a fuzzy compromise approach to water resource systems planning under uncertainty abstract a fuzzy compromise approach to decision analysis is described within the context of water resource systems planning under uncertainty the approach allows various sources of uncertainty and is intended to provide a flexible form of group decision support the example compares the electre method with the fuzzy compromise approach the comparison is intended to demonstrate the benefits of adopting a multicriteria decision analysis technique which presents subjectivity within its proper context while maintaining an intuitive and transparent technique for ranking alternatives the fuzzy compromise approach allows a family of possible conditions to be reviewed and supports group decisions through fuzzy sets designed to reflect collective opinions and conflicting judgements ranking of alternatives is accomplished with fuzzy ranking measures designed to illustrate the effect of risk tolerance differences among decision makers two distinct ranking measures are used a centroid measure and a fuzzy comparison measure based on a fuzzy goal

on consistency and ranking of alternatives in fuzzy ahp abstract in fuzzy ahp where pairwise comparisons are described by membership values the treatment of consistency has largely been sketchy this paper proposes a fuzzy consistency definition with consideration of a tolerance deviation essentially the fuzzy ratios of relative importance allowing certain tolerance deviation are formulated as constraints on the membership values of the local priorities the fuzzy local and global weights are determined via the extension principle the alternatives are ranked on the basis of the global weights by application of a maximum minimum set ranking method our analysis uses only the data which are considered as consistent the proposed approach is computationally efficient as it consists of solving only linear programs an example is included for illustrative purpose

an iterative approach for estimation of student performances based on linguistic evaluations in group decision analysis numerous approaches have been suggested in an attempt to solve the problem of aggregation of individual fuzzy opinions to form a group consensus as the basis of a group decision in this study an optimization model which reflects different points of view of many decision makers by weighting fuzzy opinions is proposed for the evaluation of student performances in student centered learning an iterative algorithm is provided for the solution of this model and the consequent theorem is proved experimental results show that the proposed iterative algorithm yields more efficient results than do the classical optimization methods moreover the wabl weighted averaging based on the levels method produces more accurate results than do the other frequently used defuzzification methods such as coa center of area and mom mean of maxima

a fuzzy simple additive weighting system under group decision making for facility location selection with objective subjective attributes this work presents a new fuzzy multiple attributes decision making fmadm approach i e fuzzy simple additive weighting system fsaws for solving facility location selection problems by using objective subjective attributes under group decision making gdm conditions the proposed system integrates fuzzy set theory fst the factor rating system frs and simple additive weighting saw to evaluate facility locations alternatives the fsaws is applied to deal with both qualitative and quantitative dimensions the fsaws process considers the importance of each decision maker and the total scores for alternative locations are then derived by homo heterogeneous group of decision makers finally a numerical example illustrates the procedure of the proposed fsaws

fuzzy group decision making for evaluating the rate if aggregative risk in software development in this paper we present a new algorithm to evaluate the rate of aggregative risk in software development using fuzzy set theory under the fuzzy group decision making environment the proposed algorithm has the following advantages 1 it does not need to form the fuzzy assessment matrices for attributes 2 it does not need to perform the complicated defuzzification operations of fuzzy numbers using the centroid method the proposed algorithm is more efficient and faster in evaluating the rate of aggregative risk in software development under the fuzzy group decision making environment

structured pseudospectra for nonlinear eigenvalue problems in this paper we introduce structured pseudospectra for nonlinear eigenvalue problems and derive computable formulae the results are applied to the sensitivity analysis of the eigenvalues of a second order system arising from structural dynamics and of a time delay system arising from laser physics in the former case a comparison is made with the results obtained in the framework of random eigenvalue problems

