improving linguistic pairwise comparison consistency via linguistic discrete regions linguistic pairwise comparison matrices are widely used in decision making procedures however the matrices often give conflicting results when there are multiple criteria under consideration despite intensive research achieving consistency of such matrices remains a daunting task in this paper a novel approach based on linguistic discrete region is proposed to address the challenge unlike existing methods that require a single value for each comparison our approach allows a comparison to be expressed by a discrete region with multiple linguistic terms such front end gives users more freedom to express their opinions in the back end we propose an iterative searching algorithm that is able to achieve approximate optimal consistency for the comparison matrices with discrete region values the final results are single value matrices that not only guarantee approximate optimal consistency but comply with evaluators intentions a well as our approach does not modify any linguistic values like many existing methods we have conducted extensive evaluations and our empirical study confirms that the linguistic discrete region based approach significantly improves the consistency of linguistic pairwise comparison matrices

least square completion and inconsistency repair methods for additively consistent fuzzy preference relations in this paper we explore the group decision making gdm problems with incomplete additively consistent fuzzy preference relations some properties of additively consistent fuzzy preference relations are also discussed a sufficient and necessary condition is proposed to keep the additive consistency of fuzzy preference relations methods for determining the priority weights of fuzzy preference relations are provided least square completion and inconsistency repair methods are developed to deal with incomplete and inconsistent fuzzy preference relations some numerical examples are also given to illustrate the proposed approaches

existence results for the flow of viscoelastic fluids with a differential constitutive law where 2 is the symmetric extra stress tensor the total stress is given by g pl i where p is the hydrodynamic pressure 4 is the rate of deformation tensor g u vu vu u being the velocity field a is the relaxation time a2 the retardation time 0 i a a1 and q is the fluid viscosity the symbol a d t denotes an objective frame indifferent derivative i 181 more precisely

optimal aggregation of fuzzy preference relations with an application to broadband internet service selection this paper investigates the aggregation of multiple fuzzy preference relations into a collective fuzzy preference relation in fuzzy group decision analysis and proposes an optimization based aggregation approach to assess the relative importance weights of the multiple fuzzy preference relations the proposed approach that is analytical in nature assesses the weights by minimizing the sum of squared distances between any two weighted fuzzy preference relations relevant theorems are offered in support of the proposed approach multiplicative preference relations are also incorporated into the approach using an appropriate transformation technique an eigenvector method is introduced to derive the priorities from the collective fuzzy preference relation the proposed aggregation approach is tested using two numerical examples a third example involving broadband internet service selection is offered to illustrate that the proposed aggregation approach provides a simple effective and practical way of aggregating multiple fuzzy preference relations in real life situations

global existence results for oldroyd b fluids in exterior domains the case of non small coupling parameters consider the set of equations describing oldroyd b fluids in an exterior domain it is shown that this set of equations admits a unique global solution in a certain function space provided the initial data but not necessarily the coupling constant is small enough

a consistency improving method in the analytic hierarchy process in this paper we propose a method to modify a given comparison matrix by which the consistency ratio cr value of the modified matrix is less than that of the original one and give an algorithm to derive a positive reciprocal matrix with acceptable consistency i e cr 0 1 then the convergence theorem for the given algorithm is established and its practicality is shown by some examples

