fuzzy goal programming complementary slackness conditions and computational schemes abstract goal programming gp is an important category in linear programming and multiobjective versions which minimize the deviation among value of each objective function and its goal with satisfying other constraints of problem in this paper we deal with fuzzy goal programming fgp which is a generalized problem in vague nature where parameters relations and goals are given as fuzzy quantities with respect to imprecise data recently inuiguchi et al m inuiguchi j ramik t tanio m vlach satisficing solutions and duality in interval and fuzzy linear programming fuzzy sets and systems 135 2003 151 177 have proved some important dual theorems on fgp which are very close to the same crisp versions in continuation to their works based on fuzzy extensions of relations we get complementary slackness conditions for fgp which have an essential role in many optimization techniques moreover we obtain the most optimistic and pessimistic satisficing solutions employing these conditions and present a convex combination of them which covers the satisficing solutions for a fixed level of certainty our practical schemes implement an efficient interior point algorithm as sub procedure so they are polynomial time algorithms

on duality in linear programming under fuzzy environment a pair of linear primal dual problems is introduced under fuzzy environment and appropriate results are proved to establish the duality relationship between them possible extensions are also suggested

optimality conditions for linear programming problems with fuzzy coefficients the optimality conditions for linear programming problems with fuzzy coefficients are derived in this paper two solution concepts are proposed by considering the orderings on the set of all fuzzy numbers the solution concepts proposed in this paper will follow from the similar solution concept called the nondominated solution in the multiobjective programming problem under these settings the optimality conditions will be naturally elicited

an implementation of the dual affine scaling algorithm for minimum cost flow on bipartite uncapacitated networks this paper describes an implementation of the dual affine scaling algorithm for linear programming specialized to solve minimum cost flow problems on bipartite uncapacitated networks this implementation uses a preconditioned conjugate gradient algorithm to solve the system of linear equations that determines the search direction at each iteration of the interior point algorithm two preconditioners are considered a diagonal preconditioner and a preconditioner based on the incidence matrix of an approximate maximum weighted spanning tree of the network under dual nondegeneracy this spanning tree allows for early identification of the optimal solution by applying an epsilon perturbation to the cost vector an optimal extreme point primal solution is produced in the presence of dual degeneracy the implementation is tested by solving several large instances of randomly generated assignment problems comparing solution times with the network simplex code netflo and the relaxation algorithm code relax

reasonable properties for the ordering of fuzzy quantities ii as a continuation of the first part related to the first and second class of ordering approaches this paper deals with the fulfilment of reasonable properties in the third class of ordering approaches to do so we briefly introduce fuzzy relations on which the third class of approaches is based then we recall some transitivity related concepts and an ordering procedure based on a acyclic fuzzy relation acyclicity is a very weak restriction on a fuzzy relation we prove that many fuzzy relations used for the comparison of fuzzy quantities satisfy some conditions stronger than acyclicity so we give a widely applicable formulation to derive a total ranking order from a fuzzy relation with our formulation we examine all the ordering indices in the third class with respect to the proposed axioms in part i

concurrent error detection in finite field arithmetic operations using pipelined and systolic architectures in this work we consider detection of errors in polynomial dual and normal bases arithmetic operations error detection is performed by recomputing with the shifted operand method while the operation unit is in use this scheme is efficient for pipelined architectures particularly systolic arrays additionally one semisystolic multiplier for each of the polynomial dual type i and type ii optimal normal bases is presented the results show that for having better or similar space and time overheads compared to a number of related previous work the multipliers have generally a higher error detection capability e g the error detection capability of the reso based scheme for single and multiple stuck at faults in a polynomial basis multiplier is 100 percent finally we also comment on how reso can be used for concurrent error correction to deal with transient faults

satisficing solutions and duality in interval and fuzzy linear programming in this paper we introduce a class of fuzzy linear programming problems and define the concepts of feasible and satisficing solutions the necessary tools for dealing with such problems in this way we show that the class of crisp classical lp problems can be embedded into the class of flp ones moreover for flp problems we define the concept of duality and prove the weak and strong duality theorems further we define a class of interval linear programming problems as a special subclass of flp problems and apply the previous results to this special case

an efficient optimal normal basis type ii multiplier this paper presents a new parallel multiplier for the galois field gf 2 sup m whose elements are represented using the optimal normal basis of type ii the proposed multiplier requires 1 5 m sup 2 m xor gates as compared to 2 m sup 2 m xor gates required by the massey omura multiplier the time complexities of the proposed and the massey omura multipliers are similar

