on quantum characteristic exponents the definition of quantum characteristic exponents for a general quantum dynamical map is given the basic properties of this notion and illustrative models are presented

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

determination of elastic stresses from discrete data on stress orientations the problem considered in this paper deals with reconstruction of stress fields in a plane elastic domain from discrete data on stress orientations the problem is reduced to the determination of unknown coefficients in linear combinations of holomorphic functions used for the representation of complex potentials in plane elasticity the coefficients are found by fitting the data to the calculated principal directions this leads to an overdetermined system of linear algebraic equations which elements are subjected to experimental errors the system is homogeneous therefore the coefficients cannot be determined uniquely however it allows for the unique reconstruction of stress trajectories the determination of maximum shear stresses is non unique it can be multiplied by i an arbitrary real positive constant if principal directions are non harmonic function of spatial coordinates or ii a real valued positively defined bi holomorphic function that depends on four real constants if principal directions are harmonic the determination of the mean stresses is performed by integration which introduces another real additive constant into the complete solution the proposed technique is capable of identification of singular isotropic points in the field of stress trajectories this is illustrated in examples that use for the reconstruction either synthetic or real data from photoelasticity and geophysics

integrability in time dependent systems with one degree of freedom the notion of integrability is discussed for classical nonautonomous systems with one degree of freedom the analysis is focused on models which are linearly spanned by finite lie algebras by constructing the autonomous extension of the time dependent hamiltonian we prove the existence of two invariants in involution which are shown to obey the criterion of functional independence the implication of this result is that chaotic motion cannot exist in these systems in addition if the invariant manifold is compact then the system is liouville integrable as an application we discuss regimes of integrability in models of dynamical tunneling and parametric resonance and in the dynamics of two level systems under generic classical fields a corresponding quantum algebraic structure is shown to exist which satisfies analog conditions of liouville integrability and reproduces the classical dynamics in an appropriate limit within the weyl wigner formalism the quantum analog is then conjectured to be integrable as well

an analytical relation between entropy production and quantum lyapunov exponents for gaussian bipartite systems we study and compare the information loss of a large class of gaussian bipartite systems it includes the usual caldeira leggett type model as well as anosov models parametric oscillators the inverted oscillator environment etc which exhibit instability one of the most important characteristics of chaotic systems we establish a rigorous connection between the quantum lyapunov exponents and coherence loss and show that in the case of unstable environments coherence loss is completely determined by the upper quantum lyapunov exponent a behavior which is more universal than that of the caldeira leggett type model

positive lyapunov exponents for schrodinger operators with quasi periodic potentials we present a new simple way to estimate the rate of exponential growth lyapunov exponent of solutions of the finite difference schrodinger equation h e psi n mathop limits def psi n 1 psi n 1 lambda f alpha n theta psi n heref is a non constant real analytic function of period 1 and is irrational for large we prove that the lyapunov exponent is positive for every energye in the spectrum ofh and a e in particular the absolutely continuous spectrum ofh is empty in the continuum we study the quasi periodic operator onl2 r h frac d 2 dx 2 k 2 cos x cos alpha x theta for largek and show that for wide intervals of low energies the lyapunov exponent is positive the main idea which originated from m herman s subharmonic argument 11 is to deform the phase to the complex plane this enables us to avoid small denominator problems by moving them off the axis making estimates much easier to perform we recover the information for real using an elementary extension of jensen s formula subharmonicity

a direct method of parameter estimation for steady state flow in heterogeneous aquifers with unknown boundary conditions 1 we propose a novel direct method for estimating steady state hydrogeological model parameters and model state variables in an aquifer where boundary conditions are unknown the method is adapted from a recently developed potential theory technique for solving general inverse reconstruction problems unlike many inverse techniques used for groundwater model calibration the new method is not based on fitting and optimizing an objective function which usually requires forward simulation and iterative parameter updates instead it directly incorporates noisy observed data hydraulic heads and flow rates at the measurement points in a single step without solving a boundary value problem the new method is computationally efficient and is robust to the presence of observation errors it has been tested on two dimensional groundwater flow problems with regular and irregular geometries different heterogeneity patterns variances of heterogeneity and error magnitudes in all cases parameters hydraulic conductivities converge to the correct or expected values and are thus unique based on which heads and flow fields are constructed directly via a set of analytical expressions accurate boundary conditions are then inferred from these fields the accuracy of the direct method also improves with increasing amount of observed data lower measurement errors and grid refinement under natural flow i e no pumping the direct method yields an equivalent conductivity of the aquifer suggesting that the method can be used as an inexpensive characterization tool with which both aquifer parameters and aquifer boundary conditions can be inferred