analytic hierarchy process ahp in group decision making and its optimization with an allocation of information granularity in group decision making one strives to reconcile differences of opinions judgments expressed by individual members of the group fuzzy decision making mechanisms bring a great deal of flexibility by admitting membership degrees we are offered flexibility to exploit different aggregation mechanisms and navigate a process of interaction among decision makers to achieve an increasing level of consistency within the group while the studies reported so far exploit more or less sophisticated ways of adjusting transforming initial judgments preferences of individuals in this paper we bring forward a concept of information granularity here information granularity is viewed as an essential asset which offers a decision maker a tangible level of flexibility using some initial preferences conveyed by each individual that can be adjusted with the intent to reach a higher level of consensus our study is concerned with an extension of the well known analytic hierarchy process to the group decision making scenario more specifically the admitted level of granularity gives rise to a granular matrix of pairwise comparisons the granular entries represented e g by intervals or fuzzy sets supply a required flexibility using the fact that we select the most suitable numeric representative of the reciprocal matrix the proposed concept of granular reciprocal matrices is used to optimize a performance index which comes as an additive combination of two components the first one expresses a level of consistency of the individual pairwise comparison matrices by exploiting the admitted level of granularity we aim at the minimization of the corresponding inconsistency index the second part of the performance index quantifies a level of disagreement in terms of the individual preferences the flexibility offered by the level of granularity is used to increase the level of consensus within the group given an implicit nature of relationships between the realizations of the granular pairwise matrices and the values of the performance index we consider using particle swarm optimization as an optimization vehicle two scenarios of allocation of granularity among decision makers are considered namely a uniform allocation of granularity and nonuniform distribution of granularity where the levels of allocated granularity are also subject to optimization a number of numeric studies are provided to illustrate an essence of the method

schur majorization inequalities for symmetrized sums with applications to tensor products we show that if w y and x z are four vectors in rn then a number of schur majorizations hold between symmetrized vector functions of w x y and z e g wi xj i j yi zj i j where the left hand expression means the vector of dimension n2 consisting of all sums wi xj of the co ordinates of w and x arranged in lexicographic order among other things we get vector and matrix versions of muirhead s theorem for scalar inequalities from the vector inequalities follow many scalar inequalities for symmetrized sums some of which are scattered through the inequality literature in section 2 applications are given to matrix inequalities for tensor products e g if a b and c are hermitian and a b then a c b c

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

group decision making with a fuzzy linguistic majority abstract the determination of solutions in group decision making is considered the point of departure is a collection of individual fuzzy preference relations a solution is derived either directly from the individual fuzzy preference relations or by constructing first a social fuzzy preference relation as opposed to conventional approaches in which a crisp threshold type majority rule is used we employ a fuzzy majority rule specified by a fuzzy linguistic quantifier e g most much more than 50 etc a calculus of linguistically quantified propositions is applied using the fuzzy majority various solution concepts are derived mainly of the type of core minimax opposition set and consensus winner

the ordinal consistency of a fuzzy preference relation in this paper we first analyze the rationality of weak transitivity of a fuzzy preference relation defined by tanino fuzzy preference orderings in group decision making fuzzy sets and systems 12 1984 117 131 we then propose a revised definition of weak transitivity we call it ordinal consistency we propose the ordinal consistency index oci to measure the degree of ordinal consistency of a fuzzy preference relation which is to count the unreasonable 3 cycles in a directed graph that represents the fuzzy preference relation afterwards a procedure to compute the order consistency index and to locate each cycle as well as to find the inconsistent judgments in the fuzzy preference relation is proposed in order to repair the inconsistency of a fuzzy preference relation an algorithm is developed to find and remove 3 cycles in the graph the algorithm eliminates 3 cycles in a graph more effectively and the proposed method for improving consistency method aims to preserve the initial preference information of the decision maker furthermore the method can be used not only for a strict fuzzy preference relation but also for non strict fuzzy preference relation finally we provide some examples to show the effectiveness and validity of the proposed method

global well posedness for the phan thein tanner model in critical besov spaces without damping in this paper we mainly investigate the cauchy problem for the phan thein tanner ptt model the ppt model can be viewed as navier stokes equations coupled with a nonlinear transport system this model is derived from network theory of the polymeric fluid we study about the global well posedness of the ptt model in critical besov space when the initial data are a small perturbation around the equilibrium the strong solution in critical besov space is proved to be globally existed in this paper we mainly investigate the cauchy problem for the phan thein tanner ptt model the ppt model can be viewed as navier stokes equations coupled with a nonlinear transport system this model is derived from network theory of the polymeric fluid we study about the global well posedness of the ptt model in critical besov space when the initial data are a small perturbation around the equilibrium the strong solution in critical besov space is proved to be globally existed