boundary behavior of interior point algorithms in linear programming this paper studies the boundary behavior of some interior point algorithms for linear programming the algorithms considered are karmarkar s projective rescaling algorithm the linear rescaling algorithm which was proposed as a variation on karmarkar s algorithm and the logarithmic barrier technique the study includes both the continuous trajectories of the vector fields induced by these algorithms and also the discrete orbits it is shown that although the algorithms are defined on the interior of the feasible polyhedron they actually determine differentiable vector fields on the closed polyhedron conditions are given under which a vector field gives rise to trajectories that each visit the neighborhoods of all the vertices of the klee minty cube the linear rescaling algorithm satisfies these conditions thus limits of such trajectories obtained when a starting point is pushed to the boundary may have an exponential number of breakpoints it is shown that limits of projective rescaling trajectories may have a linear number of such breakpoints however projective rescaling trajectories may visit the neighborhoods of linearly many vertices the behavior of the linear rescaling algorithm near vertices is analyzed it is proved that all the trajectories have a unique asymptotic direction of convergence to the optimum

a consistent metric for performance evaluation of multi object filters the concept of a miss distance or error between a reference quantity and its estimated controlled value plays a fundamental role in any filtering control problem yet there is no satisfactory notion of a miss distance in the well established field of multi object filtering in this paper we outline the inconsistencies of existing metrics in the context of multi object miss distances for performance evaluation we then propose a new mathematically and intuitively consistent metric that addresses the drawbacks of current multi object performance evaluation metrics

duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables linear programming problems with trapezoidal fuzzy variables fvlp have recently attracted some interest some methods have been developed for solving these problems by introducing and solving certain auxiliary problems here we apply a linear ranking function to order trapezoidal fuzzy numbers then we establish the dual problem of the linear programming problem with trapezoidal fuzzy variables and hence deduce some duality results in particular we prove that the auxiliary problem is indeed the dual of the fvlp problem having established the dual problem the results will then follow as natural extensions of duality results for linear programming problems with crisp data finally using the results we develop a new dual algorithm for solving the fvlp problem directly making use of the primal simplex tableau this algorithm will be useful for sensitivity or post optimality analysis when using primal simplex tableaus

linear programming with fuzzy coefficients in constraints abstract this paper presents a new method for solving linear programming problems with fuzzy coefficients in constraints it is shown that such problems can be reduced to a linear semi infinite programming problem the relations between optimal solutions and extreme points of the linear semi infinite program are established a cutting plane algorithm is introduced with a convergence proof and a numerical example is included to illustrate the solution procedure

sequential monte carlo with kernel embedded mappings the mapping particle filter abstract in this work a novel sequential monte carlo filter is introduced which aims at an efficient sampling of the state space particles are pushed forward from the prediction to the posterior density using a sequence of mappings that minimizes the kullback leibler divergence between the posterior and the sequence of intermediate densities the sequence of mappings represents a gradient flow based on the principles of local optimal transport a key ingredient of the mappings is that they are embedded in a reproducing kernel hilbert space which allows for a practical and efficient monte carlo algorithm the kernel embedding provides a direct means to calculate the gradient of the kullback leibler divergence leading to quick convergence using well known gradient based stochastic optimization algorithms evaluation of the method is conducted in the chaotic lorenz 63 system the lorenz 96 system which is a coarse prototype of atmospheric dynamics and an epidemic model that describes cholera dynamics no resampling is required in the mapping particle filter even for long recursive sequences the number of effective particles remains close to the total number of particles in all the sequence hence the mapping particle filter does not suffer from sample impoverishment

sequential quasi monte carlo this is a written discussion of the paper sequential quasi monte carlo sampling by m gerber and n chopin following the presentation given before the royal statistical society in london on december 10th 2014

an implementation of karmarkar s algorithm for linear programming this paper describes the implementation of power series dual affine scaling variants of karmarkar s algorithm for linear programming based on a continuous version of karmarkar s algorithm two variants resulting from first and second order approximations of the continuous trajectory are implemented and tested linear programs are expressed in an inequality form which allows for the inexact computation of the algorithm s direction of improvement resulting in a significant computational advantage implementation issues particular to this family of algorithms such as treatment of dense columns are discussed the code is tested on several standard linear programming problems and compares favorably with the simplex codeminos 4 0

