Showing papers by "Florentin Smarandache published in 2009"

Improved exponential estimator for population variance using two auxiliary variables

Abstract: In this paper exponential ratio and exponential product type estimators using two auxiliary variables are proposed for estimating unknown popoulation variance S 2 y. Problem is extended to the case of two-phase sampling. Theoretical results are supported by an empirical study

Improvement in Estimating the Population Mean Using Exponential Estimator in Simple Random Sampling

Abstract: This study proposes some exponential ratio-type estimators for estimating the population mean of the variable under study, using known values of certain population parameter(s). Under simple random sampling without replacement (SRSWOR) scheme, mean square error (MSE) equations of all proposed estimators are obtained and compared with each other. The theoretical results are supported by a numerical illustration.

An Introduction to Neutrosophic Probability Applied in Quantum Physics

Abstract: In this paper one generalizes the classical probability and imprecise probability to the notion of “neutrosophic probability” in order to be able to model Heisenberg’s Uncertainty Principle of a particle’s behavior, Schrodinger’s Cat Theory, and the state of bosons which do not obey Pauli’s Exclusion Principle (in quantum physics). Neutrosophic probability is close related to neutrosophic logic and neutrosophic set, and etymologically derived from “neutrosophy” [58, 59].

An introduction to DSmT

Abstract: 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

Combination of Qualitative Information with 2-Tuple Linguistic Representation in DSmT

Abstract: Modern systems for information retrieval, fusion and management need to deal more and more with information coming from human experts usually expressed qualitatively in natural language with linguistic labels. In this paper, we propose and use two new 2-Tuple linguistic representation models (i.e., a distribution function model (DFM) and an improved Herrera-Martinez’s model) jointly with the fusion rules developed in Dezert-Smarandache Theory (DSmT), in order to combine efficiently qualitative information expressed in term of qualitative belief functions. The two models both preserve the precision and improve the efficiency of the fusion of linguistic information expressing the global expert’s opinion. However, DFM is more general and efficient than the latter, especially for unbalanced linguistic labels. Some simple examples are also provided to show how the 2-Tuple qualitative fusion rules are performed and their advantages.

Advances and applications of DSmT for information fusion - Collected works - Volume 3

Abstract: This volume has about 760 pages, split into 25 chapters, from 41 contributors. First part of this book presents advances of Dezert-Smarandache Theory (DSmT) which is becoming one of the most comprehensive and flexible fusion theory based on belief functions. It can work in all fusion spaces: power set, hyper-power set, and super-power set, and has various fusion and conditioning rules that can be applied depending on each application. Some new generalized rules are introduced in this volume with codes for implementing some of them. For the qualitative fusion, the DSm Field and Linear Algebra of Refined Label (FLARL) is proposed which can convert any numerical fusion rule to a qualitative fusion rule. When one needs to work on a refined frame of discernment, the refinement can be done using Smarandache's algebraic codification. New interpretations and implementations of the fusion rules based on sampling techniques and referee functions are proposed, including the probabilistic proportional conflict redistribution rule. A new probabilistic transformation of mass of belief is also presented which outperforms the classical pignistic transformation in term of probabilistic information content. The second part of the book presents applications of DSmT in target tracking, in satellite image fusion, in snow-avalanche risk assessment, in multi-biometric match score fusion, in assessment of an attribute information retrieved based on the sensor data or human originated information, in sensor management, in automatic goal allocation for a planetary rover, in computer-aided medical diagnosis, in multiple camera fusion for tracking objects on ground plane, in object identification, in fusion of Electronic Support Measures allegiance reports, in map regenerating forest stands, etc.

N-norm and N-conorm in Neutrosophic Logic and Set, and the Neutrosophic Topologies

Abstract: In this paper we present the N-norms/N-conorms in neutrosophic logic and set as extensions of T-norms/T-conorms in fuzzy logic and set. Also, as an extension of the Intuitionistic Fuzzy Topology we present the Neutrosophic Topologies.

Groups as graphs

Abstract: 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.

A Family of Estimators for Estimating Population Mean in Stratified Sampling under Non-Response

Abstract: Khoshnevisan et al. (2007) proposed a general family of estimators for population mean using known value of some population parameters in simple random sampling. The objective of this paper is to propose a family of combined-type estimators in stratified random sampling adapting the family of estimators proposed by Khoshnevisan et al. (2007) under non-response. The properties of proposed family have been discussed. We have also obtained the expressions for optimum sample sizes of the strata in respect to cost of the survey. Results are also supported by numerical analysis.

An introduction to DSmT

Abstract: 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.

On PT-Symmetric Periodic Potential, Quark Confinement, and Other Impossible Pursuits

Abstract: As we know, it has been quite common nowadays for particle physicists to think ofsix impossible things before breakfast, just like what their cosmology fellows used todo. In the present paper, we discuss a number of those impossible things, includingPT-symmetric periodic potential, its link with condensed matter nuclear science, andpossible neat link with Quark confinement theory. In recent years, the PT-symmetryand its related periodic potential have gained considerable interests among physicists.We begin with a review of some results from a preceding paper discussing derivation ofPT-symmetric periodic potential from biquaternion Klein-Gordon equation and proceedfurther with the remaining issues. Further observation is of course recommended inorder to refute or verify this proposition.

Estimation of Mean in Presence of Non Response Using Exponential Estimator

Abstract: 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.