a fuzzy approach to select the location of the distribution center abstract the location selection of distribution center dc is one of the most important decision issues for logistics managers owing to vague concept frequently represented in decision data a new multiple criteria decision making method is proposed to solve the distribution center location selection problem under fuzzy environment in the proposed method the ratings of each alternative and the weight of each criterion are described by linguistic variables which can be expressed in triangular fuzzy numbers the final evaluation value of each dc location is also expressed in a triangular fuzzy number by calculating the difference of final evaluation value between each pair of dc locations a fuzzy preference relation matrix is constructed to represent the intensity of the preferences of one plant location over another and then a stepwise ranking procedure is proposed to determine the ranking order of all candidate locations finally a numerical example is solved to illustrate the procedure of the proposed method at the end of this paper

applications of the extent analysis method on fuzzy ahp in this paper a new approach for handling fuzzy ahp is introduced with the use of triangular fuzzy numbers for pairwise comprison scale of fuzzy ahp and the use of the extent analysis method for the synthetic extent value si of the pairwise comparison by applying the principle of the comparison of fuzzy numbers that is v m1 m2 1 iff m1 m2 v m2 m1 hgt m1 m2 m1 d the vectors of weight with respect to each element under a certaine criterion are represented by d ai min v si sk k 1 2 n k i this decision process is demonstrated by an example

fuzzy flowsort an integration of the flowsort method and fuzzy set theory for decision making on the basis of inaccurate quantitative data nowadays most real life decision problems can be modeled as sorting problems although it is difficult to quantitatively express the evaluation criteria precisely or precise values are inadequate to model the criteria for these situations multicriteria methods can be extended by using fuzzy theory thereby providing mathematical methods able to deal with decision processes in a fuzzy environment in this context we propose a sorting method called fuzzy flowsort f flowsort based on fuzzy set theory and flowsort which is a promethee based sorting method to demonstrate the usefulness and applicability of this new method an illustrative numerical example is presented the result confirms the potential and the applicability of associating fuzzy logic with the flowsort method for processing imprecise data comparisons are made between the results provided by fuzzy flowsort and flowsort and also between fuzzy flowsort and another algorithm based on flowsort that deals with the imprecision of data when they are defined by intervals in addition the association between the results obtained with the f flowsort and flowsort methods and promethee and f promethee methods is investigated

approaches to collective decision making with fuzzy preference relations abstract recent experimental studies show that the predictive accuracy of many of the solution concepts derived from the collective decision making theory leaves much to be desired in a previous paper the author attempted to explain some of the inaccuracies in terms of the fuzzy indifference regions of the individuals participating in the voting game this paper gives straightforward generalizations of the solutions concepts in terms of the fuzzy social or individual preference relations it turns out that some of these new solution concepts cotain their nonfuzzy counterparts as subsets others in turn are subsets of their nonfuzzy counterparts we also discuss a method of aggregating individual nonfuzzy preferences so as to get a fuzzy social preference relation and furthermore a nonfuzzy social choice set

on the extent analysis method for fuzzy ahp and its applications abstract in a paper by chang d y chang applications of the extent analysis method on fuzzy ahp european journal of operational research 95 1996 649 655 an extent analysis method on fuzzy ahp was proposed to obtain a crisp priority vector from a triangular fuzzy comparison matrix it is found that the extent analysis method cannot estimate the true weights from a fuzzy comparison matrix and has led to quite a number of misapplications in the literature in this paper we show by examples that the priority vectors determined by the extent analysis method do not represent the relative importance of decision criteria or alternatives and that the misapplication of the extent analysis method to fuzzy ahp problems may lead to a wrong decision to be made and some useful decision information such as decision criteria and fuzzy comparison matrices not to be considered we show these problems to avoid any possible misapplications in the future

two new approaches for assessing the weights of fuzzy opinions in group decision analysis the aggregation of fuzzy opinions is an important component of group decision analysis with fuzzy information this paper proposes two new approaches for the assessment of the weights to be associated with fuzzy opinions these approaches involve respectively the minimization of the sum of squared distances from one weighted fuzzy opinion to another which is called the least squares distance method lsdm and the minimization of the sum of squared differences between the defuzzified values of any two weighted fuzzy opinions which is called the defuzzification based least squares method dlsm the two approaches are developed and numerical examples are presented to illustrate their simplicity and effectiveness in aggregating fuzzy opinions

