generalized simulated annealing we discuss and illustrate a new stochastic algorithm generalized simulated annealing for computationally finding the global minimum of a given not necessarily convex energy cost function defined in a continuous d dimensional space this algorithm recovers as particular cases the so called classical boltzmann machine and fast cauchy machine simulated annealings and turns out to be quicker than both

a review of some methods for ranking fuzzy subsets this paper deals with the problem of ranking n fuzzy subsets of the unit interval a number of methods suggested in the literature is reviewed and tested on a group of selected examples where the fuzzy sets can be nonnormal and or nonconvex the ranking is obtained from i the index of strict preference defined by watson ii three indexes proposed by yager iii the algorithm used by chang iv three versions of the a preference index suggested by adamo v the index defined by baas and kwakernaak vi three modified versions used by baldwin and guild vii the method proposed by kerre viii three forms of the index suggested by jain ix the four grades of dominance studied by dubois and prade in simple cases the results are good for all the methods with some exceptions in questionable cases where the decision must be probably modelled in accordance with the context in which it is imbedded the best indexes seem to be the dominances suggested by dubois and prade these indexes do not force any particular choice but clearly describe the situation hence allowing the decision maker himself to make his best choice

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

a fuzzy set preference model for consumer choice abstract a fuzzy set model for predicting consumer choice is developed by combining the vector conjoint model with fuzzy measurement in a new model that requires only ordinal data fuzzy set measurement of consumer preferences is examined by testing alternative set representations and an interactive set definition method a comparison test of predictive validity using identical data from 139 subjects showed large improvements in rank order prediction validity compared to a non fuzzy approach prediction improvements of 83 are attributable to the use of fuzzy set definitions for subject ratings with the first two of six ordered ranking predicted on average

a method for ranking fuzzy numbers and its application to decision making since fuzzy numbers represent uncertain numeric values it is difficult to rank them according to their magnitude in the paper a method for ranking fuzzy numbers is proposed the method considers the overall possibility distributions of fuzzy numbers in their evaluations for ranking and provides users with a method of changing viewpoints for evaluations users represent their viewpoints with fuzzy sets the method evaluates fuzzy numbers with a satisfaction function and the viewpoint given by users and then ranks the numbers according to their evaluation values the satisfaction function is a measure of comparisons between fuzzy numbers in order to illustrate the ranking method two numeric examples are shown and for the comparative study our method is compared with four existing ranking methods through eight examples as an example of potential applications the proposed method is applied to a decision making problem a two person game with fuzzy profit and loss the ranking method is used to analyze player choices

ranking fuzzy numbers with an area method using radius of gyration ranking fuzzy numbers plays an very important role in linguistic decision making and some other fuzzy application systems many methods have been proposed to deal with ranking fuzzy numbers chu pointed out some shortcomings of the existing distance method and proposed to rank the fuzzy numbers with the area between the centroid point and original point however drawbacks are also found in the area method for example it cannot rank fuzzy numbers when some fuzzy numbers have the same centroid point in this paper we propose a modified area method to rank fuzzy numbers the modified method can effectively rank various fuzzy numbers and their images we also used some comparative examples to illustrate the advantage of the proposed method

pedestrian movement analysis in transfer station corridor velocity based and acceleration based abstract in this paper pedestrians are classified into aggressive and conservative ones by their temper aggressive pedestrians walking through crowd in transfer station corridor is analyzed treating pedestrians as particles this paper uses the modified social force model msfm as the building block where forces involve self driving force repulsive force and friction force the proposed model in this paper is a discrete model combining the msfm and cellular automata ca model where the updating rules of the ca are redefined with msfm due to the continuity of values generated by the msfm we use the fuzzy logic to discretize the continuous values into cells pedestrians can move in one step with the observation that stimulus around pedestrians influences their acceleration directly an acceleration based movement model is presented compared to the generally reviewed velocity based movement model in the acceleration based model a discretized version of kinematic equation is presented based on the acceleration discretized with fuzzy logic in real life some pedestrians would rather keep their desired speed and this is also mimicked in this paper which is called inertia compared to the simple triangular membership function a trapezoidal membership function and a piecewise linear membership function are used to capture pedestrians inertia with the trapezoidal and the piecewise linear membership function many overlapping scenarios should be carefully handled and dubois and prade s four index method is used to completely describe the relative relationship of fuzzy quantities finally a simulation is constructed to demonstrate the effect of our model

