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University of New Mexico

Branch Mathematics and Statistics Faculty and Staff Publications

2009

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Neutrosophic Logic, Wave Mechanics, And Other Stories: Selected Works 2005-2008, Florentin Smarandache, Victor Christianto Mar 2009

Neutrosophic Logic, Wave Mechanics, And Other Stories: Selected Works 2005-2008, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

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. It is often recognized that when a mathematician meets a physics-inclined mind then the result is either a series of endless debates or publication. In our story, we prefer to publish rather than perish. Therefore, our purpose with this …


Superbimatrices And Their Generalizations, Florentin Smarandache, W.B Vasantha Kandasamy Jan 2009

Superbimatrices And Their Generalizations, Florentin Smarandache, W.B Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The systematic study of supermatrices and super linear algebra has been carried out in 2008. These new algebraic structures find their applications in fuzzy models, Leontief economic models and data-storage in computers. In this book the authors introduce the new notion of superbimatrices and generalize it to super trimatrices and super n-matrices. Study of these structures is not only interesting and innovative but is also best suited for the computerized 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 …


An Introduction To Dezert-Smarandache Theory (Dsmt), Jean Dezert, Florentin Smarandache Jan 2009

An Introduction To Dezert-Smarandache Theory (Dsmt), Jean Dezert, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or highly 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 …


Advances And Applications Of Dezert-Smarandache Theory (Dsmt) For Information Fusion (Collected Works), Vol. 3, Florentin Smarandache, Jean Dezert Jan 2009

Advances And Applications Of Dezert-Smarandache Theory (Dsmt) For Information Fusion (Collected Works), Vol. 3, Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

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 Labels (FLARL) is …


Studies In Statistical Inference, Sampling Techniques And Demography, Florentin Smarandache, Rajesh Singh, Jayant Singh Jan 2009

Studies In Statistical Inference, Sampling Techniques And Demography, Florentin Smarandache, Rajesh Singh, Jayant Singh

Branch Mathematics and Statistics Faculty and Staff Publications

This volume is a collection of five papers. Two chapters deal with problems in statistical inference, two with inferences in finite population, and one deals with demographic problem. The ideas included here will be useful for researchers doing works in these fields. The following problems have been discussed in the book: Chapter 1. In this chapter optimum statistical test procedure is discussed. The test procedures are optimum in the sense that they minimize the sum of the two error probabilities as compared to any other test. Several examples are included to illustrate the theory. Chapter 2. In testing of hypothesis …


Special Set Linear Algebra And Special Set Fuzzy Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral Jan 2009

Special Set Linear Algebra And Special Set Fuzzy Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

This book for the first time introduces the notion of special set linear algebra and special set fuzzy linear algebra. This is an extension of the book set linear algebra and set fuzzy linear algebra. These algebraic structures basically exploit only the set theoretic property, hence in applications one can include a finite number of elements without affecting the systems property. These new structures are not only the most generalized structures but they can perform multi task simultaneously; hence they would be of immense use to computer scientists. This book has five chapters. In chapter one the basic concepts about …


Groups As Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy Jan 2009

Groups As Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Through this book, for the first time we represent every finite group in the form of a graph. 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 …


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, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Kandasamy Jan 2009

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, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The new notions of super column FRM model, super row FRM model and mixed super FRM model are introduced in this book. These three models are introduced specially to analyze the biased role of the print media on 27 percent reservation for the Other Backward Classes (OBCs) in educational institutions run by the Indian Central Government. This book has four chapters. In chapter one the authors introduce the three types of super FRM models. Chapter two uses these three new super fuzzy models to study the role of media which feverishly argued against 27 percent reservation for OBCs in Central …


An Introduction To Dsmt, Florentin Smarandache, Jean Dezert Jan 2009

An Introduction To Dsmt, Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or highly 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 …


Investigation Of A Neutrosophic Group, A. Elrawy, Florentin Smarandache, Ayat A. Temraz Jan 2009

Investigation Of A Neutrosophic Group, A. Elrawy, Florentin Smarandache, Ayat A. Temraz

Branch Mathematics and Statistics Faculty and Staff Publications

We use a neutrosophic set, instead of an intuitionistic fuzzy because the neutrosophic set is more general, and it allows for independent and partial independent components, while in an intuitionistic fuzzy set, all components are totally dependent. In this article, we present and demonstrate the concept of neutrosophic invariant subgroups. We delve into the exploration of this notion to establish and study the neutrosophic quotient group. Further, we give the concept of a neutrosophic normal subgroup as a novel concept.