performance evaluation an integrated method using data envelopment analysis and fuzzy preference relations in a multi attribute decision making madm context the decision maker needs to provide his preferences over a set of decision alternatives and constructs a preference relation and then use the derived priority vector of the preference to rank various alternatives this paper proposes an integrated approach to rate decision alternatives using data envelopment analysis and preference relations this proposed approach includes three stages first pairwise efficiency scores are computed using two dea models the ccr model and the proposed cross evaluation dea model second the pairwise efficiency scores are then utilized to construct the fuzzy preference relation and the consistent fuzzy preference relation third by use of the row wise summation technique we yield a priority vector which is used for ranking decision making units dmus for the case of a single output and a single input the preference relation can be directly obtained from the original sample data the proposed approach is validated by two numerical examples

quantifiers in the formulation of multiple objective decision functions abstract we discuss the interpretation of linguistically quantified statements using fuzzy sets we indicate that there are two methods of interpreting these statements the algebraic approach and the substitution approach we then use quantified statements to express overall decision functions involving multiple objectives these statements are of the type a solution should satisfy many of the objectives using the algebraic and substitution approach we develop a whole family of forms for combining multiple objectives we show that algebraic approach corresponds to situations in which we are unconcerned about the allocation of satisfaction amongst the objectives but just interested in getting much satisfaction the substitution approach on the other hand leads to forms which are dependent upon the allocation of satisfaction between the objectives

the owa based consensus operator under linguistic representation models using position indexes when using linguistic approaches to solve decision problems we need linguistic representation models the symbolic model the 2 tuple fuzzy linguistic representation model and the continuous linguistic model are three existing linguistic representation models based on position indexes together with these three linguistic models the corresponding ordered weighted averaging operators such as the linguistic ordered weighted averaging operator the 2 tuple ordered weighted averaging operator and the extended ordered weighted averaging operator have been developed respectively in this paper we analyze the internal relationship among these operators and propose a consensus operator under the continuous linguistic model or the 2 tuple fuzzy linguistic representation model the proposed consensus operator is based on the use of the ordered weighted averaging operator and the deviation measures some desired properties of the consensus operator are also presented in particular the consensus operator provides an alternative consensus model for group decision making this consensus model preserves the original preference information given by the decision makers as much as possible and supports consensus process automatically without moderator

fuzzy sets and decision analysis abstract this survey points out recent advances in multiple attribute decision making methods dealing with fuzzy or ill defined information fuzzy maut as well as fuzzy outranking methods are reviewed aggregation procedures choice problems and treatment of interactive attributes are covered trends in research and open problems are indicated

generalized ordered modular averaging operator and its application to group decision making in this paper we propose a new class of operators called the ordered quasi modular averaging oqma operators based on the ordered modular averaging oma operators it is shown that the oqma operators are monotonic bounded idempotent commutative and quasi comonotone modular moreover we introduce the generalized ordered modular averaging goma operator which is a special case of the oqma operator some special cases of the goma operator are discussed an orness measure to reflect the or like degree of the goma operator is proposed we further extend the goma operator to the generalized ordered hybrid modular gohm operator which focuses not only on the degree of importance with respect to input arguments but also their serial positions finally a new method based on the gohm operator for multi attribute group decision making is presented and a numerical example shows that the developed approach is feasible

upper quantum lyapunov exponent and anosov relations for quantum systems driven by a classical flow we generalize the definition of quantum anosov properties and the related lyapunov exponents to the case of quantum systems driven by a classical flow i e skew product systems we show that the skew anosov properties can be interpreted as regular anosov properties in an enlarged hilbert space in the framework of a generalized floquet theory this extension allows us to describe the hyperbolicity properties of almost periodic quantum parametric oscillators and we show that their upper lyapunov exponents are positive and equal to the lyapunov exponent of the corresponding classical parametric oscillators as second example we show that the configurational quantum cat system satisfies quantum anosov properties