generalized simulated annealing for function optimization a generalized simulated annealing method has been developed and applied to the optimization of functions possibly constrained having many local extrema the method is illustrated in some difftcult pedagogical examples and used to solve a problem analyzed by bates technometrics 25 pp 373 376 1983 for which we identify an improved optimum the sensitivity of the solution to changes in the constraints and in other specifications of the problem is analyzed and discussed

homological mirror symmetry for singularities of type d we prove homological mirror symmetry for lefschetz fibrations obtained as sebastiani thom sums of polynomials of types a or d the proof is based on the behavior of the fukaya category under sebastiani thom summation of a polynomial of type d

optimization of non linear gravity models through generalized simulated annealing abstract in this paper we apply the generalized simulated annealing gsa approach to the inversion of gravity data for 2 d and 3 d density distributions we consider a modeling process where the input is the vector of model parameters m that can be density contrast mass or some coordinates and the output is described by the transformation h m d where d is the vector of data parameters we generally have access in practical problems if the vector d describes the observed actual output of the system the problem is to choose or estimate the parameters m est in order to minimize in some sense in our case in the least squares sense the difference between the observed vector d and the prescribed output of the system h m est the tests with synthetic data show the promising application of gsa in gravity inversion the results obtained suggest us that the gsa approach enables to find quickest optimization machines than the two conventional approaches boltzmann and cauchy machines

a hybrid approach to combine fuzziness and randomness in travel choice prediction abstract several approaches have been developed in order to deal with uncertainty in the prediction of travellers choices uncertainty almost always affects travel alternatives in several different choice contexts however the way in which this uncertainty affects choice options may consistently vary two main types of uncertainty can be identified randomness and fuzziness this paper discusses the use of a hybrid approach for choice modelling of travellers behaviour in choice contexts that involve conditions of high variability and uncertainty the aim of the work is to implement a hybrid methodology based on the use of a two term hybrid utility which allows taking into account at the same time the effects of both random and fuzzy uncertainty on travellers choice behaviour an application of the proposed methodology to a transit choice context is then presented

a multiple criteria linguistic decision model mcldm for human decision making abstract this paper presents a human nature like decision model which makes the decision making process easier for human beings the model which is called the multiple criteria linguistic decision model mcldm can be used to evaluate a set of alternatives over various criteria by using linguistic variables and then produces a linguistic decision output for selecting the best alternative the mcldm uses fuzzy set theory fst to deal with the imprecision measurement of decision makers dms subjective opinions which usually exist in the decision making process the decision model is originally designed for the screening of research projects however it can also be applied to problems such as program evaluation project performance evaluation and many other management decisions

fuzzy programming for multiobjective job shop scheduling with fuzzy processing time and fuzzy duedate through genetic algorithms abstract in this paper by considering the imprecise or fuzzy nature of the data in real world problems job shop scheduling with fuzzy processing time and fuzzy duedate is introduced on the basis of the agreement index of fuzzy duedate and fuzzy completion time multiobjective fuzzy job shop scheduling problems are formulated as three objective ones which not only maximize the minimum agreement index but also maximize the average agreement index and minimize the maximum fuzzy completion time having elicited the linear membership functions for the fuzzy goals of the decision maker we adopt the fuzzy decision of bellman and zadeh by incorporating the concept of similarity among individuals into the genetic algorithms using the gannt chart a genetic algorithm which is suitable for solving the formulated problems are proposed as illustrative numerical examples both 6 6 and 10 10 three objective job shop scheduling problems with fuzzy duedate and fuzzy processing time are considered and the feasibility and effectiveness of the proposed method are demonstrated by comparing with the simulated annealing method

computational applications of nonextensive statistical mechanics computational applications of the nonextensive entropy s q and nonextensive statistical mechanics a current generalization of the boltzmann gibbs bg theory are briefly reviewed the corresponding bibliography is provided as well

