arXiv math/06113472006-11-12math.GM

Vedic Mathematics: 'Vedic' or 'Mathematics' -- A Fuzzy and Neutrosophic Analysis

W. B. Vasantha Kandasamy, Florentin Smarandache

备注：: 220 pages
发表信息：: Published by Automaton, Los Angeles, USA in 2006

英文摘要：

In this book the authors probe into Vedic Mathematics (a concept that gained renown in the period of the religious fanatic and revivalist Hindutva rule in India): and explore whether it is really 'Vedic' in origin or 'Mathematics' in content. We analyzed this problem using fuzzy models like Fuzzy Cognitive Maps (FCM), Fuzzy Relational Maps (FRM) and the newly constructed fuzzy dynamical system (and its Neutrosophic analogue) that can analyze multi-experts opinion at a time using a single model. The issue of Vedic Mathematics involves religious politics, caste supremacy, apart from elementary arithmetic -- so we cannot use simple statistics for our analysis.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Neutrosophic Set is a Generalization of Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set (Picture Fuzzy Set, Ternary Fuzzy Set), Pythagorean Fuzzy Set, q-Rung Orthopair Fuzzy Set, Spherical Fuzzy Set, etc

In this paper we prove that Neutrosophic Set (NS) is an extension of Intuitionistic Fuzzy Set (IFS) no matter if the sum of single-valued neutrosophic components is < 1, or > 1, or = 1. For the case when the sum of components is 1 (as in IFS), after applying the neutrosophic aggregation operators one gets a different result from that of applying the intuitionistic fuzzy operators, since the intuitionistic fuzzy operators ignore the indeterminacy, while the neutrosophic aggregation operators take into consideration the indeterminacy at the same level as truth-membership and falsehood-nonmembers…

2019-11-29math.GM

Basic Neutrosophic Algebraic Structures and their Application to Fuzzy and Neutrosophic Models

The involvement of uncertainty of varying degrees when the total of the membership degree exceeds one or less than one, then the newer mathematical paradigm shift, Fuzzy Theory proves appropriate. For the past two or more decades, Fuzzy Theory has become the potent tool to study and analyze uncertainty involved in all problems. But, many real-world problems also abound with the concept of indeterminacy. In this book, the new, powerful tool of neutrosophy that deals with indeterminacy is utilized. Innovative neutrosophic models are described. The theory of neutrosophic graphs is introduced and …

2004-12-21math.GM

Interval Valued Bipolar Fuzzy Weighted Neutrosophic Sets and Their Application

Interval valued bipolar fuzzy weighted neutrosophic set(IVBFWN-set) is a new generalization of fuzzy set, bipolar fuzzy set, neutrosophic set and bipolar neutrosophic set so that it can handle uncertain information more flexibly in the process of decision making. Therefore, in this paper, we propose concept of IVBFWN-set and its operations. Also we give the IVBFWN-set average operator and IVBFWN-set geometric operator to aggregate the IVBFWN-sets, which can be considered as the generalizations of some existing ones under fuzzy, neutrosophic environments and so on. Finally, a decision making al…

2016-02-05math.GM

Fuzzy and Neutrosophic Analysis of Periyar's views on Untouchability

This book is organized into four chapters. In Chapter One we just introduce the basic Fuzzy and Neutrosophic tools used in the analysis of the social evil of Untouchability. Since the notion of caste is based on themind, it is appropriate to use Fuzzy and Neutrosophic theory. In Chapter Two we use the opinion of several experts to analyze the various aspects of untouchability. Here, we use the tools that have been described in Chapter One. Fuzzy Directed Graphs and Neutrosophic Directed Graphs of these Fuzzy and Neutrosophic models happen to be very dense. We have represented 16 such graphs in…

2005-11-22math.GM

Neutrosophic Logic - Generalization of the Intuitionistic Fuzzy Logic

One generalizes the intuitionistic fuzzy logic (IFL) and other logics to neutrosophic logic (NL). The distinctions between IFL and NL {and the corresponding intuitionistic fuzzy set (IFS) and neutrosophic set (NS) respectively} are presented.

2010-08-28math.GM

Fuzzy Interval Matrices, Neutrosophic Interval Matrices and their Applications

The new concept of fuzzy interval matrices has been introduced in this book for the first time. The authors have not only introduced the notion of fuzzy interval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval matrices but have also demonstrated some of its applications when the data under study is an unsupervised one and when several experts analyze the problem. Further, the authors have introduced in this book multiexpert models using these three new types of interval matrices. The new multi expert models dealt in this book are FCIMs, FRIMs, FCInMs, FRInMs, IBAMs, IB…

2006-09-04math.GM

更多相关论文收起更多论文

A Geometric Interpretation of the Neutrosophic Set - A Generalization of the Intuitionistic Fuzzy Set

In this paper we generalize the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Several examples are presented. Also, a geometric interpretation of the Neutrosophic Set is given using a Neutrosophic Cube. Many distinctions between NS and IFS are underlined.

