credibilistic markov decision processes the average case using a concept of random fuzzy variables in credibility theory we formulate a credibilistic model for unichain markov decision processes under average criteria and a credibilistically optimal policy is defined and obtained by solving the corresponding non linear mathematical programming also we give a computational example to illustrate the effectiveness of our new model

discrete time credibilistic processes construction and convergences in this paper we discuss a method of constructing a credibilistic process which is a family of fuzzy variables on credibility space applying the extension theorem in credibility theory the finite or infinite horizon credibilistic process is made up from a family of credibilistic kernels also for the markov case convergence theorems are given and credibilistic risk models for reward processes are considered whose risk is completed by the recursive equation

fuzzy optimality relation for perceptive mdps the average case in this paper the fuzzy perceptive model for average reward markov decision processes is defined and a method of computing the corresponding fuzzy perceptive values is proposed under the minorization condition for fuzzy perceptive transition matrices it is characterized by the optimal average expected reward called the average perceptive value using a fuzzy optimality relation also we give a simple numerical example

sparsity constrained contrast source inversion ultrasound imaging is used for detecting and characterizing breast lesions a state of the art imaging method is the contrast source inversion csi which solves the full wave nonlinear inverse problem however when the measurements are acquired in noisy environments csi can diverge from the correct solution after several iterations problems associated with noisy data were originally solved by including total variation tv regularization unfortunately for very noisy data tv regularization alone is not sufficient in this work compressed sensing ideas are used to regularize the inversion process by restricting the solution of the csi method to be sparse in a transformation domain the proposed method estimates the contrast source and contrast function by minimizing the mean squared error between the measured and modeled data an extra penalty term is added to measure sparsity in the transformation domain a second method that combines sparsity of the contrast source and minimal tv in the contrast function is also presented the proposed methods are tested on noise free and noisy synthetic data sets representing a scan of a cancerous breast numerical experiments show that for measurements contaminated with 1 noise the sparsity constrained csi improves the normalized mean squared error of the reconstructed speed of sound profiles up to 36 in comparison with traditional csi also for measurements contaminated with 5 noise the proposed methods improve the quality of the reconstruction up to 70 in comparison with the traditional csi method experimental results also show that the methods remain convergent to the correct speed of sound profile as the number of iterations increases

on some examples and constructions of contact manifolds the first goal of this paper is to construct examples of higher dimensional contact manifolds with specific properties our main results in this direction are the existence of tight virtually overtwisted closed contact manifolds in all dimensions and the fact that every closed contact 3 manifold which is not smoothly a rational homology sphere contact embeds with trivial normal bundle inside a hypertight closed contact 5 manifold this uses known construction procedures by bourgeois on products with tori and geiges on branched covering spaces we pass from these procedures to definitions this allows to prove a uniqueness statement in the case of contact branched coverings and to study the global properties such as tightness and fillability of the results of both constructions without relying on any auxiliary choice in the procedures a second goal allowed by these definitions is to study relations between these constructions and the notions of supporting open book as introduced by giroux and of contact fiber bundle as introduced by lerman for instance we give a definition of bourgeois contact structures on flat contact fiber bundles which is local strictly includes the results of the bourgeois construction and allows to recover an isotopy class of supporting open books on the fibers this last point relies on a reinterpretation inspired by an idea by giroux of supporting open books in terms of pairs of contact vector fields

three dimensional visco acoustic modeling using a renormalized integral equation iterative solver we present a frequency domain renormalized integral equation formulation for solving a three dimensional visco acoustic medium using an iterative solver upon applying this special renormalization the resulting integral equation operator can be proven to have a contraction property hence solving the linear system of equations using a krylov optimization method will result in a good convergence rate furthermore since the matrix vector multiplication can be done using a fast fourier transform fft technique its operation is of the order of o n log n where n is the size of the discretization grid this technique also allows us to use matrix free implementation hence the memory usage is about o n numerical tests show that the computational time and memory usage of this renormalized integral equation approach can be quite competitive with the frequency domain finite difference iterative solver further the numerical examples demonstrate that it is possible to solve a problem with over 100 million unknowns using an integral equation approach