gravitational attraction of a rectangular prism with depth dependent density the gravity effect produced by two and three dimensional bodies with nonuniform density contrast has been treated by several authors one of the first attempts in this direction made by cordell 1973 who developed a method to compute the gravity effect due to a two dimensional prism whose density decreases exponentially with depth a different approach was proposed by murthy and rao 1979 they extended the line integral method to obtain the gravity effect for bodies of arbitrary cross sections with density contrast varying linearly with depth chai and hinze 1988 have derived a wavenumber domain approach to compute the gravity effect due to a vertical prism whose density contrast varies exponentially with depth recently rao 1990 has developed a closed expression of the gravity field produced by an asymmetrical trapezoidal body whose density varies with depth following a quadratic polynomial

on the classification of quasihomogeneous functions we give a criterion for the existence of a non degenerate quasihomogeneous polynomial in a configuration i e in the space of polynomials with a fixed set of weights and clarify the relation of this criterion to the necessary condition derived from the formula for the poincare polynomial we further prove finiteness of the number of configurations for a given value of the singularity index for the value 3 of this index which is of particular interest in string theory a constructive version of this proof implies an algorithm for the calculation of all non degenerate configurations

measurement of membership functions and their acquisition abstract three basic views of the representation of membership functions are reviewed together with fundamental measurement of linguistic terms of linguistic variables the conclusion is that such measurements are either on an ordinal or an interval scale based on whether the appropriate axioms are validated by the empirical data with an allowance for stochastic variation the conjoint measurement is introduced for the case of multi dimensional linguistic variables whose linguistic terms are compositions of two or finitely many more component linguistic terms of distinct independent linguistic variables it is shown that any composition of distinct independent component linguistic terms of component linguistic variables by any t norm or s norm or any finite convext linear combination preserves the monotonic weak order property of the components in the composite once the scale properties of the measurement values of particular terms are validated composition procedures may be applied to the experimental data to obtain compound membership functions of fuzzy sets induced by meaningful representations of compositions of linguistic terms of linguistic variables finally four methods of membership acquisition and construction are reviewed from the perspective of fundamental measurement

triangulated categories of matrix factorizations for regular systems of weights with e 1 abstract we construct a full strongly exceptional collection in the triangulated category of graded matrix factorizations of a polynomial associated to a nondegenerate regular system of weights whose smallest exponents are equal to 1 in the associated grothendieck group the strongly exceptional collection defines a root basis of a generalized root system of sign l 0 2 and a coxeter element of finite order whose primitive eigenvector is a regular element in the expanded symmetric domain of type iv with respect to the weyl group

gravitational and magnetic anomaly inversion using a tree based geometry representation gravitational and magnetic anomaly inversion of homogeneous 2d and 3d structures is treated using a geometric parameterization that can represent multiple arbitrary polygons or polyhedra and a local optimization scheme based on a hill climbing method this geometry representation uses a tree data structure which defines a set of boolean operations performed on convex polygons a variable length list of points whose convex hull defines a convex polygon operand resides in each leaf node of the tree the overall optimization algorithm proceeds in two steps step one optimizes geometric transformations performed on different convex polygons this step provides approximate size and location data the second step optimizes the points located on all convex hulls simultaneously giving a more accurate representation of the geometry though not an inherent restriction only the geometry is optimized not including material values such as density or susceptibility results based on synthetic and measured data show that the method accurately reconstructs various structures from gravity and magnetic anomaly data in addition to purely homogeneous structures a parabolic density distribution is inverted for 2d inversion

application of weighting functions to the ranking of fuzzy numbers this paper proposes a new ranking method for fuzzy numbers which uses a defuzzification of fuzzy numbers and a weighting function following saeidifar and pasha 2008 first we define a weighted distance measure on fuzzy numbers and then by minimizing this distance the weighted interval and point approximations of fuzzy numbers are obtained these indices are applied to rank the fuzzy numbers this method is new and interesting for ranking fuzzy numbers and it can be applied for solving and optimizing engineering and economics problems in a fuzzy environment

the preference order of fuzzy numbers abstract many fuzzy number ranking approaches are developed in the literature for multiattribute decision making problems almost all of the existing approaches focus on quantity measurement of fuzzy numbers for ranking purpose in this paper we consider the ranking process to determine a decision maker s preference order of fuzzy numbers a new ranking index is proposed to not only take quantity measurement but incorporate quality factor into consideration for the need of general decision making problems for measuring quantity several cuts of fuzzy numbers are used a signal noise ratio is defined to evaluate quality of a fuzzy number this ratio considers the middle point and spread of each cut of fuzzy numbers as the signal and noise respectively a fuzzy number with the stronger signal and the weaker noise is considered better moreover the associated levels are treated as the degree of belief about the cut and used as weights in the index for strengthening the influence of cut with higher levels the membership functions of fuzzy numbers are not necessarily to be known beforehand while applying this index only a few left and right boundary values of cuts of fuzzy numbers are required we have proved the feature of the proposed index in a particular case several examples are also used to illustrate the feature and applicability in ranking fuzzy numbers