normal ordering in the theory of correlation functions of exactly solvable models we study models of quantum statistical mechanics which can be solved by the algebraic bethe ansatz the general method of calculating correlation functions is based on the method of determinant representations the auxiliary fock space and auxiliary bose fields are introduced in order to remove the two body scattering and represent correlation functions as a mean value of a determinant of a fredholm integral operator the representation has a simple form for large space and time separations in this paper we explain how to calculate the mean value in the auxiliary fock space of an asymptotic expression of the fredholm determinant it is necessary for the evaluation of the asymptotic form of the physical correlation functions

riemann hilbert approach to a generalised sine kernel and applications we investigate the asymptotic behavior of a generalized sine kernel acting on a finite size interval q q we determine its asymptotic resolvent as well as the first terms in the asymptotic expansion of its fredholm determinant further we apply our results to build the resolvent of truncated wiener hopf operators generated by holomorphic symbols finally the leading asymptotics of the fredholm determinant allows us to establish the asymptotic estimates of certain oscillatory multidimensional coupled integrals that appear in the study of correlation functions of quantum integrable models

structured pseudospectra in structural engineering this paper presents a new method for computing the pseudospectra of a matrix that respects a prescribed sparsity structure the pseudospectrum is defined as the set of points in the complex plane to which an eigenvalue of the matrix can be shifted by a perturbation of a certain size a canonical form for sparsity preserving perturbations is given and a computable formula for the corresponding structured pseudospectra is derived this formula relates the computation of structured pseudospectra to the computation of the structured singular value ssv of an associated matrix although the computation of the ssv in general is an np hard problem algorithms for its approximation are available and demonstrate good performance when applied to the computation of structured pseudospectra of medium sized or highly sparse matrices the method is applied to a wing vibration problem where it is compared with the matrix polynomial approach and to the stability analysis of truss structures new measures for the vulnerability of a truss structure are proposed which are related to the distance to singularity of the associated stiffness matrix copyright 2005 john wiley sons ltd

a fuzzy extension of saaty s priority theory we present a fuzzy method for choosing among a number of alternatives under conflicting decision criteria a fuzzy version of saaty s pairwise comparison method 1980 extended by de graan 1980 and lootsma 1981 each ratio expressing the relative significance of a pair of factors is displayed in a matrix from which suitable weights can be extracted since these ratios are essentially fuzzy they express the opinion of a decision maker on the importance of a pair of factors we have adapted the above mentioned method in such a way that decision makers are asked to express their opinions in fuzzy numbers with triangular membership functions we apply the method at two distinct levels first to find fuzzy weights for the decision criteria and second to find fuzzy weights for the alternatives under each of the decision criteria by a suitable combination of these results we obtain fuzzy scores for the alternatives as well as their sensitivities using these fuzzy scores the decision makers should be able to make a choice for one of the alternatives

completely integrable equation for the quantum correlation function of nonlinear schrodinger equation correlation functions of exactly solvable models can be described by differential equations 1 in this paper we show that for the non free fermionic case differential equations should be replaced by integro differential equations we derive an integro differential equation which describes a time and temperature dependent correlation function of the penetrable bose gas the integro differential equation turns out to be the continuum generalization of the classical nonlinear schrodinger equation

spectral value sets a graphical tool for robustness analysis in this note we present a method to determine and visualize the set of all complex numbers to which at least one eigenvalue of a matrix a can be shifted by real or complex perturbations of the form a a a d e where d and e are fixed matrices and the unknown disturbance matrix satisfies 0 both real and complex perturbations are studied the graphical method may be considered as an extension of the classical root locus method to multivariable systems and multiparameter perturbations the results are illustrated by various examples