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

general transitivity conditions for fuzzy reciprocal preference matrices a reciprocal fuzzy matrix relation is a non negative matrix q qij such that qij qji 1 for all i j 1 2 n we define general transitivity conditions named fg transitivities for fuzzy reciprocal preference relations and show that they generalize some well known transitivities we also study relationships of these conditions with two models of rational preferences the so called utility model and the multidimensional model

transitivity of fuzzy preference relations an empirical study based on an experiment we show that human preferences when represented by fuzzy relations may violate transitivity we define an index of transitivity and compute the degree to which the transitivity is violated

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

a new method of obtaining the priority weights from an interval fuzzy preference relation in analyzing a multiple criteria decision making problem the decision maker may express her his opinions as an interval fuzzy or multiplicative preference relation then it is an interesting and important issue to investigate the consistency of the preference relations and obtain the reliable priority weights in this paper a new consistent interval fuzzy preference relation is defined and the corresponding properties are derived the transformation formulae between interval fuzzy and multiplicative preference relations are further given which show that two preference relations consistent interval fuzzy and multiplicative preference relations can be transformed into each other based on the transformation formula the definition of acceptably consistent interval fuzzy preference relation is given furthermore a new algorithm for obtaining the priority weights from consistent or inconsistent interval fuzzy preference relations is presented finally three numerical examples are carried out to compare the results using the proposed method with those using other existing procedures the numerical results show that the given procedure is feasible effective and not requisite to solve any mathematical programing

solving multi period project selection problems with fuzzy goal programming based on topsis and a fuzzy preference relation project portfolio managers are multi objective decision makers dms who are expected to select the best mix of projects by maximizing profits and minimizing risks over a multi period planning horizon however project portfolio decisions are complex multi objective problems with a high number of projects from which a subset has to be chosen subject to various constraints and a multitude of priorities and preferences we propose a goal programming gp approach for project portfolio selection that embraces conflicting fuzzy goals with imprecise priorities a fuzzy goal with an aspiration level and a predefined membership function is defined for each objective the impreciseness in the priorities of the membership values of the fuzzy goals is modeled with fuzzy relations this leads to type ii fuzzy sets since fuzzy relations are organized between the membership values of the fuzzy goals which are themselves fuzzy sets the proposed model is based on the technique for order preference by similarity to ideal solution topsis and fuzzy preference relations topsis is used to reduce the multi objective problem into a bi objective problem the resulting bi objective problem is solved with fuzzy gp fgp the fuzzy preference relations are used to help dms express their preferences with respect to the membership values of the fuzzy goals the proposed approach is used to solve a real life problem characterized as a fuzzy multi objective project selection with multi period planning horizon mops mpph the performance of the proposed approach is compared with a competing method in the literature we show that our approach generates high quality solutions with minimal computational efforts

additional criteria in fuzzy two level pattern recognition abstract pattern recognition with fuzzy sets is considered with regard to medical diagnostic problems an alternative interpretation of membership grade is suggested which expresses the degree of illness of a patient with respect to a certain disease a formal statement of a two level fuzzy classifier is presented the main emphasis is put on additional criteria designed to evaluate a fuzzy diagnostic decision for an unknown object two groups of criteria are formed decision making connected and domain dependent the decision making group of criteria can be viewed as related to the soft consensus measure in group decisions theory interconnections between criteria are discussed the notions proposed are illustrated with real medical data from the fields of aviation medicine and neonatology