combining a hybrid preconditioner and a optimal adjustment algorithm to accelerate the convergence of interior point methods abstract in this work the optimal adjustment algorithm for p coordinates which arose from a generalization of the optimal pair adjustment algorithm is used to accelerate the convergence of interior point methods using a hybrid iterative approach for solving the linear systems of the interior point method its main advantages are simplicity and fast initial convergence at each interior point iteration the preconditioned conjugate gradient method is used in order to solve the normal equation system the controlled cholesky factorization is adopted as the preconditioner in the first outer iterations and the splitting preconditioner is adopted in the final outer iterations the optimal adjustment algorithm is applied in the preconditioner transition in order to improve both speed and robustness numerical experiments on a set of linear programming problems showed that this approach reduces the total number of interior point iterations and running time for some classes of problems furthermore some problems were solved only when the optimal adjustment algorithm for p coordinates was used in the change of preconditioners

ranking function based solutions of fully fuzzified minimal cost flow problem the aim of minimal cost flow problem mcfp is to find the least transportation cost of a single commodity through a capacitated network this paper presents a model to deal with one particular group of such problems in which the supply and demand of nodes and the capacity and cost of edges are represented as fuzzy numbers for easier reference hereafter we refer to this group of problems as fully fuzzified mcfp to represent our model hukuhara s difference and approximated multiplication are used thereafter we sort fuzzy numbers by an order using a ranking function and show that it is a total order i e a reflexive anti symmetric transitive and complete binary relation utilizing the proposed ranking function we transform the fully fuzzified mcfp into three crisp problems solvable in polynomial time from this standpoint combinatorial algorithms are provided to solve the above mentioned problem and find the fuzzy optimal flow furthermore the proposed order is related to the importance weights of the center the left spread and the right spread of each fuzzy number thus this method is capable of handling the decision maker s risk taking by comparing some previous ranking function based works with our method the efficiency of the latter is revealed finally an application of our proposed method to petroleum industry is presented

sequentially interacting markov chain monte carlo methods we introduce a novel methodology for sampling from a sequence of probability distributions of increasing dimension and estimating their normalizing constants these problems are usually addressed using sequential monte carlo smc methods the alternative sequentially interacting markov chain monte carlo simcmc scheme proposed here works by generating interacting non markovian sequences which behave asymptotically like independent metropolis hastings mh markov chains with the desired limiting distributions contrary to smc methods this scheme allows us to iteratively improve our estimates in an mcmc like fashion we establish convergence of the algorithm under realistic verifiable assumptions and demonstrate its performance on several examples arising in bayesian time series analysis

fuzzy cooperative games arising from linear production programming problems with fuzzy parameters abstract in the present study we consider a production model in which multiple decision makers pool resources to produce finished goods such a production model which is assumed to be linear can be formulated as mathematical programming problems with fuzzy parameters from the viewpoint of experts imprecise or fuzzy understanding of the nature of parameters in a problem formulation process it is shown that a cooperative game with values of coalitions represented by fuzzy numbers arises from the linear production programming problem with fuzzy parameters and such a game is referred to as a fuzzy linear production programming game the values of coalitions of the game can be obtained by employing a parametric approach to solving the linear production programming problem with fuzzy parameters it is proven that the core of the game is not empty and an interval in the core is computed by using the ideas of sensitivity analysis and the duality theory of linear programming problems

systolic multipliers for finite fields gf 2 m two systolic architectures are developed for performing the product sum computation ab c in the finite field gf 2m of 2melements where a b and c are arbitrary elements of gf 2m the first multiplier is a serial in serial out one dimensional systolic array while the second multiplier is a parallel in parallel out two dimensional systolic array the first multiplier requires a smaller number of basic cells than the second multiplier the second multiplier heeds less average time per computation than the first multiplier if a number of computations are performed consecutively to perform single computations both multipliers require the same computational time in both cases the architectures are simple and regular and possess the properties of concurrency and modularity as a consequence they are well suited for use in vlsi systems

solutions based on fuzzy goals in fuzzy linear programming games abstract in this paper we deal with linear programming problems with fuzzy parameters from the viewpoint of experts imprecise or fuzzy understanding of the nature of parameters in a problem formulation process and consider fuzzy linear programming games arising from the linear programming problems constructing fuzzy goals of coalitions with respect to payoff in order to suitably reflect fuzzy environments in which the linear programming games are formulated we define solutions maximizing minimal fuzzy goal and solutions maximizing the sum of fuzzy goals and develop computational methods for obtaining the solutions finally we give a numerical example to illustrate construction of a fuzzy linear programming game and derivation of the solutions