localization theorems for nonlinear eigenvalue problems let t omega rightarrow mathbb c n times n be a matrix valued function that is analytic on some simply connected domain omega subset mathbb c a point lambda in omega is an eigenvalue if the matrix t lambda is singular in this article we describe new localization results for nonlinear eigenvalue problems that generalize gershgorin s theorem pseudospectral inclusion theorems and the bauer fike theorem we use our results to analyze three nonlinear eigenvalue problems an example from delay differential equations a problem due to hadeler and a quantum resonance computation

a new fuzzy weighted average fwa method based on left and right scores an application for determining a suitable location for a gas oil station the selection of a facility location from alternative locations is a multiple criteria decision making mcdm problem including both quantitative and qualitative criteria in many real life cases determining the exact values for mcdm problems and especially for facility location selection problems is difficult or impossible so the values of alternatives with respect to the criteria or and the values of criteria weights are considered as fuzzy values fuzzy numbers such that the conventional crisp approaches for solving facility location selection problems and other mcdm problems tend to be less effective for dealing with the imprecise or vagueness nature of the linguistic assessments in such conditions fuzzy mcdm methods are applied for facility location selection problem and other fuzzy mcdm problems in this paper we propose a new fuzzy weighted average fwa method based on left and right scores for fuzzy mcdm problems moreover we apply the proposed method to a real application as a result we found that the proposed method is practical for facility location selection problems besides it seems that the proposed fwa method is very accurate flexible simple and easy to use when compared to other versions of the fwa method

geometry and integrability of topological antitopological fusion integrability of equations of topological antitopological fusion being proposed by cecotti and vafa describing the ground state metric on a given 2d topological field theory tft model is proved for massive tft models these equations are reduced to a universal form being independent on the given tft model by gauge transformations for massive perturbations of topological conformal field theory models the separatrix solutions of the equations bounded at infinity are found by the isomonodromy deformations method also it is shown that the ground state metric together with some part of the underlined tft structure can be parametrized by pluriharmonic maps of the coupling space to the symmetric space of real positive definite quadratic forms

capacitated facility location network design problems abstract we introduce a combined facility location network design problem in which facilities have constraining capacities on the amount of demand they can serve this model has a number of applications in regional planning distribution telecommunications energy management and other areas our model includes the classical capacitated facility location problem cflp on a network as a special case we present a mixed integer programming formulation of the problem and several classes of valid inequalities are derived to strengthen its lp relaxation computational experience with problems with up to 40 nodes and 160 candidate links is reported and a sensitivity analysis provides insight into the behavior of the model in response to changes in key problem parameters

fuzzy multi attribute selection among transportation companies using axiomatic design and analytic hierarchy process the basic concept in axiomatic design ad is the existence of design axioms first of these axioms is the independence axiom and the second one is the information axiom information axiom proposes the selection of the best alternative that has minimum information analytic hierarchy process ahp is another multi attribute method which is a decision making method for selecting the best among a set of alternatives given some criteria the method has been extensively applied especially in large scale problems where many criteria must be considered and where the evaluation of alternatives is mostly subjective multi attribute transportation company selection is a very important activity for effective supply chain selection of the best company under determined criteria such as cost time damage loss flexibility and documentation ability using both multi attribute ad and ahp will be realized in this study the fuzzy multiattribute ad approach is also developed and it is compared by one of fuzzy ahp methods in the literature the selection process has been accomplished by aiding a software that includes crisp ad and fuzzy ad

a new fuzzy operator and its application to topology design of distributed local area networks topology design of distributed local area networks can be classified as a hard combinatorial optimization problem the problem has several conflicting objectives such as cost reliability network delay and number of hops between source and destination these objectives can conveniently be expressed in linguistic terms a key component of fuzzy logic this paper presents an approach based on fuzzy logic that combines the conflicting objectives into a single optimization function a new fuzzy operator namely the unified and or uao operator is also proposed and a decision making approach based on fuzzy rules and preference rules is introduced the uao operator is empirically compared with the well known ordered weighted averaging owa operator through application to an evolutionary algorithm results show that the uao operator exhibits comparatively better performance than the owa operator

