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...ral Tamil Nadu in India W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036, ... ...n web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: s... ... varies from women to women we are forced to analyze the problem using fuzzy mathematics. This chapter has two sections. In the first section we in... ...roduction of learning as encoding. We avoid all types of high and complicated mathematics. As our study is a psychological one, we give more import... ...speed real time environment where we may not have enough time information or computational precision to use supervised technique. Thus we say the d... ...ymposium on Mathematical Methods and Applications, held at the Department of Mathematics, IIT Madras, December 22, 2003. 135. Vasantha Kandasamy...

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...ed by the real difficulty in differentiating various kinda of mathematical research from "crypto-mathematics" - notably in the burgeoning mathematical... ...athematical research from "crypto-mathematics" - notably in the burgeoning mathematical field of Computational Complexity, often seck.i.q solutions to...

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...show, using its axioms and inference laws, that it is consistent In other words, a computational system, like the Matrix, can either be complete an... ...show, using its axioms and inference laws, that it is consistent In other words, a computational system can either be complete and inconsistent - o... ...ished independently (as is often the case in science) the basics of a new branch in Mathematics (and logic): computability or recursive functions (l... ...possess the same sense organs that we do (eyes) and may not be acquainted with our mathematics and geometry. Reality can be successfully described ...

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...AND NEUTROSOPHIC RELATIONAL MAPS W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036... ...ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail:... ...cademia Technica Militaria, Bucharest, Romania. Dr. B.S. Kirangi, Department of Mathematics and Computer Science, University of Mysore, Karnataka, I... ...of genetic algorithms cannot provide measurement for the performance empirical computational testing is necessary. Test problems for computational ... ...icient set. A system of FRE may be manipulated in a way such that the required computational effort of the proposed genetic algorithm is reduced. D... ...al, and thus one defines the neutrosophic set. One gives 227 examples from mathematics, physics, philosophy, and applications of the neutrosoph... ... Darwin (biology), Maxwell (electromagnetism), Einstein (mechanics) and Godel (mathematics). Although paradigm shifts vary from one another in thei... ...w paradigm offers for greater resources for managing complexity and controlling computational cost. This new paradigm has considerably greater expre... ...ase of FREs a system of NREs may be manipulated in a way such that the required computational effort of the proposed genetic algorithm is reduced. D...

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...re more interested to attract all types of reader we have not used very high mathematics. DEFINITION 1.1.1: An FCM is a directed graph with conc... ...ics, Masters Dissertation, Guide: Dr. W. B. Vasantha Kandasamy, Department of Mathematics, Indian Institute of Technology, (2001). 7. Bechtel, J.H... ...er, Simulating Organizational Behaviour with Fuzzy Cognitive Maps, Int. J. of Computational Intelligence and Organization, 1 (1996) 120-123. 17. Di... ...es, Masters Dissertation, Guide: Dr. W. B. Vasantha Kandasamy, Department of Mathematics, Indian Institute of Technology, (2000). 22. Kananaikal, ... ...oblem, Masters Dissertation, Guide: Dr.W.B.Vasantha Kandasamy, Department of Mathematics, Indian Institute of Technology, Chennai, (1999). 26. Ko... ...dents, Masters Dissertation, Guide: Dr.W.B.Vasantha Kandasamy, Department of Mathematics, Indian Institute of Technology, Chennai, (2001). 32. Ma...

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...erican Research Press Rehoboth 2002 József Sándor DEPARTMENT OF MATHEMATICS BABE Ş-BOLYAI UNIVERSITY 3400 CLUJ-NAPOCA, ROMANIA Geome... ...n its inexhaustible wealth, wherein it so greatly surpasses other parts of mathematics..." (K.F. Gauss, Disquisitiones arithmeticae, G ottingen, 1801... ...uable advice or support in the preparation of this material. These are the Mathematics Department of the Babe s-Bolyai University, the Domus Hun- gar... ...ntimate correlation between the Theory of numbers and other departments of Mathematics, not excluding geometry..." (Felix Klein, Evanston Colloquium L... ...bisector theorem. 11 Bibliography 1. F. Smarandache, Proposed problems of Mathematics, vol.II, Kishinev Univ. Press, Kishinev, Problem 61 (pp.41-42),... ...Numb. Theory Rel. Topics, 11(1986), 19-25. 3. B.P. Demidovich, I.A. Maron, Computational mathematics, Moscow, 1981. 4. A. Lupa s, Open problems (Roma...

