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Florentin Smarandache

Publications and source records attributed to Florentin Smarandache.

At least 55 records · Page 3Linked to original sources
arXiv2014

A family of median based estimators in simple random sampling

In this paper we have proposed a median based estimator using known value of some population parameter(s) in simple random sampling. Various existing estimators are shown particular members of the proposed estimator. The bias and mean squared error of the proposed estimator is obtained up to the first order of approximation under simple random sampling without replacement. An empirical study is carried out to judge the superiority of proposed estimator over others.

math.ST↗
arXiv2014

Difference-type estimators for estimation of mean in the presence of measurement error

In this paper we have suggested difference-type estimator for estimation of population mean of the study variable y in the presence of measurement error using auxiliary information. The optimum estimator in the suggested estimator has been identified along with its mean square error formula. It has been shown that the suggested estimator performs more efficient then other existing estimators. An empirical study is also carried out to illustrate the merits of proposed method over other traditional methods.

math.ST↗
arXiv2014

Exponential ratio-product type estimators under second order approximation in stratified random sampling

Singh et al (20009) introduced a family of exponential ratio and product type estimators in stratified random sampling. Under stratified random sampling without replacement scheme, the expressions of bias and mean square error (MSE) of Singh et al (2009) and some other estimators, up to the first- and second-order approximations are derived. Also, the theoretical findings are supported by a numerical example.

math.ST↗
arXiv2014

Two-phase sampling in estimation of population mean in the presence of non-response

The present paper presents the detail discussion on estimation of population mean in simple random sampling in the presence of non-response. Motivated by Gupta and Shabbir (2008), we have suggested the class of estimators of population mean using an auxiliary variable under non-response. A theoretical study is carried out using two-phase sampling scheme when the population mean of auxiliary variable is not known. An empirical study has also been done in the support of theoretical results.

math.ST↗
arXiv2013

Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability

In this paper, we introduce for the first time the notions of neutrosophic measure and neutrosophic integral, and we develop the 1995 notion of neutrosophic probability. We present many practical examples. It is possible to define the neutrosophic measure and consequently the neutrosophic integral and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need to solve. Neutrosophics study the indeterminacy. Indeterminacy is different from randomness. It can be caused by physical space materials and type of construction, by items involved in the space, etc.

cs.AI↗
arXiv2013

Intuitionistic Neutrosophic Soft Set

In this paper we study the concept of intuitionistic neutrosophic set of Bhowmik and Pal. We have introduced this concept in soft sets and defined intuitionistic neutrosophic soft set. Some definitions and operations have been introduced on intuitionistic neutrosophic soft set. Some properties of this concept have been established.

cs.OH↗
arXiv2013

Multivariate ratio estimation with known population proportion of two auxiliary characters for finite population

In the present study, we propose estimators based on geometric and harmonic mean for estimating population mean using information on two auxiliary attributes in simple random sampling. We have shown that, when we have multi-auxiliary attributes, estimators based on geometric mean and harmonic mean are less biased than Olkin (1958), Naik and Gupta (1996) and Singh (1967) type- estimator under certain conditions. However, the MSE of Olkin(1958) estimator and geometric and harmonic estimators are same up to the first order of approximation.

stat.AP↗
arXiv2013

On Improvement in Estimating Population Parameter(s) Using Auxiliary Information

The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling and systematic sampling. This volume is a collection of five papers. The following problems have been discussed in the book: In chapter one an estimator in systematic sampling using auxiliary information is studied in the presence of non-response. In second chapter some improved estimators are suggested using auxiliary information. In third chapter some improved ratio-type estimators are suggested and their properties are studied under second order of approximation. In chapter four and five some estimators are proposed for estimating unknown population parameter(s) and their properties are studied. This book will be helpful for the researchers and students who are working in the field of finite population estimation.

math.ST↗
arXiv2012

Mathematical Analysis of the Problems faced by the People With Disabilities (PWDs)

