the relationship between the minimum variance and minimax disparity rim quantifier problems recently liu and lou on the equivalence of some approaches to the owa operator and rim quantifier determination fuzzy sets and systems 159 2007 1673 1688 investigated the equivalence of solutions to the minimum variance and minimax disparity rim quantifier problems however their proofs are very sensitive to the assumption and some are mathematically incomplete in this regard this paper provides a counterexample of the minimax disparity rim quantifier problem for the case in which generating functions are continuous the paper also provides a correct proof of the minimax disparity rim quantifier problem for the case in which generating functions are absolutely continuous and a generalized result for the minimum variance rim quantifier problem for the case in which generating functions are lebesgue integrable based on the results the paper provides a correct relationship between the minimum variance and minimax disparity rim quantifier problems

efficient solution of rational conics we present efficient algorithms for solving legendre equations over q equivalently for finding rational points on rational conics and parametrizing all solutions unlike existing algorithms no integer factorization is required provided that the prime factors of the discriminant are known

existence of primitive divisors of lucas and lehmer numbers we prove that for n 30 every n th lucas and lehmer number has a primitive divisor this allows us to list all lucas and lehmer numbers without a primitive divisor

group decision making model using fuzzy multiple attributes analysis for the evaluation of advanced manufacturing technology selection of advanced manufacturing technology is important for improving manufacturing system competitiveness this study builds a group decision making model using fuzzy multiple attributes analysis to evaluate the suitability of manufacturing technology since numerous attributes have been considered in evaluating the manufacturing technology suitability most information available in this stage is subjective and imprecise and fuzzy sets theory provides a mathematical framework for modeling imprecision and vagueness the proposed approach involved developing a fusion method of fuzzy information which was assessed using both linguistic and numerical scales in addition an interactive decision analysis is developed to make a consistent decision when evaluating the suitability of manufacturing technology it may be necessary to improve upon the technology and naturally advanced manufacturing technology is seen as the best direction for improvement the flexible manufacturing system adopted in the taiwanese bicycle industry is used in this study to illustrate the computational process of the proposed method the results of this study are more objective and unbiased owing to being generated by a group of decision makers

constrained ordered weighted averaging aggregation with multiple comonotone constraints abstract the constrained ordered weighted averaging owa aggregation problem arises when we aim to maximize or minimize a convex combination of order statistics under linear inequality constraints that act on the variables with respect to their original sources the standalone approach to optimizing the owa under constraints is to consider all permutations of the inputs which becomes quickly infeasible when there are more than a few variables however in certain cases we can take advantage of the relationships amongst the constraints and the corresponding solution structures for example we can consider a land use allocation satisfaction problem with an auxiliary aim of balancing land types whereby the response curves for each species are non decreasing with respect to the land types this results in comonotone constraints which allow us to drastically reduce the complexity of the problem in this paper we show that if we have an arbitrary number of constraints that are comonotone i e they share the same ordering permutation of the coefficients then the optimal solution occurs for decreasing components of the solution after investigating the form of the solution in some special cases and providing theoretical results that shed light on the form of the solution we detail practical approaches to solving and give real world examples

cryptanalysis of large rsa exponent by using the lll algorithm the study of paper cryptanalysis of rsa with private key d less than n 0 2 9 2 ieee trans information theory 46 2000 1339 which boneh and durfee published in ieee transactions on information theory in july 2000 supported that when d

how well does the owa operator represent real preferences we present the results of an empirical study in which we analyze the ability of the ordered weighted average owa operator to model actual preferences in a multi attribute ranking task we compare the owa to a competing model simple additive weighting saw and we also study whether its characteristic feature the ability to represent different attitudes toward compensation among attributes is reflected in the preferences provided by subjects we find that in general the owa model fits slightly less well to empirical data subjects whose preferences are better explained by the saw model are also more consistent in their choice behavior our results furthermore indicate that preferences of most subjects are not fully compensatory thus the ability of the owa operator to represent different attitudes toward compensation can be a useful feature in modeling actual preferences the structure of the weights estimated for the owa operator also suggests that it might provide a good approximation to certain types of decision heuristics

an analytic approach for obtaining maximal entropy owa operator weights one important issue in the theory of ordered weighted averaging owa operators is the determination of the associated weights one of the first approaches suggested by o hagan determines a special class of owa operators having maximal entropy of the owa weights for a given level of orness algorithmically it is based on the solution of a constrained optimization problem in this paper using the method of lagrange multipliers we shall solve this constrained optimization problem analytically and derive a polynomial equation which is then solved to determine the optimal weighting vector

the optimal lll algorithm is still polynomial in fixed dimension in this paper we consider the open problem of the complexity of the lll algorithm in the case when the approximation parameter of the algorithm has as its extreme value 1 this case is of interest because the output is then the strongest lovasz reduced basis experiments reported by lagarias and odlyzko j acm 32 1 1985 229 seem to show that the algorithm remains polynomial in average however no bound better than a naive exponential order one is established for the worst case complexity of the optimal lll algorithm even for fixed small dimension higher than 2 here we prove that for any fixed dimension n the number of iterations of the lll algorithm is linear with respect to the size of the input it is easy to deduce from vallee j algorithms 12 1991 556 that the linear order is optimal moreover in 3 dimensions we give a tight bound for the maximum number of iterations and we characterize precisely the output basis our bound also improves the known one for the usual non optimal lll algorithm

