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...theory and when indeterminacy is involved we use neutrosophic theory. Most of the fuzzy models which deal with the analysis and study of unsupervised data make use of the directed graphs or bipartite graphs. Thus the use of graphs has become inevitable in fuzzy models. The neutrosophic models are fuzzy models that permit the factor of indeterminacy. It also plays a signifi...

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... of the fuzzy models which deal with the analysis and study of unsupervised data make use of the directed graphs or bipartite graphs. Thus the use o... ...d by fuzzy theory. The causal structure of fuzzy cognitive maps from sample data [33-34] mainly uses the notion of fuzzy signed directed graphs with... ...cations of fuzzy theory is a grand one for most of analysis of unsupervised data are very successfully carried out by the use of Fuzzy Cognitive Map... ...d an easy representation even by a lay man. Thus we can say whenever the data had a fuzzy matrix representation it is bound to get the digraph re... ... Industry Owner, Employees' Association Union Leader and an Employee. The data and the opinion are taken only from one industry. Using the opinion... ...y a role in the study of FRMs and in fact we give a method of conversion of data from FRMs to FCMs. As both the models FRMs and FCMs work on the a... ...the concept of indeterminacy. We also mention that most of the unsupervised data also involve at least to certain degrees the notion of indeterminac... ...r [9]. Adaptive Fuzzy Cognitive Maps can learn the weight from historical data. Once the FCM is trained, it lets us play what-if games (eg. what i... ... criminal cases the concerned may not be able draw conclusions based on the data provided to him. Very many relations can be indeterminable so NCMs ...

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...Graphs and matrices play a vital role in the analysis and study of several of the real world problems which are based only on unsupervised data. The fuzzy and neutrosophic tools like fuzzy cognitive maps invented by Kosko and neutrosophic cognitive maps introduced by us help in the analysis of such real world problems and they happen to be mathematical tools wh...

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...dy of several of the real world problems which are based only on unsupervised data. The fuzzy and neutrosophic tools like fuzzy cognitive maps inven... ...ed bimatrices. FCMs work on opinion of the experts given on the unsupervised data. The main advantage of this system is it can give the hidden patt... ... its interrelated definitions. FCMs have a major role to play mainly when the data concerned is an unsupervised one. Further this method is most sim... ...Further this method is most simple and an effective one as it can analyse the data by directed graphs and connection matrices. 72 DEFINITION 3.... ...ing to murder) for want of more money and so on. Thus one cannot actually get data for this but can use the expert's opinion for this unsupervised d... ...ntage of this method it is simple. It functions on expert's opinion. When the data happens to be an unsupervised one the FCM comes handy. This is t... ...n. As we have a very well known theory, which states that the strength of the data 76 depends on, the number of experts opinion we can use combin... ...ine the notion of Fuzzy cognitive bimaps. Suppose we have some unsupervised data to be analyzed and suppose it has two sets of disjoint attributes... ...s faced while running a industry or a factory cannot be put as a statistical data. Several of them are feelings involving a great deal of uncertain...

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...lass defined in the java.math package of Java. It is an extended precision data type that allows for very large numbers to be represented and manipula... ...her bases. static BigInteger base1=new BigInteger("3"); // File where the data is sent static String filename="Basevalues.txt"; static File output;... ... str1=str1+base1Value+"\n"; System.out.println(str1); // Write the data to a file. try { out.write(str1); } catch(IOExcep... ...("Could not close the file"); } } } 10 The program uses the BigInteger data type, which can hold numbers of arbitrary size, and the function base1... ... } catch(IOException ioe) { System.out.println("Could not write data to the file"); } theCount=theCount.add(BigInteger.ONE); } Sy... ...nce. static BigInteger base1=new BigInteger("3"); // The name of the file data can be sent to. static String filename="Antsymmetricvalues.txt"; sta... ...esults for all elements with index less than or equal to 2000 are given in data listing 1. Data listing 1 For term number 54, the number is divisible ... ...rse Sequence that are evenly divisible by 11 2 , and the results appear in data listing 2. Data listing 2 For term number 18, the number is divisible ... ...; static final BigInteger theHUNDRED=new BigInteger("100"); // File where data is written. static String filename="ConcatenatedSquares.txt"; static...

