrosophic Subset Semigroups by W. B. Vasantha Kandasamy ,Ilanthenral K,Florentin Smarandache Pdf

In this book the authors introduce for the first time the MOD Natural Subset Semigroups. They enjoy very many special properties. They are only semigroups even under addition. This book provides several open problems to the semigroup theorists

Mod Rectangular Natural Neutrosophic Numbers

W. B. Vasantha Kandasamy,Ilanthenral K,Florentin Smarandache
Mod Rectangular Natural Neutrosophic Numbers Book PDF

Author : W. B. Vasantha Kandasamy,Ilanthenral K,Florentin Smarandache
Publisher : Infinite Study
Page : 263 pages
File Size : 54,7 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 8210379456XXX

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Mod Rectangular Natural Neutrosophic Numbers by W. B. Vasantha Kandasamy,Ilanthenral K,Florentin Smarandache Pdf

In this book authors introduce the new notion of MOD rectangular planes. The functions on them behave very differently when compared to MOD planes (square). These are different from the usual MOD planes. Algebraic structures on these MOD rectangular planes are defined and developed.

Natural Neutrosophic Numbers and MOD Neutrosophic Numbers

W. B. Vasantha Kandasamy,K. Ilanthenral,Florentin Smarandache
Natural Neutrosophic Numbers and MOD Neutrosophic Numbers Book PDF

Author : W. B. Vasantha Kandasamy,K. Ilanthenral,Florentin Smarandache
Publisher : Infinite Study
Page : 185 pages
File Size : 40,5 Mb
Release : 2015
Category : Neutrosophic logic
ISBN : 9781599733661

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Natural Neutrosophic Numbers and MOD Neutrosophic Numbers by W. B. Vasantha Kandasamy,K. Ilanthenral,Florentin Smarandache Pdf

The authors in this book introduce a new class of natural neutrsophic numbers using MOD intervals. These natural MOD neutrosophic numbers behave in a different way for the product of two natural neutrosophic numbers can be neutrosophic zero divisors or idempotents or nilpotents. Several open problems are suggested in this book.

Smarandache Special Elements in Multiset Semigroups

W. B. Vasantha Kandasamy,Ilanthenral K
Smarandache Special Elements in Multiset Semigroups Book PDF

Author : W. B. Vasantha Kandasamy,Ilanthenral K
Publisher : Infinite Study
Page : 244 pages
File Size : 44,6 Mb
Release : 2024-07-02
Category : Mathematics
ISBN : 9781599735641

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Smarandache Special Elements in Multiset Semigroups by W. B. Vasantha Kandasamy,Ilanthenral K Pdf

Authors in this book study the notion of Smarandache element in multiset semigroups. It is important to keep on record that we define four operations on multisets viz. +, X, union and intersection in a free way. Thus all sets finite or infinite order contribute to infinite order multisets and the semigroup under any of these operations is of infinite order.

MOD Natural Neutrosophic Subset Topological Spaces and Kakutani’s Theorem

W. B. Vasantha Kandasamy,K. Ilanthenral,Florentin Smarandche
MOD Natural Neutrosophic Subset Topological Spaces and Kakutani s Theorem Book PDF

Author : W. B. Vasantha Kandasamy,K. Ilanthenral,Florentin Smarandche
Publisher : Infinite Study
Page : 128 pages
File Size : 45,5 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9781599734903

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MOD Natural Neutrosophic Subset Topological Spaces and Kakutani’s Theorem by W. B. Vasantha Kandasamy,K. Ilanthenral,Florentin Smarandche Pdf

In this book authors for the first time develop the notion of MOD natural neutrosophic subset special type of topological spaces using MOD natural neutrosophic dual numbers or MOD natural neutrosophic finite complex number or MOD natural neutrosophic-neutrosophic numbers and so on to build their respective MOD semigroups. Later they extend this concept to MOD interval subset semigroups and MOD interval neutrosophic subset semigroups. Using these MOD interval semigroups and MOD interval natural neutrosophic subset semigroups special type of subset topological spaces are built. Further using these MOD subsets we build MOD interval subset matrix semigroups and MOD interval subset matrix special type of matrix topological spaces. Likewise using MOD interval natural neutrosophic subsets matrices semigroups we can build MOD interval natural neutrosophic matrix subset special type of topological spaces. We also do build MOD subset coefficient polynomial special type of topological spaces. The final chapter mainly proposes several open conjectures about the validity of the Kakutani’s fixed point theorem for all MOD special type of subset topological spaces.