an outranking based general approach to solving group multi objective optimization problems abstract this paper presents a general approach to solving multi objective programming problems with multiple decision makers the proposal is based on optimizing a bi objective measure of collective satisfaction group satisfaction is understood as a reasonable balance between the strengths of an agreeing and an opposing coalition considering also the number of decision makers not belonging to any of these coalitions accepting the vagueness of collective satisfaction even the vagueness of person satisfaction fuzzy outranking relations and other fuzzy logic models are used our method transforms a group multi objective optimization problem into a group choice problem on a decision set composed of a relatively small set of alternatives this set contains the possible acceptable consensuses in the parameter space once such a set has been identified other well known techniques can be used to reach the final choice main advantages a each individual decision maker is concerned with his her own multi objective optimization problem only sharing decision variables own constraints and own mapping between decision variables and objective space are allowed b the search for the best agreement is not limited to portions of the pareto frontiers c no voting rule is used by the optimization algorithm no to some extent arbitrary way of handling collective preferences is needed d no assumptions of transitivity and comparability of preference relations are needed and e the concepts of satisfaction non satisfaction do not depend on distance measures or other to some extent arbitrary norms very good performance of the whole proposal is illustrated by a real size example

choice processes for non homogeneous group decision making in linguistic setting several choice processes of alternatives for non homogeneous group decision making problems assuming linguistic preference relations for expressing the opinions of individuals and linguistic values for expressing their respective power or importance degrees are presented these processes are designed using two choice degrees of alternatives based on the concept of fuzzy majority quantifier guided linguistic dominance degree and quantifier guided linguistic non dominance degree being the last one a generalization of orlovski s non dominated alternative concept in order to deal with non weighted linguistic information the linguistic ordered weighted averaging lowa operator is applied to deal with weighted linguistic information three operators of linguistic weighted information aggregation are used the linguistic weighted disjunction lwd operator the linguistic weighted conjunction lwc operator and the linguistic weighted averaging lwa operator

multiplicative data envelopment analysis cross efficiency and stochastic weight space acceptability analysis for group decision making with interval multiplicative preference relations abstract to deal with group decision making gdm with interval multiplicative preference relations imprs this paper proposes a novel method based on multiplicative data envelopment analysis dea cross efficiency and stochastic weight space acceptability analysis we first develop a multiplicative dea model to evaluate the relative efficiency of all alternatives of a given multiplicative preference relation mpr then we present a method free from consistency adjustment to derive a priority vector using the multiplicative dea cross efficiency with respect to the given mpr for gdm with imprs we consider the decision makers weights as a uniform distribution for acceptability analysis a modified unacceptability index is further defined to measure the unlikeliness for a particular alternative in a particular rank finally we develop an assignment problem model to achieve an optimal ranking by minimizing the total rank unacceptability and to compute the expected priority vector of all alternatives numerical examples are provided to show the applicability and justifications of the proposed gdm method

approach to equilibrium for a class of random quantum models of infinite range we consider random generalizations of a quantum model of infinite range introduced by emch and radin the generalizations allow a neat extension from the class l 1 of absolutely summable lattice potentials to the optimal class l 2 of square summable potentials first considered by khanin and sinai and generalised by van enter and van hemmen the approach to equilibrium in the case of a gaussian distribution is proved to be faster than for a bernoulli distribution for both short range and long range lattice potentials while exponential decay to equilibrium is excluded in the nonrandom l 1 case it is proved to occur for both short and long range potentials for gaussian distributions and for potentials of class l 2 in the bernoulli case open problems are discussed

new decision making techniques and their application in the selection of financial products we develop a new approach that uses the ordered weighted averaging owa operator in the selection of financial products in doing so we introduce the ordered weighted averaging distance owad operator and the ordered weighted averaging adequacy coefficient owaac operator these aggregation operators are very useful for decision making problems because they establish a comparison between an ideal alternative and available options in order to find the optimal choice the objective of this new model is to manipulate the attitudinal character of previous methods based on distance measures so that the decision maker can select financial products according to his or her degree of optimism which is also known as the orness measure the main advantage of using the owa operator is that we can generate a parameterized family of aggregation operators between the maximum and the minimum thus the analysis developed in the decision process by the decision maker is much more complete because he or she is able to select the particular case in accordance with his or her interests in the aggregation process the paper ends with an illustrative example that shows results obtained by using different types of aggregation operators in the selection of financial products

