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Florentin Smarandache

Publications and source records attributed to Florentin Smarandache.

At least 109 records · Page 6Linked to original sources
arXiv2009

Tracking object's type changes with fuzzy based fusion rule

In this paper the behavior of three combinational rules for temporal/sequential attribute data fusion for target type estimation are analyzed. The comparative analysis is based on: Dempster's fusion rule proposed in Dempster-Shafer Theory; Proportional Conflict Redistribution rule no. 5 (PCR5), proposed in Dezert-Smarandache Theory and one alternative class fusion rule, connecting the combination rules for information fusion with particular fuzzy operators, focusing on the t-norm based Conjunctive rule as an analog of the ordinary conjunctive rule and t-conorm based Disjunctive rule as an analog of the ordinary disjunctive rule. The way how different t-conorms and t-norms functions within TCN fusion rule influence over target type estimation performance is studied and estimated.

cs.AI↗
arXiv2009

A Class of Stationary Sequences

We define a class of sequences ${a_n}$ by $a_1=a$ and $a_{n+1}=P(a_n)$, where $P(x)$ is a polynomial with real coefficients. We then find out for which values $a$ and for which polynomials $P(x)$ these sequences will be constant after a certain rank. Then we generalize it from polynomials $P(x)$ to real functions $f(x)$.

math.GM↗
arXiv2009

Reservation for Other Backward Classes in Indian Central Government Institutions like IITs, IIMs and AIIMs- A Study of the Role of Media using Fuzzy Super FRM models

In this book the authors introduce three new types of fuzzy model called the super column Fuzzy Relational Model using super column matrices, super row fuzzy relational model using super row matrices and super mixed fuzzy relational model using supermatrices. These new models are used to study the role of media on 27 percent reservation for the other backward classes in the educational institutions run by the Indian central Government. This book has four chapters. Chapter one introduces the new notion of super fuzzy relational models using supermatrices. In chapter two these new models are used to study the problem. Conclusions and opinions are given in chapters four and three respectively.

math.GM↗
arXiv2009

A Class of DSm Conditional Rules

In this paper we introduce two new DSm fusion conditioning rules with example, and as a generalization of them a class of DSm fusion conditioning rules, and then extend them to a class of DSm conditioning rules.

cs.AI↗
arXiv2009

Ratio Estimators in Simple Random Sampling Using Information on Auxiliary Attribute

Some ratio estimators for estimating the population mean of the variable under study, which make use of information regarding the population proportion possessing certain attribute, are proposed. Under simple random sampling without replacement (SRSWOR) scheme, the expressions of bias and mean-squared error (MSE) up to the first order of approximation are derived. The results obtained have been illustrated numerically by taking some empirical population considered in the literature.

math.GM↗
arXiv2009

General combination rules for qualitative and quantitative beliefs

Martin and Osswald \cite{Martin07} have recently proposed many generalizations of combination rules on quantitative beliefs in order to manage the conflict and to consider the specificity of the responses of the experts. Since the experts express themselves usually in natural language with linguistic labels, Smarandache and Dezert \cite{Li07} have introduced a mathematical framework for dealing directly also with qualitative beliefs. In this paper we recall some element of our previous works and propose the new combination rules, developed for the fusion of both qualitative or quantitative beliefs.

cs.AI↗
arXiv2009

Superbimatrices and their generalizations

In this book, the authors introduce the new notion of superbimatrices and generalize it to supertrimatrices and super n-matrices. Study of these structures is not only interesting and innovative but is also best suited for the computerize world. The main difference between simple bimatrices and super bimatrices is that in case of simple bimatrices we have only one type of product defined on them, whereas in case of superbimatrices we have different types of products called minor and major defined using them. This book has four chapters. Chapter one describes the basic concepts to make this book a selfcontained one. Superbimatrices, semi superbimatrices, symmetric superbimatrices are introduced in chapter two. Chapter three introduces the notion of super trimatrices and the products defined using them. Chapter four gives the most generalized form of the superbimatrix, viz. super n-matrix

math.GM↗
arXiv2009

Groups as Graphs

For the first time we represent every finite group in the form of a graph in this book. The authors choose to call these graphs as identity graph, since the main role in obtaining the graph is played by the identity element of the group. This study is innovative because through this description one can immediately look at the graph and say the number of elements in the group G which are self-inversed. Also study of different properties, like the subgroups of a group, normal subgroups of a group, p-sylow subgroups of a group and conjugate elements of a group are carried out using the identity graph of the group in this book. This book has four chapters. The first chapter is introductory. The second chapter represents groups as graphs. In the third chapter, we have defined similar types of graphs for algebraic structures like commutative semigroups, loops, commutative groupoids and commutative rings. The final chapter poses 52 problems.