duality theory in fuzzy mathematical programming problems with fuzzy coefficients in this paper the notions of subgradient subdifferential and differential with respect to convex fuzzy mappings are investigated which provides the basis for the fuzzy extremum problem theory we consider the problems of minimizing or maximizing a convex fuzzy mapping over a convex set and develop the necessary and or sufficient optimality conditions furthermore the concept of saddle points and minimax theorems under fuzzy environment is discussed the results obtained are used to formulate the lagrangian dual of fuzzy programming under certain fuzzy convexity assumptions kkt conditions for fuzzy programming are derived and the perturbed convex fuzzy programming is considered finally these results are applied to fuzzy linear programming and fuzzy quadratic programming

bector chandra type duality in fuzzy linear programming with exponential membership functions in this paper we study a pair of fuzzy primal dual linear programming problems and calculate duality results using an aspiration level approach we use an exponential membership function which is in contrast to the earlier works that relied on a linear membership function as the fuzzy environment causes a duality gap we investigate how choosing the exponential membership function impacts this gap this issue is particularly important for fuzzy linear programming where in general the primal and dual objective values may not be bounded

possibility distributions of fuzzy decision variables obtained from possibilistic linear programming problems abstract in this paper several kinds of possibility distributions of fuzzy variables are studied in possibilistic linear programming problems to reflect the inherent fuzziness in fuzzy decision problems interval and triangular possibility distributions are used to express the non interactive cases between the fuzzy decision variables and exponential possibility distributions are used to represent the interrelated cases possibilistic linear programming problems based on exponential possibility distributions become non linear optimization problems in order to solve optimization problems easily algorithms for obtaining center vectors and distribution matrices in sequence are proposed by the proposed algorithms the possibility distribution of fuzzy decision variables can be obtained

duality in fuzzy multi criteria and multi constraint level linear programming a parametric approach this paper presents a parametric approach for duality in fuzzy multi criteria and multi constraint level linear programming mc2lp which extends fuzzy linear programming approaches first the mc2 simplex method is used to solve the crisp prima dual mc2lp pair and then through these crisp formulations separate membership functions are constructed for fuzzy primal and dual program by considering the corresponding primal and dual decisions for each program a set of fuzzy potential solutions is determined in terms of the membership function and the related optimal solution with a certain range of decision parameters finally using the primal and dual membership functions a fuzzy weak duality function is obtained for any pair of primal and dual fuzzy potential solutions

dynamic conditional independence models and markov chain monte carlo methods abstract in dynamic statistical modeling situations observations arise sequentially causing the model to expand by progressive incorporation of new data items and new unknown parameters for example in clinical monitoring patients and data arrive sequentially and new patient specific parameters are introduced with each new patient markov chain monte carlo mcmc might be used for continuous updating of the evolving posterior distribution but would need to be restarted from scratch at each expansion stage thus mcmc methods are often too slow for real time inference in dynamic contexts by combining mcmc with importance resampling we show how real time sequential updating of posterior distributions can be effected the proposed dynamic sampling algorithms use posterior samples from previous updating stages and exploit conditional independence between groups of parameters to allow samples of parameters no longer of interest to be discarded such as when a patient dies or is discharged we apply the