logarithmic least squares prioritization and completion methods for interval fuzzy preference relations based on geometric transitivity abstract this article introduces the notion of geometric transitivity which may be used to define consistent interval fuzzy preference relations some useful properties are presented for consistent interval fuzzy preference relations a close investigation reveals that existing methods for determining the analogous property of consistency are not robust to permutations of the pairwise judgments and not able to reflect the hesitancy in the decision maker s preference a parametric transformation formula is put forward to convert a normalized interval weight vector into a consistent interval fuzzy preference relation by minimizing the squared difference between the logarithm of the ratio of the original judgment and the logarithm of the ratio of the converted consistent one a logarithmic least squares model is developed to derive interval weights from any interval fuzzy preference relation based on geometric transitivity a logarithmic least squares model is established to rectify inconsistency for complete and inconsistent interval fuzzy preference relations and a logarithmic least squares completion approach is further developed to estimate missing values for incomplete interval fuzzy preference relations numerical examples are furnished to show the validity of the proposed models and compare with other existing methods

multiple attribute decision making based on fuzzy preference information on alternatives ranking and weighting this paper investigates the multiple attribute decision making madm problem with fuzzy preference information on alternatives and proposes an eigenvector method to rank them three optimization models are introduced to assess the relative importance weights of attributes in a madm problem which integrate subjective fuzzy preference relations and objective information in different ways since the decisions these models lead to are based on both subjective and objective information they are more balanced and credible than those that consider only one type of information an example is provided to illustrate the application of the proposed models

group majorization the convex hulls of sets of matrices and the diagonal element singular value inequalities abstract a group induced preorder on matrix space permits the description of the convex hulls of sets of proper and improper real matrices with given singular values and also permits a new proof of the necessity of the known relations between the diagonal elements and singular values of a real matrix

managing non homogeneous information in group decision making within the frame of decision aid literature decision making problems with multiple sources of information have drawn the attention of researchers from a wide spectrum of disciplines in decision situations with multiple individuals each one has his own knowledge on the alternatives of the decision problem the use of information assessed in different domains is not a seldom situation this non homogeneous information can be represented as values belonging to domains with different nature as linguistic numerical and interval valued or can be values assessed in label sets with different granularity multi granular linguistic information decision processes for solving these problems are composed by two phases aggregation and exploitation the main problem to deal with non homogeneous contexts is how to aggregate the information assessed in these contexts in this paper taking as base the 2 tuple fuzzy linguistic representation model we shall develop an aggregation process for dealing with non homogeneous contexts in first place we shall develop an aggregation process for combining numerical interval valued and linguistic information afterwards we shall propose different extensions of this process to deal with contexts in which can appear other type of information as intuitionistic fuzzy sets or multi granular linguistic information

consistent models of transitivity for reciprocal preferences on a finite ordinal scale in this paper we consider a decision maker who shows his her preferences for different alternatives through a finite set of ordinal values we analyze the problem of consistency taking into account some transitivity properties within this framework these properties are based on the very general class of conjunctors on the set of ordinal values each reciprocal preference relation on a finite ordinal scale has both a crisp preference and a crisp indifference relation associated to it in a natural way taking this into account we have started by analyzing the problem of propagating transitivity from the preference relation on a finite ordinal scale to the crisp preference and indifference relations after that we carried out the analysis in the opposite direction we provide some necessary and sufficient conditions for that propagation and therefore we characterize the consistent class of conjunctors in each direction

on fuzzy tournaments and their solution concepts in group decision making abstract assuming as the point of departure a set of individual or collective fuzzy tournaments complete and reciprocal binary relations representing the preferences of the particular individuals or their group as a whole respectively we define some new solution concepts in group decision making as counterparts of the respective solution concepts in the case of nonfuzzy tournaments complete and asymmetric binary relations basically the new solution concepts are mainly counterparts of some sets of undominated options uncovered sets and banks sets we consider the cases of both the conventional nonfuzzy and fuzzy majorities