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

a procedure for ordering fuzzy subsets of the unit interval abstract we introduce a function to help in the ordering of fuzzy subsets of the unit interval this function is the integral of the mean of the level sets associated with the fuzzy subsets various properties of this function are studied

a new approach for ranking fuzzy numbers based on fuzzy simulation analysis method a new approach for ranking fuzzy numbers based on a fuzzy simulation analysis fsa method is proposed a combination method including computer and math application is developed first the method is intuitive and can be used to order fuzzy numbers easily the approach is illustrated by numerical examples showing that it overcomes the shortcoming existing fuzzy ranking approaches especially when it is difficult to use other methods to solve ranking fuzzy problems

extended canonical algebras and fuchsian singularities the authors introduce a new class of finite dimensional algebras called extended canonical and determine the shape of their derived categories extended canonical algebras arise from a canonical algebra by onepoint extension or coextension by an indecomposable projective module our main results concern the case of negative euler characteristic of the corresponding weighted projective line mathbb x more specifically we establish for a base field of arbitrary characteristic a link to the fuchsian singularity r of mathbb x which for the base field of complex numbers is isomorphic to an algebra of automorphic forms by means of a recent result of orlov we show that the triangulated category of the graded singularities of r in the sense of buchweitz and orlov admits a tilting object whose endomorphism ring is the corresponding extended canonical algebra of particular interest are those cases where the attached coxeter transformation has spectral radius one a k theoretic analysis then shows that this happens exactly for 38 cases including arnold s 14 exceptional unimodal singularities the paper is related to recent independent work by kajiura saito and takahashi

traveling salesman problem and tsallis statistics a generalization of the stochastic method of simulated annealing algorithm based on tsallis statistics is proposed this algorithm is considerably faster than the traditional ones in solving the traveling salesman problem acceptable solutions are found in fewer steps and higher temperatures than both the classical and the fast simulated annealings recent developments in solving np complete problems can be incorporated and improve the performance even more

the e equilibrium in transportation networks abstract the principle of traffic equilibrium wardrop 1952 demands that the trip makers have enough knowledge of transportation networks which needs to be attained by accumulating experiences for a long time because of the complexity of traffic situation in the networks the route choice decisions for trip makers are however not always optimal objectively as a consequence it is impossible to strictly attain wardrop equilibrium in this paper a new concept of equilibrium equilibrium is proposed under the realistic assumption i e the fuzzy road information and random route choices equilibrium in the network is discussed by adopting fuzzy set theory mixed stochastic games and brouwer fixed point theorem in topological space the conclusion is that there is equilibrium in the real transportation network and this equilibrium has some deviations from the strict wardrop equilibrium the notion of equilibrium extends the traditional notion of network equilibrium it shows that traffic flow in the network converges to a region rather than to the points

a two stage logarithmic goal programming method for generating weights from interval comparison matrices a two stage logarithmic goal programming tlgp method is proposed to generate weights from interval comparison matrices which can be either consistent or inconsistent the first stage is devised to minimize the inconsistency of interval comparison matrices and the second stage is developed to generate priorities under the condition of minimal inconsistency the weights are assumed to be multiplicative rather than additive in the case of hierarchical structures a nonlinear programming method is used to aggregate local interval weights into global interval weights a simple yet practical preference ranking method is investigated to compare the interval weights of criteria or rank alternatives in a multiplicative aggregation process the proposed tlgp is also applicable to fuzzy comparison matrices when they are transformed into interval comparison matrices using a level sets and the extension principle six numerical examples including a group decision analysis problem with a group of comparison matrices a hierarchical decision problem and a fuzzy decision problem using fuzzy comparison matrix are examined to show the applications of the proposed methods comparisons with other existing procedures are made whenever possible