hesitant analytic hierarchy process abstract in traditional analytic hierarch process ahp decision makers dms are required to provide crisp judgments over paired comparisons of objectives to construct comparison matrices to enhance the modeling ability of traditional ahp we propose hesitant ahp h ahp that can consider the hesitancy experienced by the dms in decision h ahp is characterized by hesitant judgments where each hesitant judgment can be represented by several possible values different probability distributions can be used to further describe hesitant judgments according to the dms preferences based on a hesitant comparison matrix hcm that consists of hesitant judgments we define two indices to measure the consistency degree and the consensus degree of the hcm respectively from a stochastic point of view a new prioritization method is developed to derive priorities from hcms where the results are with probability interpretations we provide a step by step procedure for h ahp and demonstrate this new method with a real life decision making problem

fast multiple antenna differential decoding we present an algorithm based on lattice reduction for the fast decoding of diagonal differential modulation across multiple antenna while the complexity of the maximum likelihood ml algorithm is exponential both in the number of antenna and the rate the complexity of our approximate lattice algorithm is polynomial in the number of antennas and the rate we show that the error performance of our lattice algorithm is very close to the ml algorithm

arithmetic multivariate descartes rule let inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i be any number field or p adic field and consider f f 1 f k where f 1 f k inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i x 1 x n and no more than distinct exponent vectors occur in the monomial term expansions of the f i we prove that f has no more than 1 c n n 3 log n n geometrically isolated roots in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i n where c is an explicit and effectively computable constant depending only on inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i this gives a significantly sharper arithmetic analogue of khovanski s theorem on real fewnomials and a higher dimensional generalization of an earlier result of hendrik w lenstra jr for the special case of a single univariate polynomial we also present some further refinements of our new bounds and a higher dimensional generalization of a bound of lipshitz on p adic complex roots connections to non archimedean amoebae and computational complexity including additive complexity and solving for the geometrically isolated rational roots are discussed along the way we thus provide the foundations for an effective arithmetic analogue of fewnomial theory

solving a system of linear diophantine equations with lower and upper bounds on the variables we develop an algorithm for solving a system of diophantine equations with lower and upper bounds on the variables the algorithm is based on lattice basis reduction it first finds a short vector satisfying the system of diophantine equations and a set of vectors belonging to the nullspace of the constraint matrix due to basis reduction all these vectors are relatively short the next step is to branch on linear combinations of the null space vectors which either yields a vector that satisfies the bound constraints or provides a proof that no such vector exists the research was motivated by the need for solving constrained diophantine equations as subproblems when designing integrated circuits for video signal processing our algorithm is tested with good results on real life data and on instances from the literature

on the dispersion measure of owa operators we describe some basic features of the owa operator we turn to the problem of determining the weights associated with this operator and particularly the maximal dispersion entropy approach we consider the possibility of using minimization of dispersion after discussing concerns with both maximization and minimization of dispersion we investigate the possibility of finding an optimal solution intermediate to these extremes we next consider alternative measures of dispersion we introduce a fundamental requirement for a measure of dispersion called the preference for equal division a number of general classes of dispersion measures are provided notable among these are those based on t norm and t conorm operators

on proving the extended minimax disparity owa problem determining associated weights in the theory of ordered weighted averaging owa operators is an important issue wang and parkan information sciences 175 2005 20 29 proposed a minimax disparity approach for obtaining owa operator weights which is based on the solution of a linear program lp model for a given degree of orness recently amin and emrouznejad computers industrial engineering 50 2006 proposed an extended minimax disparity model and improved their proposed lp to obtain weights that would be as close as possible they also left an open problem related to the extended model for an even number of arguments there would be an interval for the degree of orness such that the optimal solution of the extended model could be obtained by a compact mathematical form in this paper we completely prove this open problem mathematically for all orness levels whatever the number of arguments

on the properties of owa operator weights functions with constant level of orness the result of aggregation performed by the ordered weighted averaging owa operator heavily depends upon the weighting vector used a number of methods have been presented for obtaining the associated weights in this paper we present analytic forms of owa operator weighting functions each of which has properties of rank based weights and a constant level of orness irrespective of the number of objectives considered these analytic forms provide significant advantages for generating the owa weights over previously reported methods first the owa weights can be efficiently generated by using proposed weighting functions without solving a complicated mathematical program moreover convex combinations of these specific owa operators can be used to generate the owa operators with any predefined values of orness once specific values of orness are a priori stated by the decision maker those weights have a property of constant level of orness as well finally the owa weights generated at a predefined value of orness make almost no numerical difference with maximum entropy owa weights in terms of dispersion

asymptotic behavior of solutions for a three dimensional system of globally modified navier stokes equations with a locally lipschitz delay term abstract existence uniqueness and continuity properties of solutions for a globally modified version of navier stokes equations with finite delay terms within a locally lipschitz operator are established moreover we also analyze the stationary problem and under suitable assumptions we prove that there exists a unique stationary solution which is globally asymptotically exponentially stable

solving low density subset sum problems the subset sum problem is to decide whether or not the 0 l integer programming problem s n i l a i x i m i x i 0 or 1 has a solution where the a i and m are given positive integers this problem is np complete and the difficulty of solving it is the basis of public key cryptosystems of knapsack type an algorithm is proposed that searches for a solution when given an instance of the subset sum problem this algorithm always halts in polynomial time but does not always find a solution when one exists it converts the problem to one of finding a particular short vector v in a lattice and then uses a lattice basis reduction algorithm due to a k lenstra h w lenstra jr and l lovasz to attempt to find v the performance of the proposed algorithm is analyzed let the density d of a subset sum problem be defined by d n log 2 max i a i then for almost all problems of density d d n it is proved that the lattice basis reduction algorithm locates v extensive computational tests of the algorithm suggest that it works for densities d d c n where d c n is a cutoff value that is substantially larger than 1 n this method gives a polynomial time attack on knapsack public key cryptosystems that can be expected to break them if they transmit information at rates below d c n as n