aggregation of fuzzy opinions an axiomatic approach abstract the importance of fuzzy valuations in diagnostics is mentioned the problem of aggregation of fuzzy opinions obtained from a group of experts in answer to the question has an object the property labeled a and no property labeled 1a is formulated the set of fung and fu s 10 aggregation axioms is shortly described the idea of weighting expert s opinions is formalized then a new set of aggregation axioms is presented and an aggregating operator is introduced a posteriori weighting of opinions in aggregation is examined

a note on the internal consistency of various preference representations in chiclana et al fuzzy sets and systems 97 1998 33 we presented a fuzzy multipurpose decision making model integrating different preference representations preference orderings utility functions and fuzzy preference relations we complete the decision model studying its internal consistency

a method based on pso and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts abstract group decision making is a type of decision problem in which multiple experts acting collectively analyze problems evaluate alternatives and select a solution from a collection of alternatives as the natural language is the standard representation of those concepts that humans use for communication it seems natural that they use words linguistic terms instead of numerical values to provide their opinions however while linguistic information is readily available it is not operational and thus it has to be made usable though expressing it in terms of information granules to do so granular computing which has emerged as a unified and coherent framework of designing processing and interpretation of information granules can be used the aim of this paper is to present an information granulation of the linguistic information used in group decision making problems defined in heterogeneous contexts i e where the experts have associated importance degrees reflecting their ability to handle the problem the granulation of the linguistic terms is formulated as an optimization problem solved by using the particle swarm optimization in which a performance index is maximized by a suitable mapping of the linguistic terms on information granules formalized as sets this performance index is expressed as a weighted aggregation of the individual consistency achieved by each expert

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

on quantum lyapunov exponents it was shown that quantum analysis constitutes the proper analytic basis for the quantization of lyapunov exponents in the heisenberg picture differences among various quantizations of lyapunov exponents are clarified

quantum parametric resonance the quantum mechanical equivalent of parametric resonance is studied a simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly classically stable and unstable regions in parameter space are shown to correspond to floquet operators with qualitatively different properties their eigenfunctions which are calculated exactly exhibit a transition for parameter values with classically stable solutions the eigenstates are normalizable while they cannot be normalized for parameter values with classically unstable solutions similarly the spectrum of quasi energies undergoes a specific transition these observations remain valid qualitatively for arbitrary linear systems exhibiting classically parametric resonance such as the paradigm example of a frequency modulated pendulum described by mathieu s equation

induced 2 tuple linguistic generalized aggregation operators and their application in decision making the induced 2 tuple linguistic generalized ordered weighted averaging 2 tilgowa operator is presented this new aggregation operator extends previous approaches by using generalized means order inducing variables in the reordering of the arguments and linguistic information represented with the 2 tuple linguistic approach its main advantage is that it includes a wide range of linguistic aggregation operators thus its analyses can be seen from different perspectives and we obtain a much more complete picture of the situation considered and are able to select the alternative that best fits with our interests or beliefs we further generalize the 2 tilgowa by using quasi arithmetic means and choquet integrals the result is the quasi 2 tilowa operator and the 2 tuple linguistic induced quasi arithmetic choquet integral aggregation we conclude this paper by analysing the applicability of this new approach in a multi person linguistic decision making problem concerning product management