nonlinear inversion of resistivity sounding data the resistivity interpretation problem involves the estimation of resistivity as a function of depth from the apparent resistivity values measured in the field as a function of electrode separation this is commonly done either by curve matching using master curves or by more formal linearized inversion methods the problems with linearized inversion schemes are fairly well known they require that the starting model be close to the true solution in this paper we report the results from the application of a nonlinear global optimization method known as simulated annealing sa in the direct interpretation of resistivity sounding data this method does not require a good starting model but is computationally more expensive we used the heat bath algorithm of simulated annealing in which the mean square error difference between observed and synthetic data is used as the energy function that we attempt to minimize samples are drawn from the gibbs probability distribution while the control parameter the

linear programming problems and ranking of fuzzy numbers abstract in this paper linear programming problems with fuzzy constraints and fuzzy coefficients in both matrix and right hand side of the constraint set are considered because of fuzzy coefficients in both members of each constraint ranking methods for fuzzy numbers must be considered the diversity of such methods provides a lot of different models of conventional linear programming problems from which fuzzy solutions to the former problem can be obtained

measure for the resolving power and bias effect in the nonlinear inverse analysis of geophysical potential fields several measures are proposed for the power of resolution and the bias effect of nonlinearity in the inverse analysis of geophysical potential fields they are the power of complete resolution for the entire system of both data and parameters the power of partial resolution for individual data prediction and parameter estimation and the bias for the effect of linearization of a nonlinear function relations between the measures for the resolution power and bias are derived the tradeoff relations between the resolving power and estimation variance are also demonstrated all these measures are tested on a synthetic gravity data set a two dimensional 2 d forward gravity model is employed to demonstrate the use of the measures proposed in this study the selection of the reference depth z0 and the number of nonzero eigenvalues q is highlighted based on the 2 d prism forward model the best z0 is that value that produces the least curvature in the plot of singular values versus q the choice of q i

traffic assignment model with fuzzy level of travel demand an efficient algorithm based on quasi logit formulas abstract the place of fuzzy concepts in traffic assignment ta models has been studied in recent literature keeping fuzzy level of travel demand in mind we propose a new ta model in which the travel costs of links are depended on their congestion from the results of such fuzzy ta model network planners are able to estimate the number of travelers on network links by using zero one variables the proposed model is transformed into a crisp mixed integer problem with respect to path flow variables in order to produce the logit flows from this problem damberg et al algorithm is modified then the level of certainty is maximized and perceived travel delays are minimized for a fixed certainty degree the obtained solution which is named the fuzzy equilibrium flow satisfies a quasi logit formula similar to ordinary expression of the logit route choice model eventually we examine the quality of different path enumeration techniques in the proposed model

fuzzy route choice model for traffic assignment abstract in order to represent traffic assignment on a road network we propose a new route choice model taking account of the imprecisions and the uncertainties lying in the dynamic choice process this model makes possible a more accurate description of the process than those deterministic or stochastic used in the literature we assume that drivers choose a path all the more than it is foreseen to have a lesser cost the predicted cost for each path is modelled by a fuzzy subset which can represent imprecision on network knowledge e g length of links as well as uncertainty on traffic conditions e g congested or uncongested network incident the costs of all possible paths are compared and result in an attractiveness degree for each path various comparison indices can be used to represent the different possible natures of drivers when making their decisions pessimistic optimistic risk taking risk averting the fuzzy choice model was compared with the logit model a widely used stochastic discrete choice model and has been proved to be able to find the same results the effect of advanced travellers information systems atis on drivers is modeled as a modification of the imprecision or the uncertainty of the predicted cost of a route

handling uncertainty in route choice models from probabilistic to possibilistic approaches abstract in order to design effective advanced traffic information systems atis suitable mathematical models have to be defined to simulate the effects of information on users route choice behaviour and then to incorporate it into traffic assignment models to estimate how traffic demand loads the roads network to face this problem it is necessary to deal with uncertainty that plays a crucial role in the users decision making processes to this purpose this paper first analyses how uncertainty affects users route choice process and how traffic assignment models may take it into account in literature route choice behaviour modelling is widely solved within the random utility theory framework but we show in this paper that such an approach only considers one type of uncertainty more precisely the consideration of randomness of traffic by drivers is for example hardly ever represented in classical models in spite of its importance in the management of information by drivers starting from the presented analysis a new route choice model is also proposed to represent explicitly the uncertainty lying in users route choice behaviour it is based on recent developments in possibility theory which is an alternate way to probability theory in order to represent or measure uncertainty

