Ilanthenral K's Books

In this book authors for the first time introduce the notion of distance between any two m x n matrices. If the distance is 0 or m x n there is nothing interesting.

In this book authors introduce the notion of subset vertex multigraphs for the first time. The study of subset vertex graphs was introduced in 2018, however they are not multiedged, further they were unique once the vertex subsets are given. These subset vertex multigraphs are also unique once the vertex subsets are given and the added advantage is that the number of common elements between two vertex subsets accounts for the number of edges between them, when there is no common element there is no edge between them.

In this book authors for the first time introduce the new notion of special subset vertex subgraph of subset vertex graphs introduced recently. These subset vertex graphs takes the vertex set values from the power set P(X) of any set X. The main speciality of these subset vertex graphs is that once a set of subsets from P(X) is given, the edges of the graph are fixed in a unique way, so for a given collection of subset vertices the graph is always unique.

Set linear algebras, introduced by the authors in this book, are the most generalized form of linear algebras.These structures make use of very few algebraic operations and are easily accessible to non-mathematicians as well.The dominance of computers in everyday life calls for a paradigm shift in the concepts of linear algebra. The authors believe that set linear algebra will cater to that need.

This book introduces special classes of Fuzzy and Neutrosophic Matrices. These special classes of matrices are used in the construction of multi-expert special fuzzy models using FCM, FRM and FRE and their Neutrosophic analogues (simultaneous or otherwise according to ones need). Using the six basic models, we have constructed a multi-expert multi-model called Super Special Hexagonal Fuzzy and Neutrosophic Model.Given any special input vector, these models can give the resultant using special operations. When coupled with computer programming, these operations can give the solution within a reasonable time period.Such multi-expert multi-model systems are not only a boon to social scientists, but also to anyone who wants to use Fuzzy and Neutrosophic Models.

In this book any network which can be represented as a multigraph is referred to as a multi network. Several properties of multigraphs have been described and developed in this book. When multi path or multi walk or multi trail is considered in a multigraph, it is seen that there can be many multi walks, and so on between any two nodes and this makes multigraphs very different.

In this book we define new operations mainly to construct mathematical models akin to Fuzzy Cognitive Maps (FCMs) model, Neutrosophic Cognitive Maps (NCMs) model and Fuzzy Relational Maps (FRMs) model. These new models are defined in chapter four of this book. These new models can find applications in discrete Artificial Neural Networks, soft computing, and social network analysis whenever the concept of indeterminate is involved.

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.

In this book the authors for the first time have merged vertices and edges of lattices to get a new structure which may or may not be a lattice but is always a graph. This merging is done for graph too which will be used in the merging of fuzzy models. Further merging of graphs leads to the merging of matrices; both these concepts play a vital role in merging the fuzzy and neutrosophic models. Several open conjectures are suggested.

In this book authors for the first time introduce the notion of strong neutrosophic graphs. They are very different from the usual graphs and neutrosophic graphs. Using these new structures special subgraph topological spaces are defined. Further special lattice graph of subgraphs of these graphs are defined and described. Several interesting properties using subgraphs of a strong neutrosophic graph are obtained. Several open conjectures are proposed. These new class of strong neutrosophic graphs will certainly find applications in Neutrosophic Cognitive Maps (NCM), Neutrosophic Relational Maps (NRM) and Neutrosophic Relational Equations (NRE) with appropriate modifications.

Studies to neutrosophic graphs happens to be not only innovative and interesting, but gives a new dimension to graph theory. The classic coloring of edge problem happens to give various results. Neutrosophic tree will certainly find lots of applications in data mining when certain levels of indeterminacy is involved in the problem. Several open problems are suggested.

The study of MOD Structures is new and innovative. The authors in this book propose several problems on MOD Structures, some of which are at the research level.

In this book the authors for the first time have ventured to study, analyse and investigate fuzzy and neutrosophic models and the experts opinion. To make such a study, innovative techniques and defined and developed. Several important conclusions about these models are derived using these new techniques. Open problems are suggested in this book.

Book's by Ilanthenral K

Distance in Matrices and Their Applications to Fuzzy Models and Neutrosophic Models

Distance in Matrices and Their Applications to Fuzzy Models and Neutrosophic Models

Subset Vertex Multigraphs and Neutrosophic Multigraphs for Social Multi Networks

Subset Vertex Multigraphs and Neutrosophic Multigraphs for Social Multi Networks

Special Subset Vertex Subgraphs for Social Networks

Special Subset Vertex Subgraphs for Social Networks

Set Linear Algebra and Set Fuzzy Linear Algebra

Set Linear Algebra and Set Fuzzy Linear Algebra

Special Fuzzy Matrices for Social Scientists

Special Fuzzy Matrices for Social Scientists

Multigraphs for Multi Networks

Multigraphs for Multi Networks

Special Fuzzy Matrices for Social Scientists

Special Fuzzy Matrices for Social Scientists

Subset Vertex Multigraphs and Neutrosophic Multigraphs for Social Multi Networks

Subset Vertex Multigraphs and Neutrosophic Multigraphs for Social Multi Networks

Neutrosophic Triplet Groups and their Applications to Mathematical Modelling

Neutrosophic Triplet Groups and their Applications to Mathematical Modelling

Special Type of Fixed Points of MOD Matrix Operators

Special Type of Fixed Points of MOD Matrix Operators

Pseudo Lattice Graphs and their Applications to Fuzzy and Neutrosophic Models

Pseudo Lattice Graphs and their Applications to Fuzzy and Neutrosophic Models

Strong Neutrosophic Graphs and Subgraph Topological Subspaces

Strong Neutrosophic Graphs and Subgraph Topological Subspaces

Neutrosophic Graphs: A New Dimension to Graph Theory

Neutrosophic Graphs: A New Dimension to Graph Theory

Problems on MOD Structures

Problems on MOD Structures

New Techniques to Analyse the Prediction of Fuzzy Models

New Techniques to Analyse the Prediction of Fuzzy Models

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