2011-09-21math.GM

Applications of Bimatrices to some Fuzzy and Neutrosophic Models

This book, in order to generalize the two models of fuzzy cognitive maps and neutrosophic cognitive maps, has systematically invented mathematical tools like bimatrices, trimatrices, n-matrices, bigraphs, trigraphs and n-graphs and describe some of its properties. These concepts are also extended neutrosophically in this book. Using these new tools we define fuzzy cognitive bimaps, fuzzy cognitive trimaps, fuzzy relational bimaps and fuzzy relational trimaps which exploit the new notions of bimatrices, bigraphs, trimatrices and trigraphs. It is worth mentioning that these can be extended to n-…

2005-09-04math.GM

Fuzzy and Neutrosophic Analysis of Women with HIV/AIDS

This book has six chapters. The first chapter gives a brief introduction about HIV/AIDS among rural women in Tamil Nadu. Chapter 2 is an analysis of the situation using fuzzy theory in general and Fuzzy Relational Maps (FRM)in particular. The FRM tool is specially chosen for two reasons: It can give the hidden pattern of the dynamical system and as the socio-economic condition of women infected with HIV/AIDS is interdependent we choose this special fuzzy tool called FRM. In Chapter 3, we use Fuzzy Associative Memories (FAM) to analyze the problem because FAM is the only fuzzy tool that can giv…

2005-07-02math.GM

Fuzzy Relational Equations and Neutrosophic Relational Equations

The introduction of Fuzzy Relational Equations (FREs) has made problems that were unsolvable using algebraic linear equations into solvable ones. FREs have been applied to problemsin medicine, industry, transportation and all types of social problems where the data is an unsupervised one. Yet, FREs lack the capacity to tackle problems where an element of indeterminacy is involved. This book develops the new concept of Neutrosophic Relational Equations (NREs) that have the capacity to analyze problems with indeterminacy. Here, earlier models on FREs are analyzed and new NRE models, with practic…

2004-06-30math.GM

Interval-valued neutrosophic soft sets and its decision making

In this paper, the notion of the interval valued neutrosophic soft sets ($ivn-$soft sets) is defined which is a combination of an interval valued neutrosophic sets \cite{wan-05} and a soft sets \cite{mol-99}. Our $ivn-$soft sets generalizes the concept of the soft set, fuzzy soft set, interval valued fuzzy soft set, intuitionistic fuzzy soft set, interval valued intuitionistic fuzzy soft set and neutrosophic soft set. Then, we introduce some definitions and operations on $ivn-$soft sets sets. Some properties of $ivn-$soft sets which are connected to operations have been established. Also, the …

2014-02-23math.GM

Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps

In this book we study the concepts of Fuzzy Cognitive Maps (FCMs) and their Neutrosophic analogue, the Neutrosophic Cognitive Maps (NCMs).Fuzzy Cognitive Maps are fuzzy structures that strongly resemble neural networks, and they have powerful and far-reaching consequences as a mathematical tool for modeling complex systems. Neutrosophic Cognitive Maps are generalizations of FCMs, and their unique feature is the ability to handle indeterminacy in relations between two concepts thereby bringing greater sensitivity into the results. Some of the varied applications of FCMs and NCMs which has been …

2003-11-05math.GM

Proceedings of the First International Conference on Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability and Statistics

Papers on neutrosophy (a generalization of dialectics), on neutrosophic logic, set, probability and statistics (generalizations of fuzzy logic, fuzzy set, and imprecise probability respectively), by Florentin Smarandache, Jean Dezert, S. Bhattacharya, Andrzej Buller, M. Khoshnevisan, S. Singh, Feng Liu, Gh. C. Dinulescu-Campina, Chris Lucas, and C. Gershenson.

2003-06-26math.GM

New classes of Neutrosophic Linear Algebras

This book is organized into seven chapters. Chapter one is introductory in content. The notion of neutrosophic set linear algebras and neutrosophic neutrosophic set linear algebras are introduced and their properties analysed in chapter two. Chapter three introduces the notion of neutrosophic semigroup linear algebras and neutrosophic group linear algebras. A study of their substructures are systematically carried out in this chapter. The fuzzy analogue of neutrosophic group linear algebras, neutrosophic semigroup linear algebras and neutrosophic set linear algebras are introduced in chapter f…

2010-03-09math.GM

Analysis of Social Aspects of Migrant Labourers Living With HIV/AIDS Using Fuzzy Theory and Neutrosophic Cognitive Maps: With Special Reference to Rural Tamil Nadu in India

This book has seven chapters. The first chapter is introductory in nature and it speaks about the migrant labourers. In chapter two we use Fuzzy Cognitive Maps to analyze the socio-economic problems of HIV/AIDS infected migrant labourers in rural areas of Tamil Nadu. In chapter three we analyze the role played by the government helping these migrant labourers with HIV/AIDS and factors of migration and their vulnerability in catching HIV/AIDS. For the first time Neutrosophic Cognitive Maps are used in the study of migrant labourers who have become HIV/AIDS victims. This study is done in Chapter…

2004-06-15math.GM

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 Neutorosophic analogues (simultaneous or otherwise, according to ones need). Using the six basic models, we have constructed a multi-expert multi-model called the 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 with…

2007-07-31math.GM

Introduction to Bimatrices

Generally any real-world problem is not always solvable, because in that not only a percentage of uncertainty is present, but also, a certain percentage of indeterminacy is present. The presence of uncertainty has been analyzed using fuzzy logic. In this book the amount of indeterminacy is being analyzed using neutrosophic logic. Most of these models use the concept of matrices. Matrices have certain limitation; when the models are time-dependent and any two experts' opinions are being studied simultaneously, one cannot compare both of them at each stage. The new concept of bimatrices would ce…

2005-06-21math.GM