on the issue of obtaining owa operator weights we first investigate the issue of obtaining the weights associated with the owa aggregation in the situation when we have observed data on the arguments and the aggregated value we next introduce a family of owa operators called exponential owa operators finally we look at a simple procedure for generating the weights given a required degree of orness

choosing owa operator weights in the field of social choice one of the most important issues in the theory of owa operators is the determination of associated weights this matter is essential in order to use the best suited owa operator in each aggregation process given that some aggregation processes can be seen as extensions of majority rules to the field of gradual preferences it is possible to determine the owa operator weights by taking into account the class of majority rule that we want to obtain when individuals do not grade their pairwise preferences however a difficulty with this approach is that the same majority rule can be obtained through a wide variety of owa operators for this reason a model for selecting the best suited owa operators is proposed in this paper

compatible weighting method with rank order centroid maximum entropy ordered weighted averaging approach in a situation where imprecise attribute weights such as a rank order are captured various approximate weighting methods have been proposed to aid multiattribute decision analysis among others it is well known that the rank order centroid roc weights result in the highest performance in terms of the identification of the best alternative under the ranked attribute weights in this paper we aim to reinterpret the meaning of the roc weights and to develop a compatible weighting method that is based on other well established academic disciplines the ordered weighted averaging owa method is a nonlinear aggregation method in that the weights are associated with the objects reordered according to their magnitudes in the aggregation process some interesting semantics can be attached to the approximate weights in view of the measure developed in the owa method furthermore the weights generated by the maximum entropy method show equally compatible performance with the roc weights under some condition which is demonstrated by theoretical and simulation analysis

on obtaining minimal variability owa operator weights one important issue in the theory of ordered weighted averaging owa operators is the determination of the associated weights one of the first approaches suggested by o hagan determines a special class of owa operators having maximal entropy of the owa weights for a given level of orness algorithmically it is based on the solution of a constrained optimization problem another consideration that may be of interest to a decision maker involves the variability associated with a weighting vector in particular a decision maker may desire low variability associated with a chosen weighting vector in this paper using the kuhn tucker second order sufficiency conditions for optimality we shall analytically derive the minimal variability weighting vector for any level of orness

a fast signature scheme based on congruential polynomial operations a novel digital signature scheme is proposed in which the computation time is much shorter than that of the rivest shamir adelman rsa scheme while the key length and signature length are comparable to those for the rsa scheme moreover the proposed scheme can be implemented easily and is therefore more practical for many digital signature applications the scheme is based on congruential polynomial operations whose degrees are more than three the secret key consists of two large prime numbers p and q and the public key is their product n p sup 2 q the security of this scheme depends on the difficulty of factorizing the number n variations using the number of zeros succeeding the significant bit are also proposed

trajectory statistical solutions and liouville type equations for evolution equations abstract results and applications abstract in this article we first prove from the viewpoint of infinite dynamical system sufficient conditions ensuring the existence of trajectory statistical solutions for autonomous evolution equations then we establish that the constructed trajectory statistical solutions possess invariant property and satisfy a liouville type equation moreover we reveal that the equation describing the invariant property of the trajectory statistical solutions is a particular situation of the liouville type equation finally we study the equations of three dimensional incompressible magneto micropolar fluids in detail and illustrate how to apply our abstract results to some concrete autonomous evolution equations

applying logistic regression to relevance feedback in image retrieval systems this paper deals with the problem of image retrieval from large image databases a particularly interesting problem is the retrieval of all images which are similar to one in the user s mind taking into account his her feedback which is expressed as positive or negative preferences for the images that the system progressively shows during the search here we present a novel algorithm for the incorporation of user preferences in an image retrieval system based exclusively on the visual content of the image which is stored as a vector of low level features the algorithm considers the probability of an image belonging to the set of those sought by the user and models the logit of this probability as the output of a generalized linear model whose inputs are the low level image features the image database is ranked by the output of the model and shown to the user who selects a few positive and negative samples repeating the process in an iterative way until he she is satisfied the problem of the small sample size with respect to the number of features is solved by adjusting several partial generalized linear models and combining their relevance probabilities by means of an ordered averaged weighted operator experiments were made with 40 users and they exhibited good performance in finding a target image 4 iterations on average in a database of about 4700 images the mean number of positive and negative examples is of 4 and 6 per iteration a clustering of users into sets also shows consistent patterns of behavior

invariant measures for multivalued semigroups abstract in this work we extend the concept of an invariant measure for a multivalued semigroup and when it has a global attractor we give different but equivalent definitions for such a measure as a consequence we can apply the birkhoff ergodic theorem to conclude that time averages converge almost everywhere to the spatial average

on the constrained owa aggregation problem with single constraint abstract in this note we present a simple proof for the constrained owa aggregation problem with a single constraint but with variable coefficients

