Logic and Foundations Commons^™

Cardinal Functions And Integral Functions, Florentin Smarandache, Mircea Selariu, Marian Nitu

Branch Mathematics and Statistics Faculty and Staff Publications

This paper presents the correspondences of the eccentric mathematics of cardinal and integral functions and centric mathematics, or ordinary mathematics. Centric functions will also be presented in the introductory section, because they are, although widely used in undulatory physics, little known. In centric mathematics, cardinal sine and cosine are dened as well as the integrals. Both circular and hyperbolic ones. In eccentric mathematics, all these central functions multiplies from one to innity, due to the innity of possible choices where to place a point. This point is called eccenter S(s;") which lies in the plane of unit circle UC(O;R = …

Reliability Analysis Of A Series And Parallel Network Using Triangular Intuitionistic Fuzzy Sets, D. Pandey, S. K. Tyagi, Vinesh Kumar

Applications and Applied Mathematics: An International Journal (AAM)

This paper describes a novel approach, based on intuitionistic fuzzy set theory for reliability analysis of series and parallel network. The triangular intuitionistic fuzzy sets are used to represent the failure possibility of each basic (terminal) event to get more comprehensive results for the failure possibility of the top event. The proposed technique is demonstrated on a web server LOG data used to illustrate HTTP (Hyper Text Transfer Protocol) failure

Exact Optimal Solution Of Fuzzy Critical Path Problems, Amit Kumar, Parmpreet Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a fuzzy critical path problem is chosen to show that the results, obtained by using the existing method [Liu, S.T.: Fuzzy activity times in critical path and project crashing problems. Cybernetics and Systems 34 (2), 161-172 (2003)], could be improved to reflect, more appropriate real life situations. To obtain more accurate results of fuzzy critical path problems, a new method that modifies the existing one is proposed here. To demonstrate the advantages of the proposed method it is used to solve a specific fuzzy critical path problem.

Algebraic Structures Using Super Interval Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The advantage of using super interval matrices is that one can build only one vector space using m × n interval matrices, but in case of super interval matrices we can have several such spaces depending on the partition on the interval matrix.

This book has seven chapters. Chapter one is introductory in nature, just introducing the super interval matrices or interval super matrices. In chapter two essential operations on super interval matrices are defined. Further in this chapter algebraic structures are defined on these super interval matrices using these operation. Using these super interval matrices semirings and semivector spaces …

Dsm Super Vector Space Of Refined Labels, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of supermatrices of refined labels. Authors prove super row matrix of refined labels form a group under addition. However super row matrix of refined labels do not form a group under product; it only forms a semigroup under multiplication. In this book super column matrix of refined labels and m × n matrix of refined labels are introduced and studied. We mainly study this to introduce to super vector space of refined labels using matrices. We in this book introduce the notion of semifield of refined labels using which …

Dsm Vector Spaces Of Refined Labels, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The study of DSm linear algebra of refined labels have been done by Florentin Smarandache, Jean Dezert, and Xinde Li.

In this book the authors introduce the notion of DSm vector spaces of refined labels. The reader is requested to refer the paper as the basic concepts are taken from that paper [35]. This book has six chapters. The first one is introductory in nature just giving only the needed concepts to make this book a self contained one. Chapter two introduces the notion of refined plane of labels, the three dimensional space of refined labels DSm vector spaces. Clearly …

A New Method For Fuzzy Critical Path Analysis In Project Networks With A New Representation Of Triangular Fuzzy Numbers, Amit Kumar, Parmpreet Kaur

Applications and Applied Mathematics: An International Journal (AAM)

The method for finding fuzzy optimal solution of fully fuzzy critical path (FFCP) problems i.e., critical path problems in which all the parameters are represented by fuzzy numbers, is at best scant; possibly non-existent. In this paper, a method is proposed to find the fuzzy optimal solution of FFCP problems, together with a new representation of triangular fuzzy numbers. This paper will show the advantages of using, the proposed representation over the existing representations of triangular fuzzy numbers and will present with great clarity the proposed method and illustrate its application to FFCP problems occurring in real life situations.