group decision making using fuzzy sets theory for evaluating the rate of aggregative risk in software development abstract the purpose of this study is not only to build a group decision making structure model of risk in software development but also to propose two algorithms to tackle the rate of aggregative risk in a fuzzy environment by fuzzy sets theory during any phase of the life cycle while evaluating the rate of aggregative risk one may adjust or improve the weights or grades of the factors until she he can accept it moreover our result will be more objective and unbiased since it is generated by a group of evaluators

consistency analysis of triangular fuzzy reciprocal preference relations abstract in order to simulate the uncertainty associated with impression or vagueness a decision maker may give her his judgments by means of triangular fuzzy reciprocal preference relations in the process of decision making the study of their consistency becomes a very important aspect to avoid a misleading solution based on the reciprocity property this paper proposes a new definition of consistent triangular fuzzy reciprocal preference relations the new definition is different from that reduced by consistent fuzzy reciprocal preference relations proposed by buckley 1985 the properties of consistent triangular fuzzy reciprocal preference relations in the light of the new definition are studied in detail in addition the shortcomings of the proof procedure of the proposition given by wang and chen 2008 are pointed out and the proposition is reproved by using the new definition of consistent triangular fuzzy reciprocal preference relations finally using the n 1 restricted comparison ratios a method for obtaining consistent triangular fuzzy reciprocal preference relations is proposed and an algorithm is shown to make a consistent decision ranking numerical results are further calculated to illustrate the new definition and the obtained algorithm

acceptability measurement and priority weight elicitation of triangular fuzzy multiplicative preference relations based on geometric consistency and uncertainty indices this paper investigates consistency and uncertainty measurements as well as acceptability checking for triangular fuzzy multiplicative preference relations tfmprs a geometric consistency index is proposed to measure the consistency degree of a tfmpr and thresholds of acceptable consistency are discussed for tfmprs uncertainty indices are introduced to measure indeterminacy degrees of triangular fuzzy judgments and of tfmprs and a notion of acceptable tfmprs are put forward by considering both acceptable consistency and acceptable uncertainty in tfmprs we also explore the elicitation of triangular fuzzy weights from acceptable tfmprs and the aggregation of local triangular fuzzy weights for solving hierarchical multi criteria decision making problems a geometric mean based equation and a logarithmic least square model are developed to elicit normalized acceptable triangular fuzzy multiplicative weights from an acceptable tfmpr an equation and a linear program are established to transform triangular fuzzy multiplicative weights into triangular fuzzy additive weights a geometric weighting based equation and a pair of linear programs are devised to generate global priority fuzzy weights from local triangular fuzzy multiplicative weights three numerical examples including a hierarchical multi criteria decision making problem are used to illustrate how to apply the developed framework and comparative studies are provided to show its availability and advantages

similarity solutions of the deformed maxwell bloch system the authors have found similarity reductions for the deformed maxwell bloch system to the fifth and second painleve equations asymptotics of the solutions of these equations which are relevant to two level atomic systems with pumping have also been derived

some problems on the definition of fuzzy preference relations in this paper we deal with decision making problems over an unfuzzy set of alternatives on one hand we propose the problem of finding a max min transitive relation as near as possible to a given initial preference relation under the least squares criterion and such that it does not introduce deep qualitative changes on the other hand we define a linear extension of the initial preference relation between alternatives to a preference relation between lotteries

pseudospectra and delay differential equations in this paper we present a new method for computing the pseudospectra of delay differential equations ddes with fixed finite delay this provides information on the sensitivity of eigenvalues under arbitrary perturbations of a given size and hence insight into how stability may change under variation of parameters we also investigate how differently weighted perturbations applied to the individual matrices of the delayed eigenvalue problem affect the pseudospectra furthermore we compute pseudospectra of the infinitesimal generator of the dde from which a lower bound on the maximum transient growth can be inferred to illustrate our method we consider a dde modelling a semiconductor laser subject to external feedback