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

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

building consensus in group decision making with an allocation of information granularity abstract consensus is defined as a cooperative process in which a group of decision makers develops and agrees to support a decision in the best interest of the whole it is a questioning process more than an affirming process in which the group members usually modify their choices until a high level of agreement within the group is achieved given the importance of forming an accepted decision by the entire group the consensus problem has attained a great attention as it is a major goal in group decision making in this study we propose the concept of the information granularity being regarded as an important and useful asset supporting the goal to reach consensus in group decision making by using fuzzy preference relations to represent the opinions of the decision makers we develop a concept of a granular fuzzy preference relation where each pairwise comparison is formed as a certain information granule say an interval fuzzy set rough set and alike instead of a single numeric value as being more abstract the granular format of the preference model offers the required flexibility to increase the level of agreement within the group using the fact that we select the most suitable numeric representative of the fuzzy preference relation

global small solutions of 3d incompressible oldroyd b model without damping mechanism abstract in this paper we prove the global existence of small smooth solutions to the three dimensional incompressible oldroyd b model without damping on the stress tensor the main difficulty is the lack of full dissipation in stress tensor to overcome it we construct some time weighted energies based on the special coupled structure of system such type energies show the partial dissipation of stress tensor and the strongly full dissipation of velocity in the view of treating nonlinear term as a linear term we also apply this result to 3d incompressible viscoelastic system with hookean elasticity and then prove the global existence of small solutions without the physical assumption div curl structure as previous works

global existence in critical spaces for flows of compressible viscous and heat conductive gases we are concerned with global existence and uniqueness of strong solutions for a general model of viscous and heat conductive gases the initial data are supposed to be close to a stable equilibrium with constant density and temperature using uniform estimates for the linearized system with a convection term we get global well posedness in a functional setting invariant with respect to the scaling of the associated equations in space dimension n 3 we also show a smoothing effect on the velocity and the temperature and a decay on the difference between the density and the constant reference state these results extend a previous paper devoted to the barotropic case see 5

a rational consensus model in group decision making using linguistic assessments abstract a new consensus model for the consensus reaching process in a linguistic framework is presented in heterogeneous group decision making problems called rational consensus model it is guided by some linguistic consensus and linguistic consistency meaures all the measures are calculated from a set of linguistic preference relations used to provide experts opinions this consensus model allows more rational consensus solutions to be obtained and thus more human consistency to be incorporated in decision support systems

a fuzzy multicriteria group decision making approach to select configuration items for software development selection of configuration items in software configuration management is important to determine the software quality and reduce the development time and cost the objective of this research is to develop a multicriteria group decision making model based on fuzzy set theory to improve the configuration items selection process since most information available in this stage is not numerical fuzzy set theory is used to represent the evaluation ratings of candidate items the developed model ranks candidate items into partial or complete orders that can assist decision makers in selecting more proper set of configuration items the consensus measures are also developed to determine the group acceptability of the obtained ranking orders in addition sensitivity analysis can be performed to examine the solution robustness an example of flight simulator development project is used to illustrate the concept developed

majorization doubly stochastic matrices and comparison of eigenvalues abstract 1 basic properties of majorization 2 isotone maps and algebraic operations 3 double sub and superstochasticity 4 doubly stochastic matrices 5 doubly stochastic matrices with minimum permanent 6 comparison of eigenvalues 7 doubly stochastic maps

a distance based framework to deal with ordinal and additive inconsistencies for fuzzy reciprocal preference relations consistency of preference relations is related to rationality the lack of consistency in decision making often leads to misleading solutions this paper studies the ordinal and cardinal consistency problems of fuzzy reciprocal preference relations first the concept of ordinal consistency of fuzzy reciprocal preference relations is introduced and analyzed a lp distance based method is proposed to formulate the underlying optimization problems as goal programming gp models for ordinal and additive consistency problems respectively by setting different p three gp models are obtained a a linear gp model where p 1 b a minmax gp model where p and c an extended gp model which integrates the two previous models in particular cases utilizing these models we can solve the ordinal and additive consistency problems for fuzzy reciprocal preference relations the proposed model can preserve the initial preference information as much as possible finally a numerical example and comparative analysis are provided to show effectiveness and validity of the proposed method