math.GM↗
arXiv2009

Estimation of Mean in Presence of Non Response Using Exponential Estimator

This paper considers the problem of estimating the population mean using information on auxiliary variable in presence of non response. Exponential ratio and exponential product type estimators have been suggested and their properties are studied. An empirical study is carried out to support the theoretical results.

math.GM↗
arXiv2009

Optimum Statistical Test Procedure

In this paper we obtain a test which minimizes the sum of the two error probabilities irrespective of whether $σ^2$ is known or unknown.

math.GM↗
arXiv2009

An introduction to DSmT

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning. In this introduction, we present a survey of our recent theory of plausible and paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT), developed for dealing with imprecise, uncertain and conflicting sources of information. We focus our presentation on the foundations of DSmT and on its most important rules of combination, rather than on browsing specific applications of DSmT available in literature. Several simple examples are given throughout this presentation to show the efficiency and the generality of this new approach.

cs.AI↗
arXiv2009

n-Linear Algebra of type II

This book is a continuation of the book n-linear algebra of type I and its applications. Most of the properties that could not be derived or defined for n-linear algebra of type I is made possible in this new structure: n-linear algebra of type II which is introduced in this book. In case of n-linear algebra of type II we are in a position to define linear functionals which is one of the marked difference between the n-vector spaces of type I and II. However all the applications mentioned in n-linear algebras of type I can be appropriately extended to n-linear algebras of type II. Another use of n-linear algebra (n-vector spaces) of type II is that when this structure is used in coding theory we can have different types of codes built over different finite fields whereas this is not possible in the case of n-vector spaces of type I. Finally in the case of n-vector spaces of type II, we can obtain n-eigen values from distinct fields; hence, the n-characteristic polynomials formed in them are in distinct different fields. An attractive feature of this book is that the authors have suggested 120 problems for the reader to pursue in order to understand this new notion. This book has three chapters. In the first chapter the notion of n-vector spaces of type II are introduced. This chapter gives over 50 theorems. Chapter two introduces the notion of n-inner product vector spaces of type II, n-bilinear forms and n-linear functionals. The final chapter suggests over a hundred problems. It is important that the reader is well-versed not only with linear algebra but also n-linear algebra of type I.

math.GM↗
arXiv2008

Special Classes of Set Codes and Their Applications

In this book, the authors introduce the notion of set codes, set bicodes and set n-codes. These are the most generalized notions of semigroup n-codes and group n-codes. Several types of set n-codes are defined. Several examples are given to enable the reader to understand the concept. These new classes of codes will find applications in cryptography, computer networking (where fragmenting of codes is to be carried out) and data storage (where confidentiality is to be maintained). We also describe the error detection and error correction of these codes. The authors feel that these codes would be appropriate to the computer dominated world. This book has three chapters. Chapter One gives basic concepts to make the book a self-contained one. In Chapter Two, the notion of set codes is introduced. The set bicodes and their generalization to set n-codes (n >= 3) is carried out in Chapter Three. This chapter also gives the applications of these codes in the above-mentioned fields.

math.GM↗
arXiv2008

n-Linear Algebra of type I and its applications

With the advent of computers, one needs algebraic structures that can simultaneously work with bulk data. One such algebraic structure, namely, n-linear algebras of type I are introduced in this book and its applications to n-Markov chains and n-Leontief models are given. These structures can be thought of as the generalization of bilinear algebras and bivector spaces. Several interesting n-linear algebra properties are proved. This book has four chapters. The first chapter just introduces n-group which is essential for the definition of n-vector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several related results which are analogues of the classical linear algebra theorems. In case of n-vector spaces, we can define several types of linear transformations. The notion of n-best approximations can be used for error correction in coding theory. The notion of n-eigen values can be used in deterministic modal superposition principle for undamped structures, which can find its applications in finite element analysis of mechanical structures with uncertain parameters. Further, it is suggested that the concept of n-matrices can be used in real world problems which adopts fuzzy models like Fuzzy Cognitive Maps, Fuzzy Relational Equations and Bidirectional Associative Memories. The applications of these algebraic structures are given in the third chapter. The fourth chapter suggests problems to further a reader's understanding of the subject.

math.GM↗