the nonlinear geometry of linear programming i affine and projective scaling trajectories this series of papers studies a geometric structure underlying karmarkar s projective scaling algorithm for solving linear programming problems a basic feature of the projective scaling algorithm is a vector field depending on the objective function which is defined on the interior of the polytope of feasible solutions of the linear program the geometric structure studied is the set of trajectories obtained by integrating this vector field which we call ptrajectories we also study a related vector field the affine scaling vector field and its associated trajectories called a trajectories the affine scaling vector field is associated to another linear programming algorithm the affine scaling algorithm affine and projective scaling vector fields are each defined for linear programs of a special form called strict standard form and canonical form respectively this paper derives basic properties of p trajectories and a trajectones it reviews the projective and affine scaling algorithms defines the projective and affine scaling vector fields and gives differential equations for p trajectories and a trajectories it shows that projective transformations map p trajectories into p trajectories it presents karmarkar s interpretation of a trajectories as steepest descent paths of the objective function c x with respect to the riemannian geometry ds2 z dx dx x2 restricted to the relative interior of the polytope of feasible solutions p trajectories of a canonical form linear program are radial projections of a trajectories of an associated standard form linear program as a consequence there is a polynomial time linear programming algorithm using the affine scaling vector field of this associated linear program this algorithm is essentially karmarkar s algorithm these trajectories are studied in subsequent papers by two nonlinear changes of variables called legendre transform coordinates and projective legendre transform coordinates respectively it will be shown that p trajectories have an algebraic and a geometric interpretation they are algebraic curves and they are geodesics actually distinguished chords of a geometry isometric to a hilbert geometry on a polytope combinatorially dual to the polytope of feasible solutions the a trajectories of strict standard form linear programs have similar interpretations they are algebraic curves and are geodesics of a geometry isometric to euclidean geometry received by the editors july 28 1986 and in revised form september 28 1987 and march 21 1988 1980 mathematics subject classification 1985 revision primary 90c05 secondary 52a40 34a34 research of the first author partially supported by onr contract n00014 87 k0214 d 1989 american mathematical society 0002 9947 89 1 00 25 per page

particle filtering with invertible particle flow a key challenge when designing particle filters in high dimensional state spaces is the construction of a proposal distribution that is close to the posterior distribution recent advances in particle flow filters provide a promising avenue to avoid weight degeneracy particles drawn from the prior distribution are migrated in the state space to the posterior distribution by solving partial differential equations numerous particle flow filters have been proposed based on different assumptions concerning the flow dynamics approximations are needed in the implementation of all of these filters as a result the particles do not exactly match a sample drawn from the desired posterior distribution past efforts to correct the discrepancies involve expensive calculations of importance weights in this paper we present new filters which incorporate deterministic particle flows into an encompassing particle filter framework the valuable theoretical guarantees concerning particle filter performance still apply but we can exploit the attractive performance of the particle flow methods the filters we describe involve a computationally efficient weight update step arising because the embedded particle flows we design possess an invertible mapping property we evaluate the proposed particle flow particle filters performance through numerical simulations of a challenging multitarget multisensor tracking scenario and complex high dimensional filtering examples

sequential monte carlo samplers summary we propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space each distribution being known up to a normalizing constant these probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential monte carlo methods this methodology allows us to derive simple algorithms to make parallel markov chain monte carlo algorithms interact to perform global optimization and sequential bayesian estimation and to compute ratios of normalizing constants we illustrate these algorithms for various integration tasks arising in the context of bayesian inference

duality in linear programming with fuzzy parameters and matrix games with fuzzy pay offs abstract a dual for linear programming problems with fuzzy parameters is introduced and it is shown that a two person zero sum matrix game with fuzzy pay offs is equivalent to a primal dual pair of such fuzzy linear programming problems further certain difficulties with similar studies reported in the literature are discussed

solving a special class of large scale fuzzy multiobjective integer linear programming problems we present a method useful in solving a special class of large scale multiobjective integer problems depending on the decomposition algorithm these problems involve fuzzy parameters on the right hand side of the independent constraints the presented solution method is based upon a combination of the decomposition algorithm coupled with the weighting method together with the branch and bound method an illustrative numerical example is given to clarify the theory and the method discussed in this paper

a relaxed revision of karmarkar s method a relaxed version of karmarkar s method is developed this method is proved to have the same polynomial time complexity as karmarkar s method and its efficient implementation using inexact projections is discussed computational results obtained using a preliminary implementation of the method are presented which indicate that the method is practicable

duality theorems and saddle point optimality conditions in fuzzy nonlinear programming problems based on different solution concepts under a general setting of partial ordering defined on the set of all fuzzy numbers the duality theorems and saddle point optimality conditions in fuzzy nonlinear programming problems based on two solution concepts for primal problem and three solution concepts for dual problem are derived in this paper those solution concepts are inspired by the nondominated solution concept employed in multiobjective programming problems since the ordering among fuzzy numbers introduced in this paper is a partial ordering not a total ordering we also provide a concept of fuzzy scalar inner product for fuzzy numbers then the fuzzy valued lagrangian function and the fuzzy valued lagrangian dual function are proposed via the concept of fuzzy scalar product under these settings the dual problem is formulated and the objective function of this dual problem is a point to set fuzzy valued function in this case three solution concepts for dual problem are proposed the duality theorems and saddle point optimality conditions can be naturally elicited based on these three solution concepts