indicators for the characterization of discrete choquet integrals ordered weighted averaging owa operators and their extensions are powerful tools used in numerous decision making problems this class of operator belongs to a more general family of aggregation operators where each operator of this family is understood as a discrete choquet integral aggregation operators are usually characterized by indicators in this article four indicators usually associated with the owa operator are extended to the discrete choquet integral namely the degree of balance the divergence the variance indicator and renyi entropies all of these indicators are considered from a local and a global perspective linearity of indicators for linear combinations of capacities is investigated and to illustrate the usefulness of results indicators of the probabilistic ordered weighted averaging powa operator are derived finally a numerical example is provided to discuss the results in a specific context

time series smoothing and owa aggregation in this paper an overview of the time series smoothing problem is provided and the role of data aggregation is described using a weighted average of the past observations two important features associated with this smoothing process are introduced one is the average age of the data and other is the expected variance it is noted how both of these are defined in terms of the associated weights we show the fundamental conflict between trying to keep the variance small while simultaneously using the freshest data we study the moving average and exponential smoothing methods focusing on the aggregation aspect of the data smoothing problem allows us to draw upon the work done with the ordered weighted averaging aggregation operators to suggest new methods for developing smoothing techniques a new class of smoothing operators based on the use of linearly decaying weights is introduced and is shown to have some better features than either exponential smoothing or the moving average other classes of smoothing operators are introduced we introduce the idea of an operational estimate that involves adjusting a smoothed value by other considerations

an orness measure for quasi arithmetic means in this paper an orness measure to reflect the or like degree of the quasi arithmetic mean operator is proposed with the generating function representation method some properties of a quasi arithmetic mean associated with its orness measure are analyzed then the paper focuses on two kinds of parameterized quasi arithmetic means with exponential function and power function generators respectively some properties of them are examined and compared as the aggregation value for any set always monotonically increases with the orness level the orness level can be used as a control parameter to represent the decision maker s preference a generic method to get the quasi arithmetic mean operator which makes the aggregation result consistent with its orness level is also examined finally the properties of the quasi arithmetic mean and that of the exponential and power function generators are extended to the weighted quasi arithmetic mean by considering the importance of the aggregated elements

aggregating preference rankings using owa operator weights one important issue of aggregating preference rankings is to determine the weights of different ranking places this paper proposes the use of ordered weighted averaging owa operator weights to aggregate preference rankings which allows the weights associated with different ranking places to be determined in terms of a decision maker dm s optimism level characterized by an orness degree by adjusting the dm s optimism level ties can be avoided and winner can be selected two numerical examples are examined using owa operator weights to show their applications simplicity and flexibility in aggregating preference rankings

two regularity criteria for the 3d mhd equations this work establishes two regularity criteria for the 3d incompressible mhd equations the first one is in terms of the derivative of the velocity field in one direction while the second one requires suitable boundedness of the derivative of the pressure in one direction

an efficient solution of the congruence x 2 ky 2 mpmod n the equation of the title arose in the proposed signature scheme of ong schnorr shamir the large integers n k and m are given and we are asked to find any solution x y it was believed that this task was of similar difficulty to that of factoring the modulus n we show that on the contrary a solution can easily be found if k and m are relatively prime to n under the assumption of the generalized riemann hypothesis a solution can be found by a probabilistic algorithm in o log n 2 log log k arithmetical steps on o log n bit integers the algorithm can be extended to solve the equation x 2 ky 2 m pmod n for quadratic integers k m in bf z sqrt d and to solve in integers the equation x 3 ky 3 k 2 z 3 3kxyz m pmod n

abstract framework for the theory of statistical solutions abstract an abstract framework for the theory of statistical solutions is developed for general evolution equations extending the theory initially developed for the three dimensional incompressible navier stokes equations the motivation for this concept is to model the evolution of uncertainties on the initial conditions for systems which have global solutions that are not known to be unique both concepts of statistical solution in trajectory space and in phase space are given and the corresponding results of existence of statistical solution for the associated initial value problems are proved the wide applicability of the theory is illustrated with the very incompressible navier stokes equations a reaction diffusion equation and a nonlinear wave equation all displaying the property of global existence of weak solutions without a known result of global uniqueness

integer forcing linear receivers linear receivers are often used to reduce the implementation complexity of multiple antenna systems in a traditional linear receiver architecture the receive antennas are used to separate out the codewords sent by each transmit antenna which can then be decoded individually although easy to implement this approach can be highly suboptimal when the channel matrix is near singular this paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer valued entries rather than attempting to recover transmitted codewords directly the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix the codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords provided that the effective channel is full rank these integer combinations can then be digitally solved for the original codewords this paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter s which corresponds either to a multiuser uplink scenario or to single user v blast encoding in this setting the proposed integer forcing linear receiver significantly outperforms conventional linear architectures such as the zero forcing and linear minimum mean squared error receiver in the high signal to noise ratio regime the proposed receiver attains the optimal diversity multiplexing tradeoff for the standard multiple input multiple output mimo channel with no coding across transmit antennas it is further shown that in an extended mimo model with interference the integer forcing linear receiver achieves the optimal generalized degrees of freedom

improved minimax disparity model for obtaining owa operator weights the determination of weights vector is one of the key issues in the theory of ordered weighted averaging owa operators for this reason many weight generating models have been proposed in the literature the main purpose of this note is to point out that the improved minimax disparity model which is suggested by emrouznejad and amin 2010 has infinite solutions as a consequence this model is not reliable