Duality In Fuzzy Linear Programming With Symmetric Trapezoidal Numbers, S. H. Nasseri, E. Ebrahimnejad, S. Mizuno

Applications and Applied Mathematics: An International Journal (AAM)

Linear programming problems with trapezoidal fuzzy numbers have recently attracted much interest. Various methods have been developed for solving these types of problems. Here, following the work of Ganesan and Veeramani and using the recent approach of Mahdavi-Amiri and Nasseri, we introduce the dual of the linear programming problem with symmetric trapezoidal fuzzy numbers and establish some duality results. The results will be useful for post optimality analysis.

Advances And Applications Of Dsmt For Information Fusion (In Chinese), Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Fusion Of Sources Of Evidence With Different Importances And Reliabilities, Florentin Smarandache, Jean Dezert, J.M. Tacnet

Branch Mathematics and Statistics Faculty and Staff Publications

This paper presents a new approach for combining sources of evidences with different importances and reliabilities. Usually, the combination of sources of evidences with different reliabilities is done by the classical Shafer’s discounting approach. Therefore, to consider unequal importances of sources, if any, a similar reliability discounting process is generally used, making no difference between the notion of importance and reliability. In fact, in multicriteria decision context, these notions should be clearly distinguished. This paper shows how this can be done and we provide simple examples to show the differences between both solutions for managing importances and reliabilities of sources. …

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 …

Elementary Fuzzy Matrix Theory And Fuzzy Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

This book aims to assist social scientists to analyze their problems using fuzzy models. The basic and essential fuzzy matrix theory is given. The book does not promise to give the complete properties of basic fuzzy theory or basic fuzzy matrices. Instead, the authors have only tried to give those essential basically needed to develop the fuzzy model. The authors do not present elaborate mathematical theories to work with fuzzy matrices; instead they have given only the needed properties by way of examples. The authors feel that the book should mainly help social scientists who are interested in finding out …

Special Fuzzy Matrices For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

This book is a continuation of the book, "Elementary fuzzy matrix and fuzzy models for socio-scientists" by the same authors. This book is a little advanced because we introduce a multi-expert fuzzy and neutrosophic models. It mainly tries to help social scientists to analyze any problem in which they need multi-expert systems with multi-models. To cater to this need, we have introduced new classes of fuzzy and neutrosophic special matrices. The first chapter is essentially spent on introducing the new notion of different types of special fuzzy and neutrosophic matrices, and the simple operations on them which are needed in …

A Unifying Field In Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability And Statistics - 6th Ed., Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

It was a surprise for me when in 1995 I received a manuscript from the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philosophy - revealing paradoxes - and logics. He had generalized the fuzzy logic, and introduced two new concepts: a) “neutrosophy” – study of neutralities as an extension of dialectics; b) and its derivative “neutrosophic”, such as “neutrosophic logic”, “neutrosophic set”, “neutrosophic probability”, and “neutrosophic statistics” and thus opening new ways of research in four fields: philosophy, logics, set theory, and probability/statistics. It was known to me his setting up in …

Some Neutrosophic Algebraic Structures And Neutrosophic N-Algebraic Structures, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, for the first time we introduce the notion of neutrosophic algebraic structures for groups, loops, semigroups and groupoids and also their neutrosophic N-algebraic structures. One is fully aware of the fact that many classical theorems like Lagrange, Sylow and Cauchy have been studied only in the context of finite groups. Here we try to shift the paradigm by studying and introducing these theorems to neutrosophic semigroups, neutrosophic groupoids, and neutrosophic loops. We have intentionally not given several theorems for semigroups and groupoid but have given several results with proof mainly in the case of neutrosophic loops, biloops …

Sequences Of Numbers Involved In Unsolved Problems, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Here it is a long list of sequences, functions, unsolved problems, conjectures, theorems, relationships, operations, etc. Some of them are inter-connected. 1) Consecutive Sequence: 1,12,123,1234,12345,123456,1234567,12345678,123456789,12345678910, 1234567891011,123456789101112,12345678910111213,... How many primes are there among these numbers? In a general form, the Consecutive Sequence is considered in an arbitrary numeration base B.