application of fuzzy minimum cost flow problems to network design under uncertainty this paper deals with fuzzy quantities and relations in multi objective minimum cost flow problem when t norms and t conorms are available the goal programming is applied to minimize the deviation among the multiple costs of fuzzy flows and the given targets when the fuzzy supplies and demands are satisfied to obtain the most optimistic and the most pessimistic satisficing solutions of this problem two polynomial time algorithms are introduced applying some network transformations to demonstrate the performance of this approach in actual substances network design under fuzziness is considered and an efficient scheme is proposed including genetic algorithm together with fuzzy minimum cost flow problem this scheme is applied on a pilot network for more description

possibilistic linear programming with triangular fuzzy numbers abstract we consider a mathematical programming problem where all the parameters may be fuzzy variables specified by their possibility distribution and we define the possibility distribution of the objective function the ideas are illustrated on possibilistic linear programming

descent direction algorithm with multicommodity flow problem for signal optimization and traffic assignment jointly network managers wish to optimize control parameters such as signal setting which are very related to the traffic assignment models on the other hand traffic assignment patterns as an important instrument for predicting the amount of flow on network links are dependent to control decisions according to the significance of this concept some important papers about this mutually relation are reviewed in this paper then we implement a nonlinear algorithm on a minimal cost multicommodity flow mcmf problem to optimize some control policies subject to optimal flows although we take signal times into account but this approach has a far more reaching application in urban network control and design we employ a hybrid intelligent algorithm integrating decent direction algorithm and an interior point algorithm in a mutually consistent scheme for obtaining optimal signals and equilibrium flows an example is given to illustrate the effectiveness of our scheme

a survey of convergence results on particle filtering methods for practitioners optimal filtering problems are ubiquitous in signal processing and related fields except for a restricted class of models the optimal filter does not admit a closed form expression particle filtering methods are a set of flexible and powerful sequential monte carlo methods designed to solve the optimal filtering problem numerically the posterior distribution of the state is approximated by a large set of dirac delta masses samples particles that evolve randomly in time according to the dynamics of the model and the observations the particles are interacting thus classical limit theorems relying on statistically independent samples do not apply in this paper our aim is to present a survey of convergence results on this class of methods to make them accessible to practitioners

approximating sample state vectors using the espt for computationally efficient particle filtering the extrapolated single propagation technique espt based particle filter is proposed instead of propagating all the sample state vectors using multiple numerical integrations only one sample state vector is propagated in the espt other sample states are computed at the next epoch with an accuracy of the second order taylor series expansion terms it is theoretically shown that the particle filter algorithm which uses the espt for state propagation requires up to text 90 reduced processing time than the conventional particle filter using a benchmark non linear estimation problem the performance of the modified algorithm is compared with the particle filter the experimental results confirm the theoretical analysis and demonstrate the effectiveness of the proposed method for non linear state estimation the proposed algorithm significantly reduces the processing time of the particle filter with a minor degradation in the estimation accuracy

efficient montgomery based semi systolic multiplier for even type gnb of gf 2 m efficient finite field multiplication is crucial for implementing public key cryptosystem to achieve this multipliers using gaussian normal basis have been widely explored in previous works in this paper based on proposed gaussian normal basis montgomery gnbm representation a semi systolic even type gnbm multiplier is developed analysis shows that the proposed architecture saves about 57 percent space complexity and 50 percent time complexity when compared with the only existing semi systolic even type gnb multiplier moreover due to properties of regularity and modularity the proposed multiplier is very suitable for vlsi implementation

solving fuzzy transportation problems based on extension principle abstract transportation models play an important role in logistics and supply chain management for reducing cost and improving service this paper develops a procedure to derive the fuzzy objective value of the fuzzy transportation problem in that the cost coefficients and the supply and demand quantities are fuzzy numbers the idea is based on the extension principle a pair of mathematical programs is formulated to calculate the lower and upper bounds of the fuzzy total transportation cost at possibility level from different values of the membership function of the objective value is constructed two different types of the fuzzy transportation problem are discussed one with inequality constraints and the other with equality constraints it is found that the membership function of the objective value of the equality problem is contained in that of the inequality problem since the objective value is expressed by a membership function rather than by a crisp value more information is provided for making decisions