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

a fuzzy linear programming method for group decision making with additive reciprocal fuzzy preference relations abstract the existing methods for solving the group decision making gdm problems with preference relations generally include four steps 1 estimation of missing preferences 2 consistency and consensus reaching 3 aggregation and 4 exploitation which make the gdm process complicated relatively very few research results focus on exploring the methods which can simplify this process to improve the efficiency in this paper we develop a new fuzzy linear programming method flpm to deal with the gdm problems with additive reciprocal fuzzy preference relations fprs the flpm can directly produce meaningful results without the four steps an effect index is developed to measure the decision makers dms effects in the gdm problems based on the flpm and the effect index we propose a new method to determine the dms weights a step by step procedure is further proposed to deal with the gdm problems with all the developed methods and its performance is illustrated by examples

on reconstruction of three dimensional harmonic functions from discrete data this study presents an approach for reconstruction of harmonic functions in three dimensions from the finite number of field and surface measurements the approach based on the trefftz method performs reconstruction as the best fit to the data and provides smoothness of the reconstructed function two particular algorithms are proposed the first one uses specific radial basis functions and the second one is of finite element type either of them can be applied to analyse different data types but the latter can handle larger problems the data types considered in this study also cover direct and inverse boundary value problems therefore the proposed approach is universal and capable of dealing with both well posed and ill posed formulations examples from steady heat conduction and elastostatics are examined in order to investigate the efficiency of the approach

integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations abstract the purpose of this paper is to study a fuzzy multipurpose decision making problem where the information about the alternatives provided by the experts can be of a diverse nature the information can be represented by means of preference orderings utility functions and fuzzy preference relations and our objective is to establish a general model which cover all possible representations firstly we must make the information uniform using fuzzy preference relations as uniform preference context secondly we present some selection processes for multiple preference relations based on the concept of fuzzy majority fuzzy majority is represented by a fuzzy quantifier and applied in the aggregation by means of an owa operator whose weights are calculated by the fuzzy quantifier we use two quantifier guided choice degrees of alternatives a dominance degree used to quantify the dominance that one alternative has over all the others in a fuzzy majority sense and a non dominance degree that generalises orlovski s non dominated alternative concept the application of the two above choice degrees can be carried out according to two different selection processes a sequential selection process and a conjunction selection process

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

anosov actions on noncommutative algebras an axiomatic framework for a quantum mechanical extension to the theory of anosov systems is constructed and it is shown that this retains some of the characteristic features of its classical counterpart e g nonvanishing lyapunov exponents a vectorial k property and exponential clustering the effects of quantization are investigated on two prototype examples of anosov systems namely the iterations of an automorphism of the torus the arnold cat model and the free dynamics of a particle on a surface of negative curvature it emerges that the anosov property survives quantization in the case of the former model but not of the latter one finally we show that the modular dynamics of a relativistic quantum field on the rindler wedge of minkowski space is that of an anosov system

social choice axioms for fuzzy set aggregation the problem of aggregating n fuzzy sets f1 f2 fn on a set is viewed as one of merging the opinions of n individuals e g experts that rate objects belonging to this approach contrasts with the pure set theoretic point of view and leads to interpreting already known axioms underlying fuzzy connectives in a way different from that of multiple criteria aggregation various natural properties of a voting procedure including the ones proposed by arrow are expressed in the fuzzy set setting a number of conditions limiting the choice of fuzzy set operations are proposed and classified according to whether they are imperative mainly technical or facultative families of solutions are obtained that include those proposed in earlier works the case of non homogeneous groups is briefly examined lastly the application of the voting paradigm to the management of antagonistic local decision rules in knowledge based systems is outlined

group consensus algorithms based on preference relations in many group decision making situations decision makers preferences for alternatives are expressed in preference relations including fuzzy preference relations and multiplicative preference relations an important step in the process of aggregating preference relations is to determine the importance weight of each preference relation in this paper we develop a number of goal programming models and quadratic programming models based on the idea of maximizing group consensus our models can be used to derive the importance weights of fuzzy preference relations and multiplicative preference relations we further develop iterative algorithms for reaching acceptable levels of consensus in group decision making based on fuzzy preference relations or multiplicative preference relations finally we include an illustrative example