References:

Student Conference, University of Craiova, Department of Mathematics, April 1979, "Some problems in number theory" by Florentin Smarandache.

Arizona State University, Hayden Library, "The Florentin Smarandache papers" special collection, Tempe, AZ 85287-1006, USA.

The Encyclopedia of Integer Sequences", by N. J. A. Sloane and S. Plouffe, Academic Press, San Diego, …

Fuzzy And Neutrosophic Analysis Of Women With Hiv/Aids, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Fuzzy theory is one of the best tools to analyze data, when the data under study is an unsupervised one, involving uncertainty coupled with imprecision. However, fuzzy theory cannot cater to analyzing the data involved with indeterminacy. The only tool that can involve itself with indeterminacy is the neutrosophic model. Neutrosophic models are used in the analysis of the socio-economic problems of HIV/AIDS infected women patients living in rural Tamil Nadu. Most of these women are uneducated and live in utter poverty. Till they became seriously ill they worked as daily wagers. When these women got admitted in the hospital …

Fuzzy And Neutrosophic Analysis Of Periyar’S Views On Untouchability, Florentin Smarandache, Vasantha Kandasamy, K. Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

“Day in and day out we take pride in claiming that India has a 5000 year old civilization. But the way Dalits and those suppressed are being treated by the people who wield power and authority speaks volumes for the degradations of our moral structure and civilized standards.” Ex-President of India, the late K. R. Narayanan The New Indian Express, Saturday, 12 Nov. 2005 K.R.Narayanan was a lauded hero and a distinguished victim of his Dalit background. Even in an international platform when he was on an official visit to Paris, the media headlines blazed, ‘An Untouchable at Elysee’. He …

Analysis Of Social Aspects Of Migrant Labourers Living With Hiv/Aids Using Fuzzy Theory And Neutrosophic Cognitive Maps, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic logic grew as an alternative to the existing topics and it represents a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined-ness, unknown, incompleteness, inconsistency, redundancy and contradiction. Despite various attempts to reorient logic, there has remained an essential need for an alternative system that could infuse into itself a representation of the real world. Out of this need arose the system of neutrosophy and its connected logic, neutrosophic logic. This new logic, which allows also the concept of indeterminacy to play a role in any real-world problem, was introduced first by one of the authors Florentin Smarandache. In this …

A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (Chinese Translation), Florentin Smarandache, Feng Liu

Branch Mathematics and Statistics Faculty and Staff Publications

中智学为何诞生? 中智学(neutrosophy)起源于1995年美国, 它站在东西文化交融的立场上, 从对立统一的角度探索从科学技术到文学 艺术的一切宏观及微观结构, 构造超越一切学科、超越自然科学与社会科学界限的统一场, 以解决当今认知科学、信息 科学、系统科学、经济学、量子力学等科学技术前沿难题——非确定性问题。中智学努力通过新型开放模式改造当今 各自然科学与社会科学, 实现它们的新陈代谢、改革创新和更新换代。中智学在我们中国还属空白, 故借此对学科正式 命名并引入中国。 科学是真理吗? 比如, 当今信息科学的突出问题之一就是知识表达、知识处理及知识交流中的逻辑单一性: 不是真就是假, 从而不 能面对任何矛盾和冲突。由此, 人工智能、计算机网络、数据库、信息工程, 乃至电子商务、电子政务多多少少在走死 胡同。从表面上看, 它是模糊数学或协调逻辑的问题, 而从本质上看, 它属于结构性问题, 涉及到对哲学、逻辑学、集 合论、概率论、认知科学、信息科学基本概念以及众多相关领域的重新认识、重新塑造问题。 众所周知, 我国学习西方, 只图表面, 而不注重科学的内在结构, 不懂科学的概念和原理中也有基础设施 (换句话 说, 就是基础设施的基础设施), 从而建不起高楼大厦, 更谈不上科学上的自主, 从而形成盲目跟从西方的弊病。 科学, 这个被认为是永恒的真理, 其本质上没有半点永恒, 相反, 它时刻处于新老交替、新陈代谢、自我否定、自 我淘汰的动态之中——即使存在什么永恒的真理, 也终究会被后人推翻。科学实际上是一种战争, 而中智学正是关于它 的战略战术的科学。 当今世界上高深的科学莫过于爱因斯坦的相对论, 然而一切的一切, 都是建立在恒定光速的基础上——它正 在被现代的人们推翻!