pseudospectra and stability radii for analytic matrix functions with application to time delay systems definitions for pseudospectra and stability radii of an analytic matrix function are given where the structure of the function is exploited various perturbation measures are considered and computationally tractable formulae are derived the results are applied to a class of retarded delay differential equations special properties of the pseudospectra of such equations are determined and illustrated 2006 elsevier inc all rights reserved

determinant representation for dynamical correlation functions of the quantum nonlinear schrodinger equation painleve analysis of correlation functions of the impenetrable bose gas by m jimbo t miwa y mori and m sato 1 was based on the determinant representation of these correlation functions obtained by a lenard 2 the impenetrable bose gas is the free fermionic case of the quantum nonlinear schrodinger equation in this paper we generalize the lenard determinant representation for langle psi 0 0 psi dagger x t rangle to the non free fermionic case we also include time and temeprature dependence in forthcoming publications we shall perform the jmms analysis of this correlationl function this will give us a completely integrable equation and asymptotic for the quantum correlation function of interacting fermions

quantum and classical integrability new approaches in statistical mechanics abstract the present status of the statistical mechanics sm quantum and classical of integrable models is reviewed by reporting new results for their partition functions z obtained for anyon type models in one space and one time 1 1 dimensions the methods of functional integration developed already are extended further bose fermi equivalence and anyon descriptions are natural parts of the quantum theory and the anyon phase is quantised the classical integrability is exploited throughout and both classical and quantum integrability theory are reviewed this way and related to underlying algebraic structures notably the hopf algebras quantum groups a new q boson lattice gas is solved in this connection further results to be realised within 10 years concerning integrability integrable systems coupled to large dimensional chaos provided by a heat bath and their application in physics e g to high t c superconductivity are suggested

applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy ahp the lack of consistency in decision making can lead to inconsistent conclusions in fuzzy analytic hierarchy process fuzzy ahp method it is difficult to ensure a consistent pairwise comparison furthermore establishing a pairwise comparison matrix requires nx n 1 2 judgments for a level with n criteria alternatives the number of comparisons increases as the number of criteria increases therefore the decision makers judgments will most likely be inconsistent to alleviate inconsistencies this study applies fuzzy linguistic preference relations fuzzy linprera to construct a pairwise comparison matrix with additive reciprocal property and consistency in this study the fuzzy ahp method is reviewed and then the fuzzy linprera method is proposed finally the presented method is applied to the example addressed by kahraman et al c kahraman d ruan i dogan fuzzy group decision making for facility location selection information sciences 157 2003 135 153 this study reveals that the proposed method yields consistent decision rankings from only n 1 pairwise comparisons which is the same result as in kahraman et al research the presented fuzzy linguistic preference relations method is an easy and practical way to provide a mechanism for improving consistency in fuzzy ahp method

universal results for correlations of characteristic polynomials riemann hilbert approach we prove that general correlation functions of both ratios and products of characteristic polynomials of hermitian random matrices are governed by integrable kernels of three different types a those constructed from orthogonal polynomials b those constructed from cauchy transforms of the same orthogonal polynomials and finally c those constructed from both orthogonal polynomials and their cauchy transforms these kernels are related with the riemann hilbert problem for orthogonal polynomials for the correlation functions we obtain exact expressions in the form of determinants of these kernels derived representations enable us to study asymptotics of correlation functions of characteristic polynomials via the deift zhou steepest descent stationary phase method for riemann hilbert problems and in particular to find negative moments of characteristic polynomials this reveals the universal parts of the correlation functions and moments of characteristic polynomials for an arbitrary invariant ensemble of 2 symmetry class

a statistical comparative study of different similarity measures of consensus in group decision making an essential aim in group decision making gdm problems is to achieve a high level of consensus among experts consensus is defined as general or widespread agreement and it is usually modelled mathematically via a similarity function measuring how close experts opinions or preferences are similarity functions are defined based on the use of a metric describing the distance between experts opinions or preferences in the literature different metrics or distance functions have been proposed to implement in consensus models but no study has been carried out to analyse the influence the use of different distance functions can have in the gdm process this paper presents a comparative study of the effect of the application of some different distance functions for measuring consensus in gdm by using the nonparametric wilcoxon matched pairs signed ranks test it is concluded that different distance functions can produce significantly different results moreover it is also shown that their application also has a significant effect on the speed of achieving consensus finally these results are analysed and used to derive decision support rules based on a convergent criterion that can be used to control the convergence speed of the consensus process using the compared distance functions