some induced ordered weighted averaging operators and their use for solving group decision making problems based on fuzzy preference relations abstract in r r yager d p filev operations for granular computing mixing words and numbers in proceedings of the fuzz ieee world congress on computational intelligence anchorage 1998 pp 123 128 yager and filev introduced the induced ordered weighted averaging iowa operator in this paper we provide some iowa operators to aggregate fuzzy preference relations in group decision making gdm problems these iowa operators when guided by fuzzy linguistic quantifiers allow the introduction of some semantics or meaning in the aggregation and therefore allow for a better control over the aggregation stage developed in the resolution process of the gdm problems in particular we present the importance iowa i iowa operator which applies the ordering of the argument values based upon the importance of the information sources the consistency iowa c iowa operator which applies the ordering of the argument values based upon the consistency of the information sources and the preference iowa p iowa operator which applies the ordering of the argument values based upon the relative preference values associated to each one of them we provide a procedure to deal with ties in respect to the ordering induced by the application of one of these iowa operators it consists of a sequential application of the above iowa operators we also present a selection process for gdm problems based on the concept of fuzzy majority and the above three iowa operators finally we analyse the reciprocity and consistency properties of the collective fuzzy preference relations obtained using iowa operators

aggregation of fuzzy opinions in a non homogeneous group an axiomatic treatment of an aggregation problem when the aggregated group is defined as a fuzzy group was proposed by the author in a previous paper in the present paper the fuzzy majority rule is characterized and an impossibility theorem for pure mixed rules is obtained moreover existence of absolutely decisive groups is studied

group decision making based on multiplicative consistent reciprocal preference relations the main aim of this paper is to investigate the consistency and consensus of multiplicative consistent reciprocal preference relations based on the multiplicative consistency property a straightforward method to obtain the priority vector for multiplicative consistent reciprocal preference relation is introduced together with some of its desired properties in addition some interesting properties on consistency and consensus for reciprocal preference relations are further investigated a consensus optimization model for group decision making with reciprocal preference relations is proposed which enables the decision makers to reach consensus with the highest overall consensus level numerical examples are provided to make a discussion and comparison with some existing similar methods

induced aggregation operators we introduce the induced ordered weighted averaging iowa operator in these operators the argument ordering process is guided by a variable called the order inducing value a procedure for learning the weights from data is described we suggest a number of applications of these induced owa aggregation operators first we show its possibilities in modeling nearest neighbor rules next it is applied to the aggregation of complex objects such as matrices it is also used to establish a new class of information fusion models called best yesterday models finally we extend the idea of order induced aggregation to the choquet aggregation resulting in what we call the induced choquet ordered averaging i coa operator

upper quantum lyapunov exponent and parametric oscillators we introduce a definition of upper lyapunov exponent for quantum systems in the heisenberg representation and apply it to parametric quantum oscillators we provide a simple proof that the upper quantum lyapunov exponent ranges from zero to a positive value as the parameters range from the classical system s region of stability to the instability region it is also proved that in the instability region the parametric quantum oscillator satisfies the discrete quantum anosov relations defined by emch narnhofer sewell and thirring

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

some issues on consistency of fuzzy preference relations in decision making in order to avoid misleading solutions the study of consistency when the decision makers express their opinions by means of preference relations becomes a very important aspect in order to avoid misleading solutions in decision making problems based on fuzzy preference relations the study of consistency is associated with the study of the transitivity property in this paper a new characterization of the consistency property defined by the additive transitivity property of the fuzzy preference relations is presented using this new characterization a method for constructing consistent fuzzy preference relations from a set of n 1 preference data is proposed applying this method it is possible to assure better consistency of the fuzzy preference relations provided by the decision makers and in such a way to avoid the inconsistent solutions in the decision making processes additionally a similar study of consistency is developed for the case of multiplicative preference relations 2002 elsevier b v all rights reserved

type 1 owa operators for aggregating uncertain information with uncertain weights induced by type 2 linguistic quantifiers the owa operator proposed by yager has been widely used to aggregate experts opinions or preferences in human decision making yager s traditional owa operator focuses exclusively on the aggregation of crisp numbers however experts usually tend to express their opinions or preferences in a very natural way via linguistic terms these linguistic terms can be modelled or expressed by type 1 fuzzy sets in this paper we define a new type of owa operator the type 1 owa operator that works as an uncertain owa operator to aggregate type 1 fuzzy sets with type 1 fuzzy weights which can be used to aggregate the linguistic opinions or preferences in human decision making with linguistic weights the procedure for performing type 1 owa operations is analysed in order to identify the linguistic weights associated to the type 1 owa operator type 2 linguistic quantifiers are proposed the problem of how to derive linguistic weights used in type 1 owa aggregation given such type of quantifier is solved examples are provided to illustrate the proposed concepts