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....3 Fuzzy compatibility relations and composition of fuzzy relations 22 1.4 Optimization Of FRE with Max-Product composition 32 1.5 Compo... ...solution based on Archimedean triangular norms 40 1.6 Solving non-linear optimization problem with FRE constraints 48 1.7 Method of sol... ...elation equations in a complete Brouwerian lattice 55 1.8 Multi-objective optimization problems with fuzzy relation equation constraints 5... ...OPERTIES 4.1 Neutrosophic relational equations: Basic Definitions 249 4.2 Optimization of NRE with max product Composition 259 4.3 Method o... ...their properties It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from X to Y, binary re... ...ominated criterion vectors is called the non-dominated set. In the absence of a mathematical specification of the decision maker’s utility function,... ...ity to determine outputs for a given set of inputs without using conventional, mathematical models. FLC follows the general strategy of control wor... ... with sup-t composition nor adjoint equation. Therefore, simple control is not “mathematically correct”. However, solutions of fuzzy relational equa... ...of the fluid under study their by changing the flow rates while analyzing as a mathematical model. So in the study of flow rates in chemical plants...

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...nitive 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 which can give the hidden pattern of the problem under investigation. This book, in order to generalize the two models, has systematically invented mathematical tools like bimatrices, trimatrices, n-matric...

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... by us help in the analysis of such real world problems and they happen to be mathematical tools which can give the hidden pattern of the problem un... ...This book, in order to generalize the two models, has systematically invented mathematical tools like bimatrices, trimatrices, n-matrices, bigraphs,... ...t will be easy for an expert to work with. He need not be a person with good mathematical background. For an expert may be a doctor or a lay man wh... ... of the NRM model we will proceed on to describe the concepts of it in a more mathematical way. DESCRIPTION OF A NRM: Neutrosophic Cognitive Ma... ... Bhattacharya and F. Smarandache. Fuzziness and Funds allocation in Portfolio Optimization. http://lanl.arxiv.org/ftp/math/papers/0203/0203073.pdf ... .... 58. Jacobson, N. Structure of Rings, Colloquium Publications, 37, American Mathematical Society, 1956. 59. Jang, S.R., C.T. Sun and E. Mizutani. ...

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...Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all a...

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...onic Slant Helices According to Bishop Frame in E3 BY ESSIN TURHAN and TALAT K¨ORPINAR . . . . . . . . . . . . . . . . . . . . . . 64 Combinatorial Optimization in VLSI Hypergraph Partitioning Using Taguchi Methods BY P.SUBBARAJ, S.SARAVANASANKAR and S.ANAND . . . . . . . . . . . . . . . . 69 Negation Switching Equivalence in Signed Graphs BY P.SIVA KOTA REDDY, K.SHI...

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...As an alternative to the existing logics we propose the Neutrosophic Logic to represent a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined, unknown, incompleteness, inconsistency, redundancy, contradiction. It is a non-classical logic. Eksioglu (1999) explains some of them: “Imprecis...

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...veloped the non-standard analysis, a formalization of analysis and a branch of mathematical logic, that rigorously defines the infinitesimals. Infor... ...native to the existing logics we propose the Neutrosophic Logic to represent a mathematical model of uncertainty, vagueness, ambiguity, imprecision, ... ...e learning based on genetic operators), evolutionary programming (a stochastic optimization strategy based on linkage between parents and their offs... ... P., Upper and Lower Probabilities Induced by a Multivalued Mapping, Annals of Mathematical Statistics, 38, 325-339, 1967. [8] Dezert, J., Autonomo... ...alysis, Princeton University Press, Princeton, NJ, 1996. [37] Shafer, Glenn, A Mathematical Theory of Evidence, Princeton University Press, NJ, 1976... ...Western Section Meeting, Santa Barbara, CA, USA, Meeting # 951 of the American Mathematical Society, March 11-12, 2000, http://www.ams.org/amsmtgs/2... ...e unity) (47) Using the concise notation , the Lagrangian associated with this optimization problem under equality constraints is given by (we consid... ...ABSTRACT: Probabilistic methods have been used to model uncertainty in many optimization problems, an alternative is to use NeuroFuzzy and Neutro... ...h as much precision as possible. The NeuroFuzzy and Neutrosophic control based optimization minimizes the system possibility of failure. Therefore...

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...e probability of complete financial ruin for the trader but no meaningful mathematical expression can model this case under the assumption of logari... ...so been theoretical advances in the esoteric area of econophysics whereby mathematical analogs have been proposed and substantiated between utility ... ...hysics seek to model natural systems in terms of solutions to constrained optimization problems. Both economic and physical state variables come in ... ... logic based on behavioral reasoning, supported in most parts by rigorous mathematical exposition or numerical simulation and sensitivity analysis. T... ...isk classification is proposed – neutrosophic logic being a new branch of mathematical logic which allows for a three-way generalization of binary f... ...ogue – options-based portfolio insurance. In this chapter we propose and mathematically prove a theorem which we have named the “theorem of consiste... ...our haploid genetic algorithm model is designed to handle only univariate optimization models. However, the problem we are studying is one of multiv... ...ation models. However, the problem we are studying is one of multivariate optimization with three parameters corresponding to the portfolio weights ... ... as given. This then essentially reduces our problem to one of univariate optimization, whereby we have to minimize the cumulative tracking error gi...

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...ed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, which rigorously defines the infinitesimals. Informall... ...n's Paradox: Let M be a mathematician who may not be characterized by his mathematical work. a) To be a mathematician, M should have some mathematic... ...ork. 31 b) The reverse judgement: if M may not be characterized by his mathematical work, then M is not a mathematician. Divine Paradox (I): ... ...false", where S(n) is a sentence relating on parameter n. Can we prove by mathematical induction that P(n) is true? d) "<A> is true if and only if <... ...., "A Practical Guide to Cooperative Learning in Collegiate Mathematics", Mathematical Association of America, Washington, D.C., 1995. ] The m... ...rning based on genetic operators), evolutionary programming (a stochastic optimization strategy based on linkage between parents and their offspring...

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...which were presented at the conference but also those papers which were submitted later and are concerned with the Smarandache type problems or other mathematical problems. Other papers are concerned with the number-theoretic Smarandache problems and will enrich the already rich stock of results on them. Readers can learn various techniques used in number theory and will g...

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...ymptotic formula 33 A. Muktibodh, etc. : Sequences of pyramidal numbers 39 R. Zhang and S. Ma : An e±cient hybrid genetic algorithm for continuous optimization problems 46 L. Mao : An introduction to Smarandache multi-spaces and mathematical combinatorics 54 M. Selariu : Smarandache stepped functions 81 X. Zhang and Y. Zhang : Sequences of numbers with alternate co...