an evaluation of the eigenvalue approach for determining the membership values in fuzzy sets abstract the membership values of the elements of a fuzzy set of key importance in any theoretical or practical application of fuzzy set theory although there are many methods that evaluate membership values the methd proposed by saaty 8 9 based on matrix of pairwise comparisons and eigenvalue theory is the backbone of many other methods in this paper we evaluate the above method by using a forward error analysis approach with the assumption that the true membership values in a fuzzy set are continuous in the interval 0 1 the results reveal that the eigenvalue method is dramatically inaccurate even for fuzzy sets with few members

almost contact 5 manifolds are contact the existence of a contact structure is proved in any homotopy class of almost contact structures on a closed 5 dimensional manifold

right veering diffeomorphisms of compact surfaces with boundary we initiate the study of the monoid of right veering diffeomorphisms on a compact oriented surface with nonempty boundary the monoid strictly contains the monoid of products of positive dehn twists we explain the relationship to tight contact structures and open book decompositions

solving multi period project selection problems with fuzzy goal programming based on topsis and a fuzzy preference relation project portfolio managers are multi objective decision makers dms who are expected to select the best mix of projects by maximizing profits and minimizing risks over a multi period planning horizon however project portfolio decisions are complex multi objective problems with a high number of projects from which a subset has to be chosen subject to various constraints and a multitude of priorities and preferences we propose a goal programming gp approach for project portfolio selection that embraces conflicting fuzzy goals with imprecise priorities a fuzzy goal with an aspiration level and a predefined membership function is defined for each objective the impreciseness in the priorities of the membership values of the fuzzy goals is modeled with fuzzy relations this leads to type ii fuzzy sets since fuzzy relations are organized between the membership values of the fuzzy goals which are themselves fuzzy sets the proposed model is based on the technique for order preference by similarity to ideal solution topsis and fuzzy preference relations topsis is used to reduce the multi objective problem into a bi objective problem the resulting bi objective problem is solved with fuzzy gp fgp the fuzzy preference relations are used to help dms express their preferences with respect to the membership values of the fuzzy goals the proposed approach is used to solve a real life problem characterized as a fuzzy multi objective project selection with multi period planning horizon mops mpph the performance of the proposed approach is compared with a competing method in the literature we show that our approach generates high quality solutions with minimal computational efforts

expected value of fuzzy variable and fuzzy expected value models this paper will present a novel concept of expected values of fuzzy variables which is essentially a type of choquet integral and coincides with that of random variables in order to calculate the expected value of general fuzzy variable a fuzzy simulation technique is also designed finally we construct a spectrum of fuzzy expected value models and integrate fuzzy simulation neural network and genetic algorithms to produce a hybrid intelligent algorithm for solving general fuzzy expected value models

transportation projects selection process using fuzzy sets theory government transportation agencies are faced with the problem of efficiently selecting a subset of transportation projects for implementation this selection process is based on multiple objectives which are often measured in incommensurable units usually the problem is treated by neglecting or biasing the qualitative characteristics of the various projects moreover the usual selection methods cannot deal effectively with the decision makers preferences or vagueness fuzzy sets theory is able to cope with inexact information and therefore is believed to be an appropriate tool for use in the projects selection process this work presents an efficient technique for the selection of transportation projects using fuzzy sets theory the selection procedure is a multiple objectives process and projects are rated both on a quantitative and qualitative basis using linguistic variables in order to describe appropriately a given transportation policy both fuzzy weighted average and noncompensatory fuzzy decision rules are used in the proposed approach in addition this work contains a case study of a selection process of interurban road projects in israel the results of the proposed method obtained by a fuzzy expert system are compared with the results obtained by an ordinary crisp process

model reference adaptive fuzzy control a linguistic space approach in this paper a model reference adaptive fuzzy controller with the adaptivity achieved by tuning both the scaling factors and the control rules is presented the proposed tuning strategy includes two parts 1 by referring a reference trajectory created in the linguistic space to tune the scaling factors and 2 by applying an auxiliary correction matrix generated by specific tuning rules to compensate the control rules since only the control signal the output error and change in output error of the plant are needed in the construction of the reference trajectory and the tuning rules the tuning strategy has the advantage of real time property simulation results with a damping process and an oscillating process as the controlled plants show the performance and adaptivity of the proposed controller

legendrian fronts for affine varieties in this article we study weinstein structures endowed with a lefschetz fibration in terms of the legendrian front projection first we provide a systematic recipe for translating from a weinstein lefschetz bifibration to a legendrian handlebody then we present several new applications of this technique to symplectic topology this includes the detection of flexibility and rigidity for several families of weinstein manifolds and the existence of closed exact lagrangian submanifolds in particular we prove that the koras russell cubic is stein deformation equivalent to c3 and we verify the affine parts of the algebraic mirrors of two weinstein 4 folds