softer optimization and control models via fuzzy linguistic quantifiers a softening of a basic formulation of multicriterion optimization and control multistage decision making is presented for optimization instead of seeking an optimal solution that best satisfies all the fuzzy objectives as has been done so far we seek an optimal solution that best satisfies most much more than 50 etc a linguistic quantifier in general of the fuzzy objectives for control we seek in turn an optimal sequence of controls that best satisfies the fuzzy constraints and fuzzy goals at most much more than 50 etc of the control stages a calculus of linguistically quantified statements based upon fuzzy sets and possibility theory is used some applications to softer evidence aggregation in expert systems are also indicated

a method for repairing the inconsistency of fuzzy preference relations this paper investigates the inconsistency problems of preference information about alternatives expressed as a fuzzy preference relation by a decision maker an analysis method is presented to identify the inconsistency and weak transitivity of a fuzzy preference relation and to repair its inconsistency to reach weak transitivity first several definitions are given on additive consistency inconsistency and weak transitivity of a fuzzy preference relation next two methods derived from graph theory are presented to judge whether a fuzzy preference relation has weak transitivity or not then an algorithm is developed to repair an inconsistent fuzzy preference relation and to make it become one with weak transitivity via a synthesis matrix which reflects the relationship between the fuzzy preference relation with additive consistency and the initial one given by a decision maker a convergence theorem is also given for the algorithm lastly two numerical examples are shown to illustrate the proposed method

a fuzzy multi criteria decision making model by associating technique for order preference by similarity to ideal solution with relative preference relation generally classical multi criteria decision making mcdm methods were extended to encompass uncertainty and vagueness of messages under fuzzy environment for solving decision making problems especially for technique for order preference by similarity to ideal solution topsis in the fuzzy extension of topsis fuzzy numbers comparison and aggregation based on fuzzy preference relation are important issues to compute distance values between alternatives and ideal or anti ideal solution or rank feasible alternatives because lots of messages are reserved by fuzzy preference relation however fuzzy preference relation on pair wise comparison is commonly too complex to calculate to avoid the drawback we use a relative preference relation improved from fuzzy preference relation in the fuzzy extension of topsis for computing distance values between alternatives and ideal or anti ideal solution or obtaining relative closeness coefficients of alternatives thus the relative preference relation on fuzzy numbers will be associated with topsis under fuzzy environment to develop a fuzzy multi criteria decision making fmcdm model through the association above fmcdm problems can be easily solved by the model further we compare the proposed model with other methods to demonstrate the model s feasibility and rationality

a generalization of fuzzy multistage decision making and control via linguistic quantifiers abstract multistage incision making control under fuzziness is considered at each control stage a fuzzy constraint is imposed on the control applied and a fuzzy goal is imposed on the state attained an optimal sequence of controls is sought which maximizes the membership function of the fuzzy decision which is assumed to be the intersection of fuzzy constraints and fuzzy goals thin is basically equivalent to the determination of an optimal sequence of controls which best satisfies the fuzzy constraints and fuzzy goals at nil the control stages the generalization proposed in the paper replaces the strict all the something milder for example most thus we seek an optimal sequence of controls which best satisfies the fuzzy constraints and fuzzy goals at for example most of the control stages a calculus of linguistically quantified statements based upon fuzzy sets and possibility theory is used first the algebraic method is employed the resulting control problem is solved by dy