robust stability of linear systems described by higher order dynamic equations the stability radius of higher order differential and difference systems with respect to various classes of complex affine perturbations of the coefficient matrices is studied different perturbation norms are considered the aim is to derive robustness criteria that are expressed directly in terms of the original data previous results on robust stability of hurwitz and schur polynomials are extended to monic matrix polynomials for disturbances acting via a uniform input matrix computable formulas are obtained whereas for perturbations with multiple input matrices structured singular values are involved

dual field formulation of quantum integrable models equal time correlators are studied in completely integrable models the main example is the quantum non linear schrodinger equation introduction of an auxiliary fock space permits us to represent the generating functional of correlators in the form of a determinant of the integral operator

an efficient algorithm for facility location in the presence of forbidden regions abstract this paper investigates a constrained form of the classical weber problem specifically we consider the problem of locating a new facility in the presence of convex polygonal forbidden regions such that the sum of the weighted distances from the new facility to n existing facilities is minimized it is assumed that a forbidden region is an area in the plane where travel and facility location are not permitted and that distance is measured using the euclidean distance metric a solution procedure for this nonconvex programming problem is presented it is shown that by iteratively solving a series of unconstrained problems this procedure terminates at a local optimum to the original constrained problem numerical examples are presented

direct approach processes in group decision making using linguistic owa operators abstract in a linguistic framework several group decision making processes by direct approach are presented these processes are designed using the linguistic ordered weighted averaging lowa operator to do so first a study is made of the properties and the axiomatic of lowa operator showing the rationality of its aggregation way and secondly we present the use of lowa operator to solve group decision making problems from individuals linguistic preference relations

the riemann hilbert problem associated with the quantum nonlinear schrodinger equation we consider the dynamical correlation functions of the quantum nonlinear schrodinger equation in a previous paper we found that the dynamical correlation functions can be described by the vacuum expectation value of an operator valued fredholm determinant in this paper we show that a riemann hilbert problem can be associated with this fredholm determinant this riemann hilbert problem formulation permits us to write down completely integrable equations for the fredholm determinant and to perform an asymptotic analysis for the correlation function

fuzzy group decision making for facility location selection the selection of a facility location among alternative locations is a multicriteria decision making problem including both quantitative and qualitative criteria the conventional approaches to facility location problem tend to be less effective in dealing with the imprecise or vagueness nature of the linguistic assessment under many situations the values of the qualitative criteria are often imprecisely defined for the decision makers the aim of the paper is to solve facility location problems using different solution approaches of fuzzy multi attribute group decision making the paper includes four different fuzzy multi attribute group decision making approaches the first one is a fuzzy model of group decision proposed by blin the second is the fuzzy synthetic evaluation the third is yager s weighted goals method and the last one is fuzzy analytic hierarchy process although four approaches have the same objective of selecting the best facility location alternative they come from different theoretic backgrounds and relate differently to the discipline of multi attribute group decision making these approaches are extended to select the best facility location alternative by taking into account quantitative and qualitative criteria a short comparative analysis among the approaches and a numeric example to each approach are given

potential applications of fuzzy sets in industrial safety engineering abstract this paper discusses potential applications of fuzzy set theory to risk analysis in the area of industrial safety engineering vagueness and imprecision in mathematical quantification of risk are equated with fuzziness rather than randomness the concept of risk evaluation using linguistic representation of the likelihood of the occurrence of a hazardous event exposure and possible consequences of that event is proposed the approximate reasoning technique based on fuzzy logic is used to derive fuzzy values of risk