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...rsive. We can expect to find that we can reduce all the activities of the brain to computational, mechanically solvable, recursive functions. The b... ...measurement and by organizing the results and presenting them using the language of mathematics. This does not atone for its primordial sin: that it... ...d measurement and organizes the results, often presenting them in the language of mathematics. In some quarters, these practices lends it an air o... ...measurement and by organizing its results and presenting them using the language of mathematics. This does not atone for its primordial sin: that it...

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...rsive. We can expect to find that we can reduce all the activities of the brain to computational, mechanically solvable, recursive functions. The b... ...ractitioners sought to disguise its nature as a social science by applying complex mathematics where common sense and direct experimentation would ... ...ifferently to the same transformation? Arithmetic, formal logic, and, by extension, mathematics and physics deal with proving identities in equation... ...ecognized as an important contribution and applied to problems in geometry, logic, mathematics, computation and physics. One of the first questions... ...t infinite sets are organized in a hierarchy. Russel and Whitehead concluded that mathematics was a branch of the logic of sets and that it is ana... ...ations require an "intuition of mathematical order" without which no creativity in mathematics is possible. He described how some of his creative w... ...show, using its axioms and inference laws, that it is consistent In other words, a computational system can either be complete and inconsistent - o... ...show, using its axioms and inference laws, that it is consistent In other words, a computational system, like the Matrix, can either be complete an...

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... Neutrosophic Cognitive Maps W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036, Indi... ...a E-mail: vasantha@iitm.ac.in Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA E-mail: smara... ...t Kardaras and Mentzas [48] introduce Fuzzy Cognitive Maps (FCMs) as a computational modeling formalism which tackles the complexity and allows th... ... many times since it may quite properly be regarded as an area of applied mathematics. The subject finds its place in the work of Euler. Subsequent ... ...e Maps The great scientist Albert Einstein said, "So far as the laws of mathematics refer to reality, they are not certain. And so far as they are... ...ic Cognitive Maps which is a revolutionary method in the field of applied mathematics because it specially studies uncertainty and indeterminacy. As... ...se A. B. Tomè. Rule based Fuzzy Cognitive Maps -- Fuzzy Causal Relations, Computational Intelligence Modelling, Control and Automaton, Edited by M.M... ...imulating Organizational Behaviour with Fuzzy Cognitive Maps, Int. J. of Computational Intelligence and Organization, 1 (1996) 120-123. 29. Diamond... ...alysis, MIS Quarterly, 10 (1986) 45-55. 75. Ndousse, T.D., and T. Okuda. Computational Intelligence for Distributed Fault Management in Networks us...

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...h different financial goals, different levels of risk tolerance and different personal preferences, liquid assets, etc. In part 2, we have defined a computational model for a simple portfolio insurance strategy using a protective put and computationally derive the investor’s governing utility structures underlying such a strategy under alternative market scenarios. In Par...

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...r integer on further development of number theory called it. Rather, number theory is an integer nature of disciplines and it is the oldest branch of mathematics concerned by the study methods, can be divided into elementary number theory, number theory, analytic number theory, algebraic number theory, transcendental number theory, computational number theory, combinatoric...

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...ir comments and recommendations on these papers: I. Balacenoiu, Department of Mathematics, University of Craiova, Romania; C. Corduneanu, Departmen... ...eutrosophic Probability and Statistics) Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA 0.1 In... ..., and start again. We may add rules that don’t preserve monotonicity. In bio-mathematics Heitkoetter and Beasley (1993-1999) present the evolutiona... ...ich are used “to describe computer-based problem solving systems which employ computational models of some of the known mechanisms of evolution as k... ...= 1 and i = 0, and 0 [ t, i, f [ 1); from "CRC Concise Concise Encyclopedia of Mathematics", by Eric W. Weisstein, 1998, the fuzzy logic is "an exte... ...ty with the classical probability theory, with boolean logic and has a feasible computational complexity [46] for problems of small dimension. The DST... ... h e extension to larger frame of discernment is possible but requires a higher computational burden. The general and direct analytic computation of f... ...ngs even in absence of new data [3]. Similar oscillations were demonstrated by computational models of human working memory that treated mental proc... ...ogress has been made in our ability to model and deal with uncertainty through computationally - orientated techniques. In finance, there is a long-...