following a moving target monte carlo inference for dynamic bayesian models markov chain monte carlo mcmc sampling is a numerically intensive simulation technique which has greatly improved the practicality of bayesian inference and prediction however mcmc sampling is too slow to be of practical use in problems involving a large number of posterior target distributions as in dynamic modelling and predictive model selection alternative simulation techniques for tracking moving target distributions known as particle filters which combine importance sampling importance resampling and mcmc sampling tend to suffer from a progressive degeneration as the target sequence evolves we propose a new technique based on these same simulation methodologies which does not suffer from this progressive degeneration

interactive fuzzy programming for two level linear fractional programming problems with fuzzy parameters in this paper we present interactive fuzzy programming for two level linear fractional programming problems with fuzzy parameters using the level sets of fuzzy parameters the corresponding nonfuzzy two level linear fractional programming problem is introduced in our interactive method after determining fuzzy goals of decision makers at both levels a satisfactory solution is derived efficiently by updating a minimal satisfactory level of the decision maker at the upper level with considerations of overall satisfactory balance between both levels the satisfactory solution well balanced between both levels is easily computed by combined use of the bisection method the phase one of the simplex method and the variable transformation method by charnes and cooper an illustrative numerical example for two level linear fractional programming problems with fuzzy parameters is provided to demonstrate the feasibility of the proposed method

fault detection architectures for field multiplication using polynomial bases in many cryptographic schemes the most time consuming basic arithmetic operation is the finite field multiplication and its hardware implementation for bit parallel operation may require millions of logic gates some of these gates may become faulty in the field due to natural causes or malicious attacks which may lead to the generation of erroneous outputs by the multiplier in this paper we propose new architectures to detect erroneous outputs caused by certain types of faults in bit parallel and bit serial polynomial basis multipliers over finite fields of characteristic two in particular parity prediction schemes are developed for detecting errors due to single and certain multiple stuck at faults although the issue of detecting soft errors in registers is not considered the proposed schemes have the advantage that they can be used with any irreducible binary polynomial chosen to define the finite field

improved particle filters for multi target tracking we present a novel approach for improving particle filters for multi target tracking the suggested approach is based on drift homotopy for stochastic differential equations drift homotopy is used to design a markov chain monte carlo step which is appended to the particle filter and aims to bring the particle filter samples closer to the observations while at the same time respecting the target dynamics we have used the proposed approach on the problem of multi target tracking with a nonlinear observation model the numerical results show that the suggested approach can improve significantly the performance of a particle filter

the solution and duality of imprecise network problems duality properties have been investigated by many researchers in the recent literature they are introduced in this paper for a fully fuzzified version of the minimal cost flow problem which is a basic model in network flow theory this model illustrates the least cost of the shipment of a commodity through a capacitated network in terms of the imprecisely known available supplies at certain nodes which should be transmitted to fulfil uncertain demands at other nodes first we review on the most valuable results on fuzzy duality concepts to facilitate the discussion of this paper by applying hukuhara s difference approximated and exact multiplication and wu s scalar production we exhibit the flow in network models then we use combinatorial algorithms on a reduced problem which is derived from fully fuzzified mcfp to acquire fuzzy optimal flows to give duality theorems we utilize a total order on fuzzy numbers due to the level of risk and realize optimality conditions for providing some efficient combinatorial algorithms finally we compare our results with the previous worthwhile works to demonstrate the efficiency and power of our scheme and the reasonability of our solutions in actual decision making problems

neural net solutions to fuzzy linear programming we show how a neural net with sign restrictions on its weights can be trained to produce approximate solutions to fuzzy linear programming problems the neural net approximates the joint solution buckley 1995 to the fuzzy linear program

a variation on karmarkar s algorithm for solving linear programming problems the algorithm described here is a variation on karmarkar s algorithm for linear programming it has several advantages over karmarkar s original algorithm in the first place it applies to the standard form of a linear programming problem and produces a monotone decreasing sequence of values of the objective function the minimum value of the objective function does not have to be known in advance secondly in the absence of degeneracy the algorithm converges to an optimal basic feasible solution with the nonbasic variables converging monotonically to zero this makes it possible to identify an optimal basis before the algorithm converges