comparison of fuzzy numbers using possibility programming comments and new concepts abstract comparing fuzzy numbers using the possibility programming approach was presented by negi and lee 1 in this paper we are going to state some comments concerning their approach the case of comparing different fuzzy numbers is considered also the formulation of the crisp problem in the case of fuzzy linear programming and fuzzy multiobjective linear programming is discussed and a new modified model in each case is stated our proposed approach is illustrated by numerical examples

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

the fuzzy shortest path problem and its most vital arcs abstract the shortest path problem is to find the shortest distance between two specified nodes in a network an arc is called a single most vital arc in the network if its removal from the network results in the greatest increase in the shortest distance the availability of arcs plays a key role in network problems the most vital arcs problems provide a means by which the importance of arc s availability can be measured in the traditional shortest path problem the arc lengths are assumed to be crisp numbers in this paper we consider the case that the arc lengths are fuzzy numbers in particular we derive the membership function of the shortest distance by using a fuzzy linear programming approach based on this result we then propose an algorithm for finding the single most vital arc in a network

maximally graded matrix factorizations for an invertible polynomial of chain type abstract in 1977 orlik randell construct a nice integral basis of the middle homology group of the milnor fiber associated to an invertible polynomial of chain type and they conjectured that it is represented by a distinguished basis of vanishing cycles the purpose of this paper is to prove the algebraic counterpart of the orlik randell conjecture under the homological mirror symmetry we may expect that the triangulated category of maximally graded matrix factorizations for the berglund hubsch transposed polynomial admits a full exceptional collection with a nice numerical property indeed we show that the category admits a lefschetz decomposition with respect to a polarization in the sense of kuznetsov smirnov whose euler matrix are calculated in terms of the zeta function of the inverse of the polarization as a corollary it turns out that the homological mirror symmetry holds at the level of the grothendieck group in the following sense the grothendieck group of the category with the euler form is isomorphic to the middle homology group with the quasi seifert form with a suitable sign

generalized statistical mechanics connection with thermodynamics the authors show the manner through which the recent generalization by tsallis 1988 of the boltzmann gibbs statistics becomes consistent with a generalized thermodynamics preserving the legendre transformation framework of standard thermodynamics in addition to that they generalize the shannon additivity

an extension to fuzzy mcdm an extension to the fuzzy multiple criteria decision making mcdm model is suggested in this work where the ratings of alternatives versus criteria and the importance weights of all criteria are assessed in linguistic values represented by fuzzy numbers moreover values of alternatives under objective criteria are normalized by a suggested approach meanwhile the membership function of the final fuzzy evaluation value of each alternative can be developed in addition a riemann integral based mean of removals is suggested to rank all the final fuzzy evaluation values for final decision making so that the ranking procedure can be clearly formulated finally a numerical example demonstrates the feasibility of the proposed model

linear inversion of gravity data for 3 d density distributions we have developed an improved levenburg marquart technique to rapidly invert bouguer gravity data for a 3 d density distribution as a source of the observed field this technique is designed to replace tedious forward modeling with an automatic solver that determines density models constrained by geologic information supplied by the user where such information is not available objective models are generated the technique estimates the density distribution within the source volume using a least squares inverse solution that is obtained iteratively by singular value decomposition using orthogonal decomposition of matrices with sequential householder transformations the source volume is subdivided into a series of right rectangular prisms of specified size but of unknown density this discretization allows the construction of a system of linear equations relating the observed gravity field to the unknown density distribution convergence of the solution to the system is tightly controlled by a damping pa

matrix factorizations and representations of quivers ii type ade case abstract we study a triangulated category of graded matrix factorizations for a polynomial of type ade we show that it is equivalent to the derived category of finitely generated modules over the path algebra of the corresponding dynkin quiver also we discuss a special stability condition for the triangulated category in the sense of t bridgeland which is naturally defined by the grading