models to determine parameterized ordered weighted averaging operators using optimization criteria this paper proposes a general optimization model for determining ordered weighted averaging owa operators and three specific models for generating monotonic and symmetric owa operators as well as those with any function shape in these models entropy and variance concepts are generalized as general dispersion indices for use in the objective functions while the ordinary orness level constraints are used in the constraint equations as a special case we define an orness function for monotonic owa operators which measures the closeness of the aggregation value to the maximum value and a medianness function for symmetric owa operators which measures the closeness of the aggregation value to the median value we also extend the commonly used models for determining owa operators under given orness values to determine monotonic owa operators with given orness function values and symmetric owa operators with given medianness function values analytical solutions and properties of these models are discussed we also provide analytical solutions of the maximum entropy and minimum variance problems with given linear medianness values by setting different forms of the objective function and constraints the parameterized owa operator family elements can achieve various distributions in any desired shape two examples are given to show the owa operator elements distributed in quadratic and gaussian distribution function shapes

owa operators with maximal renyi entropy this paper lays bare a parametric class of ordered weighted averaging owa operators with maximal renyi entropy owa weights for any level of orness in particular we shall formulate an extended approach to decision making with owa operators by introducing considerations of maximizing information content in the aggregation according to a general parametric class of dispersion measures

a priori identification of preferred alternatives of owa operators by relational analysis of arguments we present a reverse decision aiding method that is distinct from previously reported ordered weighted averaging owa aggregation methods the proposed method is implemented in two phases in the first phase potentially best alternative defined as one having any weighting vector that enables it to be at least as good as the others is identified in the second phase the maximum and the minimum attitudinal characters for such an alternative are computed as the highest and the lowest values which it can attain under the weights set identified in the first phase these two phases are governed only by the relational analysis of input arguments without soliciting the decision maker to supply a specific attitudinal character the proposed method can be applied to cases when it is difficult to obtain a precise attitudinal character and when even if a precise one is obtained the owa operator weights are different depending on the weights generating methods adopted further if uncertain attitudinal character in the form of the interval number is available its projection into the results of the proposed method yields less alternatives of consideration in some cases a single best alternative the proposed method also allows for a priori identification of alternatives prone to change at a particular range of attitudinal character

effective hilbert irreducibility in this paper we prove by entirely elementary means a very effective version of the hilbert irreducibility theorem we then apply our theorem to construct a probabilistic irreducibility test for sparse multivariate polynomials over arbitrary perfect fields for the usual coefficient fields the test runs in polynomial time in the input size

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

a preemptive goal programming method for aggregating owa operator weights in group decision making this paper reveals that owa operator weights cannot be aggregated by the weighted arithmetic or geometric average method in group decision making a preemptive goal programming method pgpm is proposed for aggregating owa operator weights which is an extension of the minimax disparity approach developed earlier by the same authors the effectiveness of pgpm is illustrated with a numerical example

median value and median interval of a fuzzy number median value and median interval of a fuzzy number are investigated effects of concentration and dilation of a trapezoidal fuzzy number on the location of the median value and the median interval are studied relationship between the median interval and the mean interval is explored central value and central interval of a fuzzy number are proposed

parameterized defuzzification with continuous weighted quasi arithmetic means an extension parameterized aggregation becomes an attractive idea in many applications by applying the quasi arithmetic mean based defuzzification method and its orness measure we extend the properties of discrete quasi arithmetic mean with an orness measure to the case of continuous weighted quasi arithmetic means and apply them to the parameterized estimation of fuzzy or random variables when facing the uncertainty of these variables the decision maker can obtain the crisp value estimation which is always consistent with his her preference information two families of continuous weighted quasi arithmetic means with exponential and power function generators are discussed combining these conclusions with that of the discrete case we can understand better the properties of quasi arithmetic means and extend their possible applications

integer programming with a fixed number of variables it is shown that the integer linear programming problem with a fixed number of variables is polynomially solvable the proof depends on methods from geometry of numbers

regularity of trajectory attractor and upper semicontinuity of global attractor for a 2d non newtonian fluid abstract there are two results within this paper the one is the regularity of trajectory attractor and the trajectory asymptotic smoothing effect of the incompressible non newtonian fluid on 2d bounded domains for which the solution to each initial value could be non unique the other is the upper semicontinuity of global attractors of the addressed fluid when the spatial domains vary from m to r l l where m m 1 is an expanding sequence of simply connected bounded and smooth subdomains of such that m as m that is let a and a m be the global attractors of the fluid corresponding to and m respectively we establish that for any neighborhood o a of a the global attractor a m enters o a if m is large enough

a minimax disparity approach for obtaining owa operator weights one of the key issues in the theory of ordered weighted averaging owa operators is the determination of owa operator weights in this paper a minimax disparity approach for obtaining owa operator weights is proposed this involves the formulation and solution of a linear programming lp model for a given degree of orness the proposed approach generates the owa operator weights by minimizing the maximum difference between any two adjacent weights a numerical example is provided to illustrate the application of the proposed approach in generating viable owa operator weights in a simple and effective way