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...1,10}, C={z E JRJz=(an + b)/(cn + d), a,b,c,d E JR, cd>O, n=l,p}? 8. Fie data multimea A = {-3,-2,-1,1,2,3}. Sa se determine submultimile lui A: A... ...J-l(X) = ..;x, x E [0, +00). 12. Fie {A = 1,2,3,4,5,6,7,8,9} §i <p E F(A) data eu ajutorul tabelului a) Sa se determine <p({2,3,5}); <p({1,3, 7,9})... ...0) xay <=} y = 2x; 11) xay <=} y2 = x 2 ; 12) xay <=} x . Y = O. 7. Este data multimea A §i relatia binara a ~ A 2 . Sa se demon­ streze ca a este ... ...= {(I,3),(1,I),(3,1),(1,2),(2,I),(2,2), (3,3),(3,2),(2,3),(5,5)}. 8. Fie data mul~imea A = {I, 2,3,4,5,6,7,8, 9} §i sistemul de submuitimi S = {Ai ... ...<.p: A ~ B, un de A = {1,2,3,4,5,6,7,8,9} §i B = {a, b, c, d, e, f}, este data de tabelul Sa se determine <.p(A), <.p({2,3,5}), <.p({5,6,7,8}), <.p(... ... 0; 13) a: x 2 +y2 = 16; 14) a: y = x2-3x+l; 15) a: 2xy = y2+5. 25. Este data relatia a cu D et = [-3; 5J §i Pet = [-4; 7J. a) Perechea (-4,5) apa... ...dicati toate perechile ordonate (x, y) E a cu x = 0. Explicati. 26. Fiind data functia f( x), calculati valorile ei in punctele indi- cate. 1) f(x) ... ...x-_-l-:"7); 8) f(x) = JJX+2 - 2; 10) f(x) = (Jx/(x + 4) - 2)2. 35. Este data funetia: f: E IR -- 1R, f(X)={ x2-2x-2, x 2:: 1, 2x - 1, x < l. a) ... ...nitiile 1 - 3, fiecare element al multimii initiale M figureaza 0 singura data. Paralel cu combinatiile in care fie care din cele n elemente diferit...

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...to control pollution by improving the system performance using hierarchical genetic fuzzy control algorithm. This study is carried out using the past data reported by Shimada et al (1995). Health hazards suffered by the agriculture labourers; caused by the chemicals used as fertilizers and pesticides is analysed in chapter four using RTD matrices. Chapter five gives a meth...

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...In this chapter, we have used the fuzzy control method to find the correct measure of pressure and speed of kiln. Using data from Alathur cement industry, we have used mean of maximum method of fuzzy control with the data and we found the pressure and speed of kiln. Here the speed and pressure of kiln are important parameters in the kiln, beca...

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...lgorithm to Control Process Variables of Decision Tables in Chemical Plants 56 3.4 Use of Hierarchical Genetic Fuzzy Control Algorithm in the Real Data 58 3.5 Conclusions 73 Chapter Four IDENTIFICATION OF THE MAXIMUM AGE GROUP IN WHICH THE AGRICULTURAL LABOURERS SUFFER HEALTH HAZARDS DUE TO CHEMICAL POLLUTION USING RTD MATRIX 75 4.1 Introduction 75 4.2 Estimati...

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...is organized into seven chapters. The first one is introductory in nature. In the second chapter authors give the unique and new way of analyzing the data which is time dependent. In chapter three the authors for the first time define the new concept of matrices with linguistic variables. In chapter four authors have used super matrices in super fuzzy models like super FCM...

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...Preface 5 Chapter One INTRODUCTION 7 Chapter Two AVERAGE TIME DEPENDENT (ATD) DATA MATRIX 9 Chapter Three FUZZY LINGUISTIC MATRICES AND THEIR APPLICATIONS 43 Chapter Four SUPERMATRICES AND THEIR APPLICATIONS 65 Chapter Five INTERVAL MATRICES AND NATURAL CLASS OF INTERVALS 149 Chapter Six DSM...