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

an investigation into relations between some transitivity related concepts abstract there exists a variety of transitivity notions in the literature to eliminate the possible inconsistency adherent to a fuzzy preference relation in ranking fuzzy quantities or alternatives the relationships among max min transitivity restricted max min transitivity quasitransitivity weak transitivity consistency and acyclicity are investigated we point out that max min transitivity and transitivity are very strong restrictions on a fuzzy preference relation and acyclicity is the weakest one with a certain transitivity condition an ordering procedure is suggested to obtain a total order relation among fuzzy quantities or alternatives based on a fuzzy preference relation

integrating multiplicative preference relations in a multipurpose decision making model based on fuzzy preference relations the aim of this paper is to study the integration of multiplicative preference relation as a preference representation structure in fuzzy multipurpose decision makingproblems assumingfuzzy multipurpose decision makingproblems under di4erent preference representation structures ordering utilities and fuzzy preference relations and using the fuzzy preference relations as uniform representation elements the multiplicative preference relations are incorporated in the decision problem by means of a transformation function between multiplicative and fuzzy preference relations a consistency study of this transformation function which demonstrates that it does not change the informative content of multiplicative preference relation is shown as a consequence a selection process based on fuzzy majority for multipurpose decision makingproblems under multiplicative preference relations is presented to design it an aggregation operator of information called ordered weighted geometric operator is introduced and two choice degrees the quanti7er guided dominance degree and the quanti7er guided non dominance degree are de7ned for multiplicative preference relations c 2001 elsevier science b v all rights reserved

global solutions for incompressible viscoelastic fluids we prove the existence of both local and global smooth solutions to the cauchy problem in the whole space and the periodic problem in the n dimensional torus for the incompressible viscoelastic system of oldroyd b type in the case of near equilibrium initial data the results hold in both two and three dimensional spaces the results and methods presented in this paper are also valid for a wide range of elastic complex fluids such as magnetohydrodynamics liquid crystals and mixture problems

modeling and simulation of three dimensional planar contraction flow of viscoelastic fluids with ptt giesekus and fene p constitutive models abstract the planar contraction flow is a representative benchmark problem that is often used as a stringent test for the robustness of the numerical method to predict real flow patterns of viscoelastic fluids a numerical methodology based on the penalty finite element method with a decoupled algorithm is presented in the study to simulate three dimensional flow of viscoelastic fluids through planar contraction the viscoelastic rheological responses are described by using three kind differential constitutive models including the phan thien tanner ptt model the giesekus model and the finite extensible nonlinear elastic dumbbell with a peterlin closure approximation fene p model the discrete elastic viscous split stress devss formulation in cooperating with the inconsistent streamline upwind su scheme is employed to improve the computational stability the simulation results of flow velocity and stress on different sections of the flow field are compared with quinzani s experimental results that detected by laser doppler velocimetry and flow induced birefringence technologies it is found that the simulation results predicted with three kind differential constitutive models agree well with the experimental results the numerical methodology proposed in the study can be used successfully to predict complex flow patterns of viscoelastic fluids

the incompressible limit in l p type critical spaces this paper aims at justifying the low mach number convergence to the incompressible navier stokes equations for viscous compressible flows in the ill prepared data case the fluid domain is either the whole space or the torus a number of works have been dedicated to this classical issue all of them being to our knowledge related to l 2 spaces and to energy type arguments in the present paper we investigate the low mach number convergence in the l p type critical regularity framework more precisely in the barotropic case the divergence free part of the initial velocity field just has to be bounded in the critical besov space dot b d p 1 p r cap dot b 1 infty 1 for some suitable p r in 2 4 times 1 infty we still require l 2 type bounds on the low frequencies of the potential part of the velocity and on the density though an assumption which seems to be unavoidable in the ill prepared data framework because of acoustic waves in the last part of the paper our results are extended to the full navier stokes system for heat conducting fluids

the ordinal consistency of an incomplete reciprocal preference relation the ordinal consistency is the usual weak transitivity condition that a logical and consistent person should use if he she does not want to express inconsistent opinions and therefore becomes the minimum requirement condition that a consistent reciprocal preference relation should verify in this paper we define and study the ordinal consistency of an incomplete reciprocal preference relation we then develop an algorithm to judge whether an incomplete reciprocal preference relation is ordinally consistent this proposed algorithm can also find all cycles of length 3 to n in the incomplete digraph of the incomplete reciprocal preference relation based on this proposed algorithm and two rules we develop another algorithm to repair an inconsistent incomplete reciprocal preference relation and to convert it to one with ordinal consistency our algorithm eliminates the cycles of length 3 to n in the digraph of an incomplete reciprocal preference relation most effectively our proposed method can preserve the initial preference information as much as possible furthermore the proposed method can be used for an incomplete reciprocal preference relation with strict comparison and non strict comparison information finally the effectiveness and validity of the proposed method are illustrated with examples