sentences over integral domains and their computational complexities letrbe a hilbertian domain and letkbe its fraction field let x1 xn y be a quantifier free arithmetical formula overr we may also take x1 xn y to be an arithmetical formula overkx1 xn and write it as y in this paper we show that ifrhas enough non units and x1 xn y x1 xn y called an n sentence is true inr then y y is true inkx1 xn also ifr kt wherekis an infinite integral domain and x1 xn y x1 xn y is true inr then y y is true inrx1 xn these results are applied to find the upper and lower bounds of the time complexities of various decision problems on diophantine equations with parameters and arithmetical sentences some of the results are 1 the decision problem of sentences and diophantine equations with parameters over the ring of integers of a global field are co np complete 2 the decision problem of sentences over the ring of integers of a global field is np complete 3 letkbe an infinite domain the time complexities of the decision problems of equations with parameters and sentences over the polynomial ringkt are polynomial time reducible to factoring polynomials overk 4 the decision problem of sentences over all algebraic integer rings is in p 5 the decision problem of sentences over all integral domains with characteristic 0 is in p 6 the time complexity of the decision problem of sentences over all integral domains is polynomial time reducible to factoring integers overzand factoring polynomials over finite fields

an efficient pruning method for decision alternatives of owa operators in this paper we present an efficient method for pruning decision alternatives in the case of using ordered weighted averaging owa operators for decision making the proposed method helps to identify inferior alternatives that are less likely to be selected out of competing alternatives as the owa aggregation proceeds it thus enables us to diminish the number of alternatives before applying the owa operators the reordering process unique to the owa aggregation plays an important role in identifying inferior alternatives the efficacy of the proposed method is demonstrated by simulation analysis in which artificial decision problems of diverse sizes are generated and then examined with four scenarios pruning alternatives pruning alternatives with rank order owa weights pruning alternatives with a normalized decision problem and pruning alternatives with both a normalized decision problem and rank order owa weights the proposed method is easy to use and the simulation results show that the number of alternatives can be reduced drastically by applying this method

an analytic approach to obtain the least square deviation owa operator weights an important issue in the theory of ordered weighted averaging owa operators is the determination of the associated weights one important approach suggested by wang luo and liu in 2007 determines a special class of owa operators with the least square deviation lsd of owa weights for a given orness level in this paper using the method of lagrange multipliers we solve this constrained optimization problem analytically and derive a polynomial equation to determine the optimal weighting vector numerical examples illustrate our proposed approach

asymptotic regularity of trajectory attractor and trajectory statistical solution for the 3d globally modified navier stokes equations abstract we first prove the existence and regularity of the trajectory attractor for a three dimensional system of globally modified navier stokes equations then we use the natural translation semigroup and trajectory attractor to construct the trajectory statistical solutions in the trajectory space in our construction the trajectory statistical solution is an invariant borel probability measure which is supported by the trajectory attractor and is invariant under the action of the translation semigroup as a byproduct of the regularity of the trajectory attractor we obtain the asymptotic regularity of the trajectory statistical solution in the sense that it is supported by a set in the trajectory space in which all weak solutions are in fact strong solutions

a new approach to solve the constrained owa aggregation problem constrained ordered weighted averaging owa aggregation attempts to optimize the owa aggregation problem with multiple constraints it is inherently nonlinear and yager presented a novel method to transform the nonlinear problem to a mixed integer linear problem later a simple algorithm for exact computation of optimal solutions to a single constrained owa aggregation problem was presented in this paper we deal with the same problem but in completely different ways in a sense that it is linearized by utilizing the reordering property of the owa operators we attempt to solve the linear programming problem via the extreme points in lieu of using a linear programming package for the purpose of deriving an explicit formula for the optimal solution furthermore we consider its dual problem that leads to an equivalent optimal solution finally the proposed method is extended to the owa optimization problem with multiple constraints including the attitudinal character as well as a range of incomplete arguments

the owa aggregation with uncertain descriptions on weights and input arguments since the ordered weighted averaging owa operator was introduced by yager to provide a method for aggregating multiple inputs that lie between the max and min operators much research that deals with uncertain information on input arguments instead of numerical values has been conducted due to the fact that information provided by human beings is in fact often vague and imprecise in this paper the owa operators with uncertain weights such as interval or weak ordinal descriptions coupled with interval input arguments are presented in order to identify the superior course of action among a multitude of courses of action with the help of relaxation of information representation a burden of information specification imposed on decision maker can be to some extent relieved and thus with regard to the parameters we can obtain a less specific expression that renders human judgments readily available to perform the owa aggregation we take into account the strength of preference based on a probabilistic measure and present a way of ordering the input arguments specified by interval numbers as well as two heuristic algorithms to allocate uncertain weights to the ordered input arguments for prioritizing the courses of action

dual rsa and its security analysis we present new variants of an rsa whose key generation algorithms output two distinct rsa key pairs having the same public and private exponents this family of variants called dual rsa can be used in scenarios that require two instances of rsa with the advantage of reducing the storage requirements for the keys two applications for dual rsa blind signatures and authentication secrecy are proposed in addition we also provide the security analysis of dual rsa compared to normal rsa the security boundary should be raised when applying dual rsa to the types of small d small e and rebalanced rsa

on the analytic representation of the leximin ordering and its application to flexible constraint propagation we discuss the basic formulation of constraint propagation problems and extend it to the flexible constraint propagation environment where constraints are represented as fuzzy subsets some methods for ordering alternative solutions with respect to a collection of flexible constraints are discussed along with their drawbacks among the methods introduced is the leximin method where we note its lack of an analytic formulation with the aid of the ordered weighted averaging owa operator we suggest an analytic formulation for the leximin method some properties of this formulation are provided we then describe the application of this new formulation for the leximin method to situations in which the constraints are describable in a linear fashion we show how we can use mixed integer programming techniques to find an optimal solution