This book has eight chapters. Chapter one just gives references to the materials used in this book. Analysis of the collected date is carried out in chapter two. Chapter three introduces a New Fuzzy Cognitive Relational Maps (FCRMs)bimodel to study the socio-economic problems of PWDs. Economic problems faced by PWDs is analysed in chapter four using Special Fuzzy Cognitive Maps (SFCMs) model introduced by the authors. Chapter five carries out the study of interrelated problems faced by the PWDs and the caretakers. In chapter six we use the new FCRM bimodel to analyse the problems faced by the rural PWDs. This data was collected from charity homes run by NGOs and others in and near Chennai is carried out in chapter seven. Conclusions based on this study are given the end of this chapter. The final chapter gives the suggestions and conclusions from our study in chapter two to six and also from the interviews and discussions with them.

math.GM↗
arXiv2012

Erasure Techniques in MRD codes

This book is organized into six chapters. The first chapter introduces the basic algebraic structures essential to make this book a self contained one. Algebraic linear codes and their basic properties are discussed in chapter two. In chapter three the authors study the basic properties of erasure decoding in maximum rank distance codes. Some decoding techniques about MRD codes are described and discussed in chapter four of this book. Rank distance codes with complementary duals and MRD codes with complementary duals are introduced and their applications are discussed. Chapter five introduces the notion of integer rank distance codes. The final chapter introduces some concatenation techniques.

math.GM↗
arXiv2012

The Geometry of Homological Triangles

This book is addressed to students, professors and researchers of geometry, who will find herein many interesting and original results. The originality of the book The Geometry of Homological Triangles consists in using the homology of triangles as a "filter" through which remarkable notions and theorems from the geometry of the triangle are unitarily passed. Our research is structured in seven chapters, the first four are dedicated to the homology of the triangles, while the last ones to their applications.

math.GM↗
arXiv2012

Fuzzy Linguistic Topological Spaces

This book has five chapters. Chapter one is introductory in nature. Fuzzy linguistic spaces are introduced in chapter two. Fuzzy linguistic vector spaces are introduced in chapter three. Chapter four introduces fuzzy linguistic models. The final chapter suggests over 100 problems and some of them are at research level.

math.GM↗
arXiv2012

Natural Product Xn on matrices

This book has eight chapters. The first chapter is introductory in nature. Polynomials with matrix coefficients are introduced in chapter two. Algebraic structures on these polynomials with matrix coefficients is defined and described in chapter three. Chapter four introduces natural product on matrices. Natural product on super matrices is introduced in chapter five. Super matrix linear algebra is introduced in chapter six. Chapter seven claims only after this notion becomes popular we can find interesting applications of them. The final chapter suggests over 100 problems some of which are at research level.

math.GM↗
arXiv2011

DSm Vector Spaces of Refined Labels

In this book the authors introduce the notion of DSm vector spaces of refined labels. They also realize the refined labels as a plane and a n-dimensional space. Further, using these refined labels, several algebraic structures are defined. Finally DSm semivector space or refined labels is described. Authors also propose some research problems.

math.GM↗
arXiv2011

Finite Neutrosophic Complex Numbers

In this book for the first time the authors introduce the notion of real neutrosophic complex numbers. Further the new notion of finite complex modulo integers is defined. For every $C(Z_n)$ the complex modulo integer $i_F$ is such that $2F_i = n - 1$. Several algebraic structures on $C(Z_n)$ are introduced and studied. Further the notion of complex neutrosophic modulo integers is introduced. Vector spaces and linear algebras are constructed using these neutrosophic complex modulo integers.

math.GM↗
arXiv2011

Algebraic Structures Using Super Interval Matrices

In this book super interval matrices using the special type of intervals of the form [0, a] are introduced. Several algebraic structures like semigroups, groups, semirings, rings, semivector spaces and vector spaces are introduced. Special fuzzy linear algebras are introduced using the concept of super fuzzy interval matrices.

math.GM↗
arXiv2011

Contradiction measures and specificity degrees of basic belief assignments

In the theory of belief functions, many measures of uncertainty have been introduced. However, it is not always easy to understand what these measures really try to represent. In this paper, we re-interpret some measures of uncertainty in the theory of belief functions. We present some interests and drawbacks of the existing measures. On these observations, we introduce a measure of contradiction. Therefore, we present some degrees of non-specificity and Bayesianity of a mass. We propose a degree of specificity based on the distance between a mass and its most specific associated mass. We also show how to use the degree of specificity to measure the specificity of a fusion rule. Illustrations on simple examples are given.

cs.AI↗