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...nference system can be applied to decision making. Chapter 3 gives one application of interval neutrosophic sets and logic in the field of relational databases. Neutrosophic data model is the generalization of fuzzy data model and paraconsistent data model. Here, we generalize various set-theoretic and relation-theoretic operations of fuzzy data model to neutrosophic data ...

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...eutrosophic Logic . . . . . . . . . . . . . . . 32 2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3 Neutrosophic Relational Data Model 39 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.2 Fuzzy Relations and Operations . . . . . . . . . . . . . . . . . . . . 42 3.2.1 Set-theoretic operations on Fuzzy relations . . . . ...

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... notions of matrices are given in section one in order to make the book self contained. Section two gives the properties of fuzzy matrices. Since the data need to be transformed into fuzzy models, some elementary properties of graphs are given. Further, this section provides details of how to prepare a linguistic questionnaire to make use of in these fuzzy models when the ...

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... – C) –1 < 0. The reader is expected to construct real models by taking data's from several industries. Thus one can develop several other proper... ...a role in the study of NRMs and in fact we give a method of conversion of data from NRMs to NCMs. As both the models NRMs and NCMs work on the ad...

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...terval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval matrices but have also demonstrated some of its applications when the data under study is an unsupervised one and when several experts analyze the problem....

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...h was introduced by Bart Kosko in the year 1986. We also give several of its interrelated definitions. FCMs have a major role to play mainly when the data concerned is an unsupervised one. Further this method is most simple and an effective one as it can analyse the data by directed graphs and connection matrices. DEFINITION 1.2.1: An FCM is a directed graph with concepts...

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...power of the DSmT framework. In this third Volume, DSmT is applied to the entire spectrum of the Information Fusion that would interest any reader in data, sensor, information, and mathematical fusion topics. Highlighted in Figure 1 are the contemporary issues that include the links between (1) data conditioning and information management, (2) combined situation and impact...

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...ents . . . . . . . . . 409 13.7 References . . . . . . . . . . . 409 Chapter 14 Performance evaluation of a tracking algorithm including attribute data 411 by J. Dezert, A. Tchamova, L. Bojilov and P. Konstantinova 14.1 Introduction . . . . . . . . . . 412 14.2 Problemformulation . . . . . . . . . 412 14.2.1 Kinematic likelihood ratios for GDA . . . . . 413 14.2.2...

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...s and information fusion. So, we hope that this second volume on DSmT will continue to stir up some interests to researchers and engineers working in data fusion and in artificial intelligence....

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...entation . . . . . . . . . 298 11.4 Classifiers fusion in Radar target recognition . . . . . . 300 11.4.1 Classifiers . . . . . . . . . 300 11.4.2 Database . . . . . . . . . 300 11.4.3 Model . . . . . . . . . . 301 11.4.4 Results . . . . . . . . . 301 11.5 Conclusion . . . . . . . . . . . 303 11.6 References . . . . . . . . . . . 303 Chapter 12 Multitarget Tracking...

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...hort technical paper advocates a bootstrapping algorithm from which we can form a statistically reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing’s osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing’s osteosarcoma, cannot increase ...

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...g, edited by Yan-Qing Zhang and Tsau Young Lin, Georgia State University, Atlanta, USA, 305-308, 2006................462 57. Neutrosophic Relational Data Model, by Haibin Wang, Rajshekhar Sunderraman, Florentin Smarandache, André Rogatko, in (Society for Mathematics of Uncertainty, Creighton University), Vol. II, 19-35, 2008.......480 58. Neutrosophic Logic Based Semant...

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...hort technical paper advocates a bootstrapping algorithm from which we can form a statistically reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing’s osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing’s osteosarcoma, cannot increase ...

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...g, edited by Yan-Qing Zhang and Tsau Young Lin, Georgia State University, Atlanta, USA, 305-308, 2006................462 57. Neutrosophic Relational Data Model, by Haibin Wang, Rajshekhar Sunderraman, Florentin Smarandache, André Rogatko, in (Society for Mathematics of Uncertainty, Creighton University), Vol. II, 19-35, 2008.......480 58. Neutrosophic Logic Based Semant...