Proceedings Of The First International Conference On Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability And Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In 1960s Abraham Robinson has developed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, that rigorously defines the infinitesimals. Informally, an infinitesimal is an infinitely small number. Formally, x is said to be infinitesimal if and only if for all positive integers n one has xxx < 1/n. Let &>0 be a such infinitesimal number. The hyper-real number set is an extension of the real number set, which includes classes of infinite numbers and classes of infinitesimal numbers. Let’s consider the non-standard finite numbers 1+ = 1+&, where “1” is its standard part and “&” its non-standard part, …

On Minimal Regular Graphs With Given Constraintsm, Che Sheng Gan

Student Works (2000-2009)

A classical question in graph theory has been the search of cages. The problem of determining the smallest (r,g)-cage is unsolved for most pairs of (r,g) and is extremely hard in the general case. Finding the crossing number of a graph is another challenging problem in graph theory. The crossing numbers of very few classes of graphs arc known. In this thesis, we would like to (a) investigate those smallest regular graphs with given girths and having small crossing numbers. In particular, we investigate those smallest regular graphs with given girths and crossing number c, for c ∈ {0, 1, …

Subiecte Posibile Pentru Examenul De Admitere În Liceu Şi Examenul De Capacitate (In Romanian), Florentin Smarandache, Constantin Coanda, Gheorghe Duta

Branch Mathematics and Statistics Faculty and Staff Publications

Prezenta lucrare" încearcă să pună la dispoziţia elevilor şi profesorilor instrumente de evaluare a cunoştinţelor la toate capitolele din actuala programă de matematică. " În evoluţia adolescenţi/or din ţara noastră etapa admiterii în liceu mobilizează eforturi şi emoţii cu totul speciale. 'Actuala lucrare se doreşte a fi un sfljtuitor permanent În perioada fierbinte dintre e.;wmenul de capacitate şi admiterea În liceu. Testele cuprinse in această culegere au un caracter complementar faţă de multe materiale scrise În vederea sprijinirii celor ce se pregătesc pentru astfel de examene şi se referă la intreaga materie cuprinsă În programele analitice de aritmetică, algebră şi …

Only Problems, Not Solutions! (Fourth Edition), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Generalisations Et Generalites, Florentin Smarandache, Eleonora Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

"Généralisations et Généralités" , pourquoi ce titre? Parce Que l'auteur a voulu rassembler ici Quelques-unes de ses recherches originales C Qui sont donc des "s~n:§rali tés") , df'2ls diverses branches des mathématiques (algèl)re, thôorie des nombres, Gométrie, analyse, linguistique, mathématiQues distrayantes) , mêlne si les articles qui composent ce recueil n'ont pas toujours de liaison entre eux.

Investigation Of The Properties Of The Iterations Of A Homeomorphism On A Metric Space, Murray B. Peterson, Jr.

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Considerable study has been made concerning the properties of the iterations of a homeomorphism on a metric space. Much of this material is scattered throughout the literature and understood solely by a specialist. The main object of this paper is to put into readable form proofs of theorems found in G.T. Whyburn's "Analytic Topology" pertaining to this topic in topology. Properties of the decomposition space of point-orbits induced by the iterations of a homeomorphism will compose a major part of the study. Some theorems will be established through series of lemmas required to fill in much of the detail lacking …