Kaluza-Klein-Carmeli Metric from Quaternion-Clifford Space, Lorentz' Force, and Some Observables

Abstract: It was known for quite long time that a quaternion space can be generalized to a Clifford space, and vice versa; but how to find its neat link with more convenient metric form in the General Relativity theory, has not been explored extensively. We begin with a representation of group with non-zero quaternions to derive closed FLRW metric [1], and from there obtains Carmeli metric, which can be extended further to become 5D and 6D metric (which we propose to call Kaluza-Klein-Carmeli metric). Thereafter we discuss some plausible implications of this metric, beyond describing a galaxy’s spiraling motion and redshift data as these have been done by Carmeli and Hartnett [4, 5, 6]. In subsequent section we explain Podkletnov’s rotating disc experiment. We also note possible implications to quantum gravity. Further observations are of course recommended in order to refute or verify this proposition.

An introduction to the neutrosophic probability applied in quantum physics

Abstract: In this paper one generalizes the classical probability and imprecise probability to the notion of "neutrosophic probability" in order to be able to model Heisenberg's Uncertainty Principle of a particle's behavior, Schrodinger's Cat Theory, and the state of bosons which do not obey Pauli's Exclusion Principle (in quantum physics). Neutrosophic probability is close related to neutrosophic logic and neutrosophic set, and etymologically derived from "neutrosophy".

Degree of Negation of an Axiom

Abstract: In this article we present the two classical negations of Euclid's Fifth Postulate (done by Lobachevski-Bolyai-Gauss, and respectively by Riemann), and in addition of these we propose a partial negation (or a degree of negation) of an axiom in geometry. The most important contribution of this article is the introduction of the degree of negation (or partial negation) of an axiom and, more general, of a scientific or humanistic proposition (theorem, lemma, etc.) in any field - which works somehow like the negation in fuzzy logic (with a degree of truth, and a degree of falsehood), or like in neutrosophic logic [with a degree of truth, a degree of falsehood, and a degree of neutrality (i.e. neither truth nor falsehood, but ambiguous, unknown, indeterminate)].

n-Linear Algebra of type II

Abstract: 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.

n-ARY FUZZY LOGIC AND NEUTROSOPHIC LOGIC OPERATORS

Abstract: We extend Knuth’s 16 Boolean binary logic operators to fuzzy logic and neutrosophic logic binary operators. Then we generalize them to n–ary fuzzy logic and neutrosophic logic operators using the smarandache codification of the Venn diagram and a defined vector neutrosophic law. In such way, new operators in neutrosophic logic/set/probability are built.

A Class of DSm Conditioning Rules 1

Abstract: 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.

District Level Analysis of Urbanization from Rural-to-Urban Migration in the Rajasthan State

Abstract: Migration has various dimensions; urbanization due to migration is one of them. In Rajasthan State, District level analysis of urbanization due to migrants shows trend invariably for all the districts of the state though the contribution in urbanization by the migrants varies from district to district. In some districts the share of migrants moving to urban areas is very impressive though in others it is not that much high. The migrants' contribution in urbanization is on the rising over the decades. In this paper district level migration in the Rajasthan state is examined in relation to total urbanization and urbanization due to migration.

On PT-Symmetric Periodic Potential, Quark Confinement, and Other Impossible Pursuits

Abstract: As we know, it has been quite common nowadays for particle physicists to think of six impossible things before breakfast, just like what their cosmology fellows used to do. In the present paper, we discuss a number of those impossible things, including PT-symmetric periodic potential, its link with condensed matter nuclear science, and possible neat link with Quark confinement theory. In recent years, the PT-symmetry and its related periodic potential have gained considerable interests among physicists. We begin with a review of some results from a preceding paper discussing derivation of PT-symmetric periodic potential from biquaternion Klein-Gordon equation and proceed further with the remaining issues. Further observation is of course recommended in order to refute or verify this proposition.

Alternatives to Pearson’s and Spearman’s Correlation Coefficients

Abstract: This article presents several alternatives to Pearson’s correlation coefficient and many examples. In the samples where the rank in a discrete variable counts more than the variable values, the mixture of Pearson’s and Spearman’s gives a better result.

Comments on "A new combination of evidence based on compromise" by K. Yamada

Abstract: Basically, most combination rules are mainly based on a conjunctive operator and propose a specific way of redistributing the global (or the partial) conflicting belief mass among some elements of the power-set (or the hyper-power set) of the frame of discernment. Using the conjunctive rule means that if the experts agree (i.e. their testimonies have a non-empty intersection), we consider them as reliable and if they are in conflict (empty intersection), at least one of the experts is considered unreliable see Dubois and Prade (1988). Then, the disjunctive combination rule can be employed instead see Dubois and Prade (1986). However the disjunctive rule is generally not used because it deteriorates the specificity of the expert’s responses, i.e. the combined mass is usually less specific after the disjunctive fusion than the mass of each source taken separately. If the reliability of the experts is unknown, there are different techniques to estimate it Elouedi et al. (2004); Martin et al. (2008).

General combination rules for qualitative and quantitative beliefs

Abstract: 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.

Neutrosophic Logic, Wave Mechanics, and Other Stories

Abstract: There is beginning for anything; we used to hear that phrase. The same wisdom word applies to us too. What began in 2005 as a short email on some ideas related to interpretation of the Wave Mechanics results in a number of papers and books up to now. Some of these papers can be found in Progress in Physics or elsewhere.

District Level Analysis of Urbanization from Rural-to-Urban Migration in the Rajasthan State

Abstract: Migration has various dimensions; urbanization due to migration is one of them. In Rajasthan State, district level analysis of urbanization due to migrants shows trend invariably for all districts of the state, though the contribution in urbanization by migrants varies from district to district. In some districts the share of migrants moving to urban areas is very impressive, in others it is not that much high. The migrants' contribution is on the raising over the decades. In this paper, the district level migration in the Rajasthan State is examined in relation to total urbanization and urbanization due to migration.

Superbimatrices and their generalizations

Abstract: 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