concurrent error detection in montgomery multiplication over binary extension fields multiplication is one of the most important operations in finite field arithmetic it is used in cryptographic and coding applications such as elliptic curve cryptography and reed solomon codes in this paper we consider the finite field multiplication used in elliptic curve cryptography and design concurrent error detection circuits it is shown in the literature that the montgomery multiplication can be used in cryptography to accelerate the scalar multiplication here we use a parity based concurrent error detection approach to increase the reliability of different montgomery multipliers available in the literature first we consider bit serial montgomery multiplication and propose an error detection circuit then we apply the same technique on the digit serial montgomery multiplication finally we consider low time complexity bit parallel montgomery multiplication and design the required components to implement the concurrent error detection circuits asic implementations have been completed to analyze the time and area overheads of the proposed schemes also the error detection capability is investigated by software simulations we show that our approach results in efficient error detection schemes with small time and area overheads

fuzziness and branch and bound procedures applications to separation sequencing abstract the aim of the paper is to identify optimal and near optimal distillation sequences according to a particular objective function definition the potential solutions are valuated from the point of view of practical considerations rather than purely costing methods four rules of thumb addressing column sequencing expressed in vague and imprecise terms are implemented and quantified by the fuzzy set theory the integer programming problem is solved by a branch and bound procedure where the bounding and branching schemes are carried out from the four heuristic rules with fuzzy quantification furthermore the fuzzy set theory is also implemented for modelling data uncertainties particularly the partial molar flow rates from the results obtained with the fuzzy branch and bound procedure involving fuzzy data we conclude that fuzzy set theory can be considered as a promising tool for modelling uncertainty and vagueness and may have many other applications in process systems engineering

a generalized asymmetric student t distribution with application to financial econometrics this paper proposes a new class of asymmetric student t ast distributions and investigates its properties gives procedures for estimation and indicates applications in financial econometrics we derive analytical expressions for the cdf quantile function moments and quantities useful in financial econometric applications such as the expected shortfall a stochastic representation of the distribution is also given although the ast density does not satisfy the usual regularity conditions for maximum likelihood estimation we establish consistency asymptotic normality and efficiency of ml estimators and derive an explicit analytical expression for the asymptotic covariance matrix a monte carlo study indicates generally good finite sample conformity with these asymptotic properties

possible and necessary optimality tests in possibilistic linear programming problems in this paper two kinds of optimality concepts are introduced into fuzzy linear programming problems in order to discuss the rationality of an obtained solution one is possible optimality evaluating the possibility degree to which the solution is optimal the other the dual concept is necessary optimality evaluating the necessity degree to which the solution is optimal when possibility distributions are defined by closed intervals degrees of possible and necessary optimalities become binary necessary and sufficient conditions for possible and necessary optimalities are induced in this case extending the results methods of calculating the degrees of possible and necessary optimalities are proposed some numerical examples are given to demonstrate the proposed methods

evolutionary algorithm solution to fuzzy problems fuzzy linear programming in this paper we wish to find solutions to the fully fuzzified linear program where all the parameters and variables are fuzzy numbers we first change the problem of maximizing a fuzzy number the value of the objective function into a multi objective fuzzy linear programming problem we prove that fuzzy flexible programming can be used to explore the whole undominated set to the multi objective fuzzy linear program an evolutionary algorithm is designed to solve the fuzzy flexible program and we apply this program to two applications to generate good solutions

approximations of the optimal importance density using gaussian particle flow importance sampling abstractrecently developed particle flow algorithms provide an alternative to importance sampling for drawing particles from a posterior distribution and a number of particle filters based on this principle have been proposed samples are drawn from the prior and then moved according to some dynamics over an interval of pseudo time such that their final values are distributed according to the desired posterior in practice implementing a particle flow sampler requires multiple layers of approximation with the result that the final samples do not in general have the correct posterior distribution in this article we consider using an approximate gaussian flow for sampling with a class of nonlinear gaussian models we use the particle flow within an importance sampler correcting for the discrepancy between the target and actual densities with importance weights we present a suitable numerical integration procedure for use with this flow and an accompanying step size control algorithm in a filtering co

solutions for fuzzy matrix games in this paper we deal with two person zero sum games with fuzzy payoffs and fuzzy goals we have presented two models for studying two person zero sum matrix games with fuzzy payoffs and fuzzy goals we assume that each player has a fuzzy goal for each of the payoffs we obtained that the fuzzy relation approach and the max min solution are equivalent

some properties of extended fuzzy preference relations using modalities abstract a fuzzy preference relation is extended to six kinds of relations between fuzzy sets the properties of the six extended relations are investigated especially a sufficient condition for reducing the extended relations to four kinds is discussed when fuzzy sets are bounded and normal and some examples are given to illustrate it further a sufficient condition for the extended negative relations to coincide with the extended inverse relations is described