recursive formulas for the overlaps between bethe states and product states in xxz heisenberg chains we consider the problem of computing the overlaps between the bethe states of the xxz spin 1 2 chain and generic states we derive recursive formulas for the overlaps between some simple product states and off shell bethe states within the framework of the algebraic bethe ansatz these recursive formulas can be used to prove in a simple and straightforward way the recently obtained results for the overlaps of the bethe states with the n el state the dimer state and the q deformed dimer state however these recursive formulas are derived for a broader class of states and represent a concrete starting point for the computation of rather general overlaps our approach can be easily extended to other one dimensional bethe ansatz integrable models

determinant formula for the six vertex model with reflecting end using the quantum inverse scattering method for the xxz model with open boundary conditions we obtained the determinant formula for the six vertex model with reflecting end

the direct linearization of a class of nonlinear evolution equations the paper deals with the direct linearization an approach used to generate particular solutions of the partial differential equations that can be solved through the inverse scattering transform linear integral equations are presented which enable one to find broad classes of solutions to certain nonlinear evolution equations in 1 1 and 2 1 dimensions

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

exact solvability and asymptotic aspects of generalized xx0 spin chains abstract building on our earlier work saeedian et al 2018 we introduce and study generalized xx0 models we explicitly construct a long range interacting spin chain referred to as the selberg model and study the correlation functions of the selberg and xx0 models using a matrix integral representation of the generalized xx0 model and applying asymptotic analysis in non intersecting brownian motion the phase structure of the selberg model is determined we find that tails of the tracy widom distribution of gaussian unitary ensemble govern a discrete to continuous third order phase transition in selberg model the same method also reproduces the gross witten phase transition of the original xx0 model finally we conjecture universal features for the phase structure of the generalized xx0 model

fuzzy method in group decision making abstract this paper investigates the problems of decision making with multiple judge multiple criteria in a fuzzy environment where the performance of alternatives and the importance of criteria are imprecisely defined and represented by fuzzy sets a fuzzy model associated with the solution algorithm is proposed on the basis of an level weighted fuzzy preference relation a numerical example is solved for illustration

on form factors of the conjugated field in the nonlinear schrodinger model izergin korepin s lattice discretization of the nonlinear schrodinger model along with oota s inverse problem provides one with determinant representations for the form factors of the lattice discretized conjugated field operator we prove that these form factors converge in the zero lattice spacing limit to those of the conjugated field operator in the continuous model we also compute the large volume asymptotic behavior of such form factors in the continuous model these are in particular characterized by fredholm determinants of operators acting on closed contours we provide a way of defining these fredholm determinants in the case of generic parameters

integral representations for correlation functions of the xxz chain at finite temperature we derive a novel multiple integral representation for a generating function of the z z correlation functions of the spin xxz chain at finite temperature and finite longitudinal magnetic field our work combines algebraic bethe ansatz techniques for the calculation of matrix elements with the quantum transfer matrix approach to thermodynamics

temperature correlators of the impenetrable bose gas as an integrable system it is shown that the temperature equal time correlators of impenetrable bosons in one space dimension are described by a classical integrable system partial differential equations for two point as well as for multipoint correlators are obtained the short distance and low density expansions are constructed

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

large time and distance asymptotics of field correlation function of impenetrable bosons at finite temperature abstract asymptotics of the temperature time dependent correlation function of two fields one dimensional bosons with infinite point like repulsion is calculated

determinant formula for the six vertex model the partition function of a six vertex model with domain wall boundary conditions is considered on the finite lattice the authors show that the partition function satisfies a recursive relation they solve the recursion relation by a determinant formula this gives a determinant representation for the partition function they use the quantum inverse scattering method qism

fuzzy hyperrings hv rings based on fuzzy universal sets the aim of this paper is to define and study the concept of a fuzzy hyperring which depends on the concept of a fuzzy universal set a correspondence relation between a fuzzy hyperring based on a fuzzy universal set and both ordinary and fuzzy hyperideal in the sense of davvaz is obtained