group choice under fuzzy information the group choice problem under fuzzy information about the criteria the choice has to satisfy or and about the elements among which the choice has to be made is analyzed two ways of making choice on a set of elements a are considered in detail 1 non deterministic choice the group or the individual is able to select only some subset of elements s mostly preferred with respect to given criteria without indicating any preference intensity on s the elements of s are called significant 2 deterministic choice the group or the individual is able to order all elements in a according to the strength of the expressed preferences socially satisfactory group choice function ssgcf under fuzzy information is defined as a choice function compatible with four elementary requirements formulated similarly to the classical conditions u p i and d firstly presented by the founder of the modern group choice theory k arrow two theorems of existence of such a function are proved and used for formulating a principle called incoherence principle in group choice a deterministic group choice is incompatible with deterministic individual choices either a non deterministic group choice can be obtained on the basis of deterministic individual choices or a deterministic group choice on the basis of non deterministic individual choices conformably to a phenomenon known in the group choice theory as manipulating the individual choices it is proved that there is a ssgcf resistant against manipulating and mapping the individual preference orderings into a non deterministic choice of the group an individual has a right to be decisive if his her significant elements are recognised to be significant for all the group it is proved that there is a group choice function mapping the individual choices into a non deterministic choice of the group and compatible with conditions u p i and the requirement each individual to be decisive

distance based consensus models for fuzzy and multiplicative preference relations this paper proposes a distance based consensus model for fuzzy preference relations where the weights of fuzzy preference relations are automatically determined two indices an individual to group consensus index ici and a group consensus index gci are introduced an iterative consensus reaching algorithm is presented and the process terminates until both the ici and gci are controlled within predefined thresholds the model and algorithm are then extended to handle multiplicative preference relations finally two examples are illustrated and comparative analyses demonstrate the effectiveness of the proposed methods

multiperson decision making based on multiplicative preference relations abstract a multiperson decision making problem where the information about the alternatives provided by the experts can be presented by means of different preference representation structures preference orderings utility functions and multiplicative preference relations is studied assuming the multiplicative preference relation as the uniform element of the preference representation a multiplicative decision model based on fuzzy majority is presented to choose the best alternatives in this decision model several transformation functions are obtained to relate preference orderings and utility functions with multiplicative preference relations the decision model uses the ordered weighted geometric operator to aggregate information and two choice degrees to rank the alternatives quantifier guided dominance degree and quantifier guided non dominance degree the consistency of the model is analysed to prove that it acts coherently

on hydrodynamics of viscoelastic fluids in this paper we study a hydrodynamic system describing fluids with viscoelastic properties after a brief examination of the relations between several models we shall concentrate on a few analytical issues concerning them in particular we establish local existence and global existence with small initial data of classical solutions for an oldroyd system without an artificially postulated damping mechanism

transitivity frameworks for reciprocal relations cycle transitivity versus fg transitivity for a reciprocal relation q on a set of alternatives a two transitivity frameworks which generalize both t transitivity and stochastic transitivity are compared the framework of cycle transitivity introduced by the present authors soc choice welf to appear and which is based upon the ordering of the numbers q a b q b c and q c a for all a b c a 3 and the framework of fg transitivity introduced by switalski fuzzy sets and systems 137 2003 85 as an immediate generalization of stochastic transitivity the rules that enable to express fg transitivity in the form of cycle transitivity and cycle transitivity in the form of fg transitivity illustrate that for reciprocal relations the concept of cycle transitivity provides a framework that can cover more types of transitivity