MOD Relational Maps Models and MOD Natural Neutrosophic Relational Maps Models

W. B. Vasantha Kandasamy,Ilanthenral K.,Florentin Smarandache
MOD Relational Maps Models and MOD Natural Neutrosophic Relational Maps Models Book PDF

Author : W. B. Vasantha Kandasamy,Ilanthenral K.,Florentin Smarandache
Publisher : Infinite Study
Page : 128 pages
File Size : 44,9 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9781599734637

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MOD Relational Maps Models and MOD Natural Neutrosophic Relational Maps Models by W. B. Vasantha Kandasamy,Ilanthenral K.,Florentin Smarandache Pdf

In this book the authors for the first time construct MOD Relational Maps model analogous to Fuzzy Relational Maps (FRMs) model or Neutrosophic Relational Maps (NRMs) model using the MOD rectangular or relational matrix. The advantage of using these models is that the MOD fixed point pair or MOD limit cycle pair is obtained after a finite number of iterations.

MOD Cognitive Maps Models and MOD Natural Neutrosophic Cognitive Maps Models

W. B. Vasantha Kandasamy, Ilanthenral K.,Florentin Smarandache
MOD Cognitive Maps Models and MOD Natural Neutrosophic Cognitive Maps Models Book PDF

Author : W. B. Vasantha Kandasamy, Ilanthenral K.,Florentin Smarandache
Publisher : Infinite Study
Page : 128 pages
File Size : 41,8 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9781599734620

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MOD Cognitive Maps Models and MOD Natural Neutrosophic Cognitive Maps Models by W. B. Vasantha Kandasamy, Ilanthenral K.,Florentin Smarandache Pdf

In this book authors for the first time introduce new mathematical models analogous to Fuzzy Cognitive Maps (FCMs) and Neutrosophic Cognitive Maps (NCMs) models. Several types of MOD Cognitive Maps models are constructed in this book. They are MOD Cognitive Maps model, MOD dual number Cognitive Maps model, MOD neutrosophic Cognitive Maps model, MOD finite complex number Cognitive Maps model, MOD special dual like number Cognitive Maps model, and MOD special quasi dual number Cognitive Maps model.

The Encyclopedia of Neutrosophic Researchers, Vol. I

Florentin Smarandache
The Encyclopedia of Neutrosophic Researchers Vol I Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 232 pages
File Size : 51,7 Mb
Release : 2016-11-12
Category : Mathematics
ISBN : 9781599734682

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The Encyclopedia of Neutrosophic Researchers, Vol. I by Florentin Smarandache Pdf

This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The 78 authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements.

MOD Graphs

W. B. Vasantha Kandasamy,Ilanthenral K,Florentin Smarandache
MOD Graphs Book PDF

Author : W. B. Vasantha Kandasamy,Ilanthenral K,Florentin Smarandache
Publisher : Infinite Study
Page : 128 pages
File Size : 54,7 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9781599734699

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MOD Graphs by W. B. Vasantha Kandasamy,Ilanthenral K,Florentin Smarandache Pdf

In this book the authors for the first time introduce, study and develop the notion of MOD graphs, MOD directed graphs, MOD finite complex number graphs, MOD neutrosophic graphs, MOD dual number graphs, and MOD directed natural neutrosophic graphs. There are open conjectures that can help researchers in the graph theory.

