In this book authors for the first time introduce the notion of MOD subsets. The S-semigroups enjoy several interesting properties. The notion of MOD universal subset and MOD absorbing subsets are defined and developed. MOD natural neutrosophic subsets forms only a semigroup under ‘+’. In fact the main feature enjoyed by this structure is they have subset idempotents with respect to ‘+’. They are S-semigroups under ‘+’. These MOD natural neutrosophic subsets of all 6 typ...

In this book authors for the first time introduce new mathematical models analogous to FCMs and NCMs. They have constructed 12 types of MOD Cognitive Maps models, such as: 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, MOD special quasi dual number Cognitive Maps model. Apart from this they have defined MOD natural neu...

In this book 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 so on. Likewise MOD directed natural neutrosophic graphs are defined. Further type I, type II and type III. MOD directed graphs and MOD natural neutrosophic graphs are defined and developed. This book has over 185 examples and over 250 figures. The notion of MOD bipartite g...

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. Such study is new innovative and certainly lead to several special important applications in the field of science, engineering, techn...

The authors approach several themes of classical geometry of the circle and complete them with some original results, showing that not everything in traditional math is revealed, and that it still has an open character. The topics were chosen according to authors’ aspiration and attraction, as a poet writes lyrics about spring according to his emotions.

In this book authors for the first time introduce in a systematic way the notion of complex valued graphs, strong complex valued graphs and complex neutrosophic valued graphs. Several interesting properties are defined, described and developed. Most of the conjectures which are open in case of usual graphs continue to be open problems in case of both complex valued graphs and strong complex valued graphs. The authors also give some applications of them in soft computing ...

The author introduces for the first time the concept of plithogeny in philosophy and, as a derivative, the concepts of plithogenic set / logic / probability / statistics in mathematics and engineering – and the degrees of contradiction (dissimilarity) between the attributes’ values that contribute to a more accurate construction of plithogenic aggregation operators and to the plithogenic relationship of inclusion (partial ordering). They resulted from practical needs in ...

The topics discussed in this book are Int-soft semigroup, Int-soft left (right) ideal, Int-soft (generalized) bi-ideal, Int-soft quasi-ideal, Int-soft interior ideal, Int-soft left (right) duo semigroup, starshaped (∈, ∈∨ qk)-fuzzy set, quasi-starshaped (∈, ∈∨ qk)-fuzzy set, semidetached mapping, semidetached semigroup, (∈, ∈ ∨qk)-fuzzy subsemi-group, (qk, ∈ ∨qk)-fuzzy subsemigroup, (∈, ∈ ∨ qk)-fuzzy subsemigroup, (qk, ∈ ∨ qk)-fuzzy subsemigroup, (∈ ∨ qk, ∈ ∨ qk)-fuzzy s...

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. These semigroups have special and distinct features. Certainly these finite structures can find applications in several important problems related to automaton theory. The authors also mentio...

In this book authors for the first time introduce the new notion of special subset vertex subgraph of subset vertex graphs. 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. The special subset vertex subgraphs...

In this book authors for the first time introduce the notion of subset vertex graph using the vertex set as the subset of the power set P(S), S is assumed in this book to be finite; however it can be finite or infinite. Theey have defined two types of subset vertex graphs, one is directed and the other one is not directed. The most important fact which must be kept in record is that for a given set of vertices there exists one and only one subset vertex graph be it of ty...

In this book authors study special type of subset vertex multi subgraphs; these multi subgraphs can be directed or otherwise. Another special feature of these subset vertex multigraphs is that we are aware of the elements in each vertex set and how it affects the structure of both subset vertex multisubgraphs and edge multisubgraphs. It is pertinent to record at this juncture that certain ego centric directed multistar graphs become empty on the removal of one edge, ther...

The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling, systematic sampling and stratified random sampling. This volume is a collection of five papers, written by nine co-authors (listed in the order of the papers): Rajesh Singh, Mukesh Kumar, Manoj Kr. Chaudhary, Cem Kadilar, Prayas Sharma, Florentin Smarandache, Anil Prajapati, Hemant Verma, and Viplav Kr. Singh. In first...

The present book aims to present some improved estimators using auxiliary and attribute information in case of simple random sampling and stratified random sampling and in some cases when non-response is present. The first and the second papers deal with the problem of estimating the finite population mean when some information on two auxiliary attributes are available. In the third paper, problems related to estimation of ratio and product of two population mean using...

The main aim of the present book is to suggest some improved estimators using auxiliary and attribute information in case of simple random sampling and stratified random sampling and some inventory models related to capacity constraints. This volume is a collection of six papers, written by five co-authors (listed in the order of the papers): Dr. Rajesh Singh, Dr. Sachin Malik, Dr. Florentin Smarandache, Dr. Neeraj Kumar, Mr. Sanjey Kumar & Pallavi Agarwal. In the...

The future can only be the Spiral Neutrosophic Evolution: - from inferior () to superior () [evolution], - and back [involution] to an inferior and superior melange (), - and over time we encounter stagnation (no evolution, no involution) or uncertainty (if it is evolution or involution) [indetermination] ... and so on, in a spiral. Therefore: evolution / involution / indetermination at a level; followed by another similar cycle: evolution / involution / indetermin...

Neutrosophic Sociology (or Neutrosociology) is the study of sociology using neutrosophic scientific methods. The huge social data that we face in sociology is full of indeterminacy: it is vague, incomplete, contradictory, hybrid, biased, ignorant, redundant, superfluous, meaningless, ambiguous, unclear, etc. That’s why the neutrosophic sciences (which deal with indeterminacy), through the process of neutrosophication, are involved, such as: neutrosophy (a new branch of...

Neutropsyche is the psychological theory that studies the soul or spirit using the neutrosophy and neutrosohic theories. Neutropsychic Personality is a neutrosophic dynamic open psychological system of tendencies to feel, think, and act specific to each individual. Neutrosophic Refined Memory: that restructured the division of memory into: consciousness, aconsciousness (which we introduce as a blend of consciousness and unconsciousness), and unconsciousness. In Neutrosop...

En el desarrollo de este capítulo vamos a definir ciertos conceptos principales de la teoría de conjuntos, los cuales son primordiales para la comprensión de este tema. La teoría de conjuntos es una rama de las matemáticas, y cuya dedicación de este capítulo, es gracias al matemático, Ferdinand Ludwing Philipp Cantor, quien es considerado el padre de la Teoría de Conjuntos, debido a ello, es que, en el año 1874, salió su primer trabajo revolucionario, con respecto a l...

El concepto estratégico de muchos modelos de gestión pública está basados en un futuro conexo. Bajo esta perspectiva se podría intentar atrapar al futuro como previsión de los resultados, delinear acciones eficaces, efectivas, proactivas y unívocas. Pero el mañana en la administración pública es el resultado de procesos emergentes, de escenarios inciertos que dependen de la conjunción de variables inestables que rompen con la tradicional certidumbre y desacomoda la actua...