geometric criteria for overtwistedness we establish geometric criteria to decide whether a contact manifold is over twisted starting with the original denition we rst relate the dierent overtwisted disks d 2n ot in each dimension and show that a manifold is overtwisted if the legendrian un knot is loose then we characterize overtwistedness in terms of open book decompositions and provide several applications

fuzzy chance constrained portfolio selection abstract this paper selects the portfolio with fuzzy returns by criteria of chance represented by credibility measure in the paper two types of credibility based portfolio selection model are provided according to two types of chance criteria by one chance criterion the objective is to maximize the investor s return at a given threshold confidence level by another chance criterion the objective is to maximize the credibility of achieving a specified return level subject to the constraints to provide a general method to solve the new models a hybrid intelligent algorithm integrating fuzzy simulation and genetic algorithm is designed in the paper two numerical examples with security returns taking different types of membership function are also given to illustrate the modelling idea of the paper and to demonstrate the effectiveness of the proposed algorithm

a convergent born series for solving the inhomogeneous helmholtz equation in arbitrarily large media we present a fast method for numerically solving the inhomogeneous helmholtz equation our iterative method is based on the born series which we modified to achieve convergence for scattering media of arbitrary size and scattering strength compared to pseudospectral time domain simulations our modified born approach is two orders of magnitude faster and nine orders of magnitude more accurate in benchmark tests in 1 2 and 3 dimensional systems

convergent scattering series solution of the inhomogeneous helmholtz equation via renormalization group and homotopy continuation approaches abstract the inhomogeneous helmholtz equation can be represented by an equivalent integral equation of the lippmann schwinger type since it is very costly to solve the lippmann schwinger equation exactly via matrix inversion researchers often try to use the popular born series which represents a physics based iterative solution however the popular born series is only guaranteed to converge if the contrast volume is sufficiently small we here use renormalization group rg and homotopy continuation hc approaches to derive novel scattering series solutions of the lippmann schwinger equation which are guaranteed to converge for arbitrary large contrast volumes perturbations our rg approach is based on the use of an auxillary set of scale dependent scattering potentials and green s operators which gradually evolve toward the real physical scattering potential and the physical green s operator respectively we show that the auxillary green s operators satisfies the renormalization group law and we derive the corresponding renormalization group flow equation by using familiar scaling arguments the hc approach comes from pure mathematics and is based on the deformation of a relatively simple reference equation initial condition into a more complicated target equation the lippmann schwinger equation for the physical scattering potential via a parameter that varies continuously between 0 and 1 our hc approach is more general than the rg approach since it involves a convergence control operator but the two approaches are nevertheless closely connected we show that the rg flow and hc equations can be implemented very efficiently using the fast fourier transform fft algorithm also we present a very efficient iterative scheme based on a combination of the zeroth order deformation equation with a floating initial we illustrate our results with a numerical example related with seismic wavefield modeling in strongly scattering media

credibility based chance constrained integer programming models for capital budgeting with fuzzy parameters in this paper we discuss a problem of capital budgeting in a fuzzy environment two types of models are proposed using credibility to measure confidence level since the proposed optimization problems are difficult to solve by traditional methods a fuzzy simulation based genetic algorithm is applied two numerical experiments demonstrate the effectiveness of the proposed algorithm

renormalization group and singular perturbations multiple scales boundary layers and reductive perturbation theory perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis with numerous examples we illustrate its application to ordinary differential equation problems involving multiple scales boundary layers with technically difficult asymptotic matching and wkb analysis in contrast to conventional methods the renormalization group approach requires neither ad hoc assumptions about the structure of perturbation series nor the use of asymptotic matching our renormalization group approach provides approximate solutions which are practically superior to those obtained conventionally although the latter can be reproduced if desired by appropriate expansion of the renormalization group approximant we show that the renormalization group equation may be interpreted as an amplitude equation and from this point of view develop reductive perturbation theory for partial differential equations describing spatially extended systems near bifurcation points deriving both amplitude equations and the center manifold s1063651x 96 00506 5