generalized ordered weighted utility proportional averaging hyperbolic absolute risk aversion operators and their applications to group decision making under the general utility we provide a new operator called gowupa operator under hara utility we present a new operator called the gowupa hara operator we put forward an orness measure of the gowupa hara operator we construct a new model for determining the weight of the gowupa hara operator we develop a new approach for multiple attributes group decision making this paper develops a new class of aggregation operator based on utility function which introduces the risk attitude of decision makers dms in the aggregation process first under the general framework of utility function we provide a new operator called the generalized ordered weighted utility proportional averaging gowupa operator and study its properties which are suitable for any utility function then under the hyperbolic absolute risk aversion hara utility function we propose another new operator named as the generalized ordered weighted utility proportional averaging hyperbolic absolute risk aversion gowupa hara operator and further investigate its families including a wide range of aggregation operators to determine the gowupa hara operator weights we put forward an orness measure of the gowupa hara operator and analyze its properties considering that different dms may have different opinions towards decision making and their opinions can be characterized by different orness measures we construct a new nonlinear optimization model to determine the optimal weights which can aggregate all the individual sets of weights into an overall set of weights furthermore based on the gowupa hara operator a method for multiple attribute group decision making magdm is developed finally an example is given to illustrate the application of the gowupa hara operator to the magdm

programming based owa operator weights with quadratic objective function yager s ordered weighted averaging owa operators are extensively employed to perform mean type aggregations their success heavily depends on proper determination of the associated weights that characterize the operators several methods have been established to determine the weights and thereby to support successful owa aggregation in this study the least square method which is one of the nonlinear programs with a quadratic objective function is reformulated by using the extreme points that correspond to its constraints and then solved by a few steps of matrix operations finally we present a new weighting method called the minimizing distances from the extreme points mdp wherein the owa operator weights that minimize the expected quadratic distance with respect to the set of extreme points are chosen a different attitudinal character leads to different extreme points and thus the mdp seeks to find the owa operator weights that are dynamically adjusted to be at the center of attitude dependent polytope

a multidimensional continued fraction based on a high order recurrence relation the paper describes and studies an iterative algorithm for finding of a set of linear forms over vectors of integers the algorithm small values of a set of linear forms over vectors of integers the algorithm uses a linear recurrence relation to generate a vector sequence the basic idea being to choose the integral coefficients in the recurrence relation in such a way that the linear forms take small values subject to the requirement that the integers should not become too large the problem of choosing good coefficients for the recurrence relation is thus related to the problem of finding a good approximation of a given vector by a vector in a certain one parameter family of lattices the novel feature of our approach is that practical formulae for the coefficients are obtained by considering the limit as the parameter tends to zero the paper discusses two rounding procedures to solve the underlying inhomogeneous diophantine approximation problem the first which we call naive rounding leads to a multidimensional continued fraction algorithm with suboptimal asymptotic convergence properties in particular when it is applied to the familiar problem of simultaneous rational approximation the algorithm reduces to the classical jacobi perron algorithm the second rounding procedure is babai s nearest plane procedure we compare the two rounding procedures numerically our experiments suggest that the multidimensional continued fraction corresponding to nearest plane rounding converges at an optimal asymptotic rate

trajectory attractor and global attractor for a two dimensional incompressible non newtonian fluid the authors construct the trajectory attractor and global attractor for an autonomous two dimensional non newtonian fluid

how to compute the volume in high dimension in some areas of theoretical computer science we feel that randomized algorithms are better and in some others we can prove that they are more efficient than the deterministic ones

tile invariants new horizons let t be a finite set of tiles the group of invariants g t introduced by pak trans ams 352 2000 5525 is a group of linear relations between the number of copies of tiles in tilings of the same region we survey known results about g the height function approach the local move property various applications and special cases

reduced and fixed complexity variants of the lll algorithm for communications the lenstra lenstra lovasz lll algorithm is a popular lattice reduction algorithm in communications in this paper variants of the lll algorithm with either reduced or fixed complexity are proposed and analyzed specifically the use of effective lll reduction for lattice decoding is presented where size reduction is only performed for pairs of consecutive basis vectors its average complexity measured by the number of floating point operations and averaged over i i d standard normal lattice bases is shown to be o n 3 log n where n is the lattice dimension this average complexity is an order lower than previously thought to address the issue of variable complexity of the lll algorithm two fixed complexity approximations are proposed one is fixed complexity effective lll for which the first vector of the basis is proven to be bounded in length the other is fixed complexity lll with deep insertion which is shown to be closely related to the well known v blast algorithm such fixed complexity structures are much desirable in hardware implementation since they allow straightforward constant throughput implementation

fundamental limits of linear equalizers diversity capacity and complexity linear equalizers les have been widely adopted for practical systems due to their low computational complexity however it is also well known that les provide inferior performance relative to a maximum likelihood equalizer mle or other near mles because les usually cannot collect the diversity order enabled by the transmitter and at the same time they lose mutual information more importantly unlike mle or near mles the performance of les has not been well quantified this hinders more general applications of les in wireless systems in this paper we reveal a fundamental link between a channel parameter orthogonality deficiency od of the channel matrix and the diversity and capacity of les we identify that when the od of channel matrix has an upper bound strictly less than 1 the same diversity order as that of mles is collected by les and the outage capacity loss relative to mles is also a constant over signal to noise ratio snr these results can be applied to designing a framework for hybrid equalizers furthermore by studying the statistical properties of the od and comparing the complexity of different equalizers we show that hybrid equalizers can trade off between performance and complexity by tuning the channel matrix od the theoretical analysis is corroborated by computer simulations