Special Type of Fixed Points of MOD Matrix Operators

W. B. Vasantha Kandasamy,Ilanthenral K,Florentin Smarandache
Special Type of Fixed Points of MOD Matrix Operators Book PDF

Author : W. B. Vasantha Kandasamy,Ilanthenral K,Florentin Smarandache
Publisher : Infinite Study
Page : 128 pages
File Size : 42,7 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9781599734590

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Special Type of Fixed Points of MOD Matrix Operators by W. B. Vasantha Kandasamy,Ilanthenral K,Florentin Smarandache Pdf

In this book authors for the first time introduce a special type of fixed points using MOD square matrix operators. These special type of fixed points are different from the usual classical fixed points. These special type of fixed points or special realized limit cycles are always guaranteed as we use only MOD matrices as operators with its entries from modulo integers. However this sort of results are NP hard problems if we use reals or complex numbers.

Special Type of Fixed Point Pairs using MOD Rectangular Matrix Operators

W. B. Vasantha Kandasamy,Ilanthenral K,Florentin Smarandache
Special Type of Fixed Point Pairs using MOD Rectangular Matrix Operators Book PDF

Author : W. B. Vasantha Kandasamy,Ilanthenral K,Florentin Smarandache
Publisher : Infinite Study
Page : 128 pages
File Size : 47,5 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9781599734606

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Special Type of Fixed Point Pairs using MOD Rectangular Matrix Operators by W. B. Vasantha Kandasamy,Ilanthenral K,Florentin Smarandache Pdf

In this book authors for the first time define a special type of fixed points using MOD rectangular matrices as operators. In this case the special fixed points or limit cycles are pairs which is arrived after a finite number of iterations. Such study is both new and innovative for it can find lots of applications in mathematical modeling.

Neutrosophic Components Semigroups and Multiset Neutrosophic Components Semigroups

Vasantha W.B. , Ilanthenral Kandasamy , Florentin Smarandache
Neutrosophic Components Semigroups and Multiset Neutrosophic Components Semigroups Book PDF

Author : Vasantha W.B. , Ilanthenral Kandasamy , Florentin Smarandache
Publisher : Infinite Study
Page : 11 pages
File Size : 50,6 Mb
Release : 2024-07-02
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic Components Semigroups and Multiset Neutrosophic Components Semigroups by Vasantha W.B. , Ilanthenral Kandasamy , Florentin Smarandache Pdf

Neutrosophic components (NC) under addition and product form different algebraic structures over different intervals. In this paper authors for the first time define the usual product and sum operations on NC. Here four different NC are defined using the four different intervals: (0, 1), [0, 1), (0, 1] and [0, 1].

A Classical Group of Neutrosophic Triplet Groups

Vasantha KandasamyW.B.,Ilanthenral Kandasamy,Florentin Smarandache
A Classical Group of Neutrosophic Triplet Groups Book PDF

Author : Vasantha KandasamyW.B.,Ilanthenral Kandasamy,Florentin Smarandache
Publisher : Infinite Study
Page : 8 pages
File Size : 42,7 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 8210379456XXX

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A Classical Group of Neutrosophic Triplet Groups by Vasantha KandasamyW.B.,Ilanthenral Kandasamy,Florentin Smarandache Pdf

Fuzzy set theory was introduced by Zadeh and was generalized to the Intuitionistic Fuzzy Set (IFS) by Atanassov. Real-world, uncertain, incomplete, indeterminate, and inconsistent data were presented philosophically as a neutrosophic set by Smarandache, who also studied the notion of neutralities that exist in all problems.

Generalized Neutrosophic Extended Triplet Group

Yingcang Ma,Xiaohong Zhang,Xiaofei Yang,Xin Zhou
Generalized Neutrosophic Extended Triplet Group Book PDF

Author : Yingcang Ma,Xiaohong Zhang,Xiaofei Yang,Xin Zhou
Publisher : Infinite Study
Page : 16 pages
File Size : 46,9 Mb
Release : 2024-07-02
Category : Mathematics
ISBN : 8210379456XXX

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Generalized Neutrosophic Extended Triplet Group by Yingcang Ma,Xiaohong Zhang,Xiaofei Yang,Xin Zhou Pdf

Neutrosophic extended triplet group is a new algebra structure and is different from the classical group. In this paper, the notion of generalized neutrosophic extended triplet group is proposed and some properties are discussed.