logistics distribution centers location problem and algorithm under fuzzy environment distribution centers location problem is concerned with how to select distribution centers from the potential set so that the total relevant cost is minimized this paper mainly investigates this problem under fuzzy environment consequentially chance constrained programming model for the problem is designed and some properties of the model are investigated tabu search algorithm genetic algorithm and fuzzy simulation algorithm are integrated to seek the approximate best solution of the model a numerical example is also given to show the application of the algorithm

minimax chance constrained programming models for fuzzy decision systems abstract the existing chance constrained programming for fuzzy decision systems is essentially a kind of maximax models optimistic models which maximize the maximum possible return this paper presents a spectrum of minimax models as opposed to maximax models based on chance constrained programming as well as chance constrained multi objective programming and chance constrained goal programming in which the minimax models will select the alternative that provides the best of the worst possible return finally a fuzzy simulation based genetic algorithm will be designed for solving minimax models and illustrated by some numerical examples

contact structures on m s2 we show that if a manifold m admits a contact structure then so does m times s 2 our proof relies on surgery theory a theorem of eliashberg on contact surgery and a theorem of bourgeois showing that if m admits a contact structure then so does m times t 2

weak and strong fillability of higher dimensional contact manifolds for contact manifolds in dimension three the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent we extend these facts to higher dimensions in particular we define a natural generalization of weak fillings and prove that it is indeed weaker at least in dimension five while also being obstructed by all known manifestations of overtwistedness we also find the first examples of contact manifolds in all dimensions that are not symplectically fillable but also cannot be called overtwisted in any reasonable sense these depend on a higher dimensional analogue of giroux torsion which we define via the existence in all dimensions of exact symplectic manifolds with disconnected contact boundary

inverse scattering theory renormalization of the lippmann schwinger equation for acoustic scattering in one dimension the most robust treatment of the inverse acoustic scattering problem is based on the reversion of the born neumann series solution of the lippmann schwinger equation an important issue for this approach to inversion is the radius of convergence of the born neumann series for fredholm integral kernels and especially for acoustic scattering for which the interaction depends on the square of the frequency by contrast it is well known that the born neumann series for the volterra integral equations in quantum scattering are absolutely convergent independent of the strength of the coupling characterizing the interaction the transformation of the lippmann schwinger equation from a fredholm to a volterra structure by renormalization has been considered previously for quantum scattering calculations and electromagnetic scattering in this paper we employ the renormalization technique to obtain a volterra equation framework for the inverse acoustic scattering series proving that this series also converges absolutely in the entire complex plane of coupling constant and frequency values the present results are for acoustic scattering in one dimension but the method is general the approach is illustrated by applications to two simple one dimensional models for acoustic scattering

reconstruction of two dimensional permittivity distribution using the distorted born iterative method the distorted born iterative method dbim is used to solve two dimensional inverse scattering problems thereby providing another general method to solve the two dimensional imaging problem when the born and the rytov approximations break down numerical simulations are performed using the dbim and the method proposed previously by the authors int j imaging syst technol vol 1 no 1 p 100 8 1989 called the born iterative method bim for several cases in which the conditions for the first order born approximation are not satisfied the results show that each method has its advantages the dbim shows faster convergence rate compared to the bim while the bim is more robust to noise contamination compared to the dbim

a fuzzy approach to markov decision processes with uncertain transition probabilities in this paper markov decision models with uncertain transition matrices which allow a matrix to fluctuate at each step in time is described by the use of fuzzy sets we find a pareto optimal policy maximizing the infinite horizon fuzzy expected discounted reward fedr over all stationary policies under some partial order the pareto optimal policies are characterized by maximal solutions of an optimal inclusion including efficient set functions as a numerical example a machine maintenance problem is considered

imprecise set and fuzzy valued probability set valued probability and fuzzy valued probability theory is used for analyzing and modeling highly uncertain probability systems in this paper the set valued probability and fuzzy valued probability are defined over the measurable space they are derived from a set and fuzzy valued measure using restricted arithmetics the range of set valued probability is the set of subsets of the unit interval and the range of fuzzy valued probability is the set of fuzzy sets of the unit interval the expectation with respect to set valued and fuzzy valued probability is defined and some properties are discussed also the fuzzy model is applied to binomial model for the price of a risky security