a primal all integer algorithm based on irreducible solutions this paper introduces an exact primal augmentation algorithm for solving general linear integer programs the algorithm iteratively substitutes one column in a tableau by other columns that correspond to irreducible solutions of certain linear diophantine inequalities we prove that various versions of our algorithm are finite it is a major concern in this paper to show how the subproblem of replacing a column can be accomplished effectively an implementation of the presented algorithms is given computational results for a number of hard 0 1 integer programs from the miplib demonstrate the practical power of the method

hard equality constrained integer knapsacks we consider the following integer feasibility problem given positive integer numbersa0 a1 a n with gcd a1 a n 1 anda a1 a n does there exist a vectorx z n 0satisfyinga x a0 we prove that if the coefficientsa1 a nhave a certain decomposable structure then the frobenius number associated witha1 a n i e the largest value ofa0 for whicha x a0 does not have a nonnegative integer solution is close to a known upper bound in the instances we consider we takea0 to be the frobenius number furthermore we show that the decomposable structure ofa1 a nmakes the solution of a lattice reformulation of our problem almost trivial since the number of lattice hyperplanes that intersect the polytope resulting from the reformulation in the direction of the last coordinate is going to be very small for branch and bound such instances are difficult to solve since they are infeasible and have large values ofa0 a i 1 i n we illustrate our results by some computational examples

on the equivalence of some approaches to the owa operator and rim quantifier determination the ordered weighted averaging owa operator is a widely used aggregation method and its determination is usually a prerequisite step in many related applications the regular increasing monotone rim quantifier can be seen as the continuous case of the owa operator with the quantifier aggregation method some approaches with optimization criteria for the determination of owa operator and rim quantifier were proposed although these problems look different at the first sight a deeper investigation can reveal the equivalence of solutions between them inspired by the solution equivalence of minimum variance problems and minimax disparity problem for owa operator we propose the minimax disparity rim quantifier problem and two minimax ratio problems for owa operator and rim quantifier respectively we investigate the equivalence of solutions for the maximum entropy and minimax ratio problems and solutions for the minimum variance and minimax disparity problems of owa operator and rim quantifier respectively by a theoretical point of view

the relationship between the maximum entropy and minimax ratio rim quantifier problems liu and lou fuzzy sets and systems 159 2007 1673 1688 investigated the equivalence of solutions to the maximum entropy and minimax ratio rim quantifier problems the paper improves liu and lou s theorems from a mathematical perspective because their theorems are not suitable for absolutely continuous generating functions the paper provides a correct proof of the minimax ratio rim quantifier problem for the case in which generating functions are absolutely continuous and a generalized solution to the maximum entropy rim quantifier problem for the case in which generating functions are lebesgue integrable based on the results the paper provides a correct relationship between the maximum entropy and minimax ratio rim quantifier problems

generalized ordered weighted utility averaging hyperbolic absolute risk aversion operators and their applications to group decision making abstract this paper develops a new class of aggregation operator based on utility function which introduces the risk attitude of decision makers dms in the aggregation process first under the general framework of utility function we provide a new operator called the generalized ordered weighted utility averaging gowua operator and study its properties which are suitable for any utility function then under the hyperbolic absolute risk aversion hara utility function we propose another new operator named as the generalized ordered weighted utility averaging hyperbolic absolute risk aversion gowua hara operator and further investigate its families including a wide range of aggregation operators to determine the gowua hara operator weights we put forward an orness measure of the gowua hara operator and analyze its properties considering that different dms may have different opinions toward decision making and their opinions can be characterized by different orness measures we construct a new optimization model to determine the optimal weights which can aggregate all the individual sets of weights into an overall set of weights furthermore based on the gowua hara operator a method for the multiple attribute group decision making magdm is developed finally an example is given to illustrate the application of the gowua hara operator to the magdm

an efficient low complexity detector for spatially multiplexed mc cdm we propose a novel suboptimum detection method for spatially multiplexed multicarrier code division multiplexing sm mc cdm communications compared to the spatially multiplexed ofdm sm ofdm the frequency domain spreading in sm mc cdm systems results in an additional diversity gain to take advantage of diversity and multiplexing while mitigating interference we design a low complexity efficient detector called unified successive interference cancellation sic detector for sm mc cdm communications further performance improvement is achieved by adopting in conjunction with the unified sic the iterative subcarrier reconstruction detection algorithm originally proposed for single antenna systems the results demonstrate significant performance improvement over other existing methods of comparable complexity a close approximation for the probability density function pdf of the proposed detector s output signal to interference plus noise ratio sinr is found and used to obtain error bounds for the bit error rate ber performance of the coded sm mc cdm transmission is also discussed in the paper

hidden number problem with hidden multipliers timed release crypto and noisy exponentiation we consider a generalisation of the hidden number problem recently introduced by boneh and venkatesan the initial problem can be stated as follows recover a number a fp such that for many known random t fp approximations to the values of at p are known here we study a version of the problem where the multipliers t are not known but rather certain approximations to them are given we present a probabilistic polynomial time solution when the error is small enough and we show that the problem cannot be solved if the error is sufficiently large we apply the result to the bit security of timed release crypto introduced by rivest shamir and wagner to noisy exponentiation black boxes and to the bit security of the inverse exponentiation we also show that it implies a certain bit security result for weil pairing on elliptic curves