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New Techniques to Analyse the Prediction of Fuzzy Models
  • Language: en
  • Pages: 244

New Techniques to Analyse the Prediction of Fuzzy Models

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.

Special Fuzzy Matrices for Social Scientists
  • Language: en
  • Pages: 303

Special Fuzzy Matrices for Social Scientists

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.

Introduction to Linear Bialgebra
  • Language: en
  • Pages: 238

Introduction to Linear Bialgebra

In the modern age of development, it has become essential for any algebraic structure to enjoy greater acceptance and research significance only when it has extensive applications to other fields.This new algebraic concept, Linear Bialgebra, is one that will find applications to several fields like bigraphs, algebraic coding/communication theory (bicodes, best biapproximations), Markov bichains, Markov bioprocess and Leonief Economic bimodels: these are also brought out in this book.Here, the linear bialgebraic structure is given sub-bistructures and super-structures called the smarandache neutrosophic linear bialgebra which will easily yield itself to the above applications.

Distance in Matrices and Their Applications to Fuzzy Models and Neutrosophic Models
  • Language: en
  • Pages: 171

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

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.

Multigraphs for Multi Networks
  • Language: en
  • Pages: 318

Multigraphs for Multi Networks

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.

Special Type of Fixed Points of MOD Matrix Operators
  • Language: en
  • Pages: 202

Special Type of Fixed Points of MOD Matrix Operators

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.

Pseudo Lattice Graphs and their Applications to Fuzzy and Neutrosophic Models
  • Language: en
  • Pages: 278

Pseudo Lattice Graphs and their Applications to Fuzzy and Neutrosophic Models

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.

Non-Associative Algebraic Structures on MOD Planes
  • Language: en
  • Pages: 212

Non-Associative Algebraic Structures on MOD Planes

In this book authors for the first time construct non-associative algebraic structures on the MOD planes. Using MOD planes we can construct infinite number of groupoids for a fixed m and all these MOD groupoids are of infinite cardinality. Special identities satisfied by these MOD groupoids build using the six types of MOD planes are studied. Further, the new concept of special pseudo zero of these groupoids are defined, described and developed. Also conditions for these MOD groupoids to have special elements like idempotent, special pseudo zero divisors and special pseudo nilpotent are obtained. Further non-associative MOD rings are constructed using MOD groupoids and commutative rings with unit. That is the MOD groupoid rings gives infinitely many non-associative ring. These rings are analysed for substructures and special elements. This study is new and innovative and several open problems are suggested.

MOD Pseudo Linear Algebras
  • Language: en
  • Pages: 271

MOD Pseudo Linear Algebras

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