the renormalization group a perturbation method for the graduate curriculum in this paper the renormalization group rg method of chen goldenfeld and oono phys rev lett 73 1994 pp 1311 1315 phys rev e 54 1996 pp 376 394 is presented in a pedagogical way to increase its visibility in applied mathematics and to argue favorably for its incorporation into the corresponding graduate curriculum the method is illustrated by some linear and nonlinear singular perturbation problems

fuzzy quadratic minimum spanning tree problem in this paper a fuzzy quadratic minimum spanning tree problem is formulated as expected value model chance constrained programming and dependent chance programming according to different decision criteria then the crisp equivalents are derived when the fuzzy costs are characterized by trapezoidal fuzzy numbers furthermore a simulation based genetic algorithm using prufer number representation is designed for solving the proposed fuzzy programming models as well as their crisp equivalents finally a numerical example is provided for illustrating the effectiveness of the genetic algorithm

fuzzy capital budgeting fuzzy equivalents of all the classical capital budgeting investment choice methods are generalised or proposed these equivalents can be used to evaluate and compare projects in which the cash ows duration time and required rate of return cost of capital are given imprecisely in the form of a fuzzy number c 2000 elsevier science b v all rights reserved

chance constrained programming with fuzzy parameters this paper extends chance constrained programming from stochastic to fuzzy environments analogous to stochastic programming some crisp equivalents of chance constraints in fuzzy environments are presented we also propose a technique of fuzzy simulation for the chance constraints which are usually hard to be converted to their crisp equivalents finally a fuzzy simulation based genetic algorithm is designed for solving this kind of problems and some numerical examples are discussed

contact homology and virtual fundamental cycles we give a construction of contact homology in the sense of eliashberg givental hofer specifically we construct coherent virtual fundamental cycles on the relevant compactified moduli spaces of pseudo holomorphic curves the aim of this work is to provide a rigorous construction of contact homology an invariant of contact manifolds and exact symplectic cobordisms due to eliashberg givental hofer eli98 egh00 the contact homology of y is defined in terms of pseudo holomorphic curve counts in the sense of gromov gro85 in the symplectization r y unfortunately the moduli spaces of such curves often suffer from a severe lack of transversality and for this reason it has until now remained an important open problem to define the relevant curve counts in full generality we will use the framework developed in par15 to construct coherent virtual fundamental cycles on the moduli spaces in question thus giving rise to the desired curve counts our methods are quite general and should apply equally well to many other moduli spaces of interest previously a number of important special cases of contact homology and closely related invariants have been constructed rigorously using generic and or automatic transversality techniques cylindrical contact homology of some three manifolds was constructed by bao

solution of the nonlinear inverse scattering problem by t matrix completion ii simulations this is part ii of the paper series on data compatible t matrix completion dctmc which is a method for solving nonlinear inverse problems part i of the series h w levinson and v a markel phys rev e 94 043317 2016 10 1103 physreve 94 043317 contains theory and here we present simulations for inverse scattering of scalar waves the underlying mathematical model is the scalar wave equation and the object function that is reconstructed is the medium susceptibility the simulations are relevant to ultrasound tomographic imaging and seismic tomography it is shown that dctmc is a viable method for solving strongly nonlinear inverse problems with large data sets it provides not only the overall shape of the object but the quantitative contrast which can correspond for instance to the variable speed of sound in the imaged medium

an empirical analysis of the use of the analytic hierarchy process for estimating membership values in a fuzzy set abstract the analytic hierarchy process ahp is now a popular multicriteria decision making method and has been applied in many diverse areas despite the debate on its theoretical foundations many researchers have been using the pairwise comparison matrix and the eigenvector method suggested by saaty for obtaining priority ratings of the decision alternatives in an ahp hierarchy these priority ratings have been used as estimates of fuzzy membership values of the elements called alternatives in ahp of a fuzzy set triantaphyllou and mann have argued that saaty s scale and the eigenvector method are inadequate for estimating fuzzy membership values this paper points out the limitations in the arguments of triantaphyllou and mann about the eigenvector method it primarily concentrates on two aspects the first pertains to saaty s condition on deleting or combining two alternatives which are near copies alternatives whose priority values are close to each other within a 10 range over all criteria the second aspect concerns the use of the eigenvector method for estimating the membership values of elements of a fuzzy set the use of the eigenvector method for estimating fuzzy membership values in a fuzzy set has been justified using the empirical analysis together with theoretical support it has been amply demonstrated in this paper that the problem lies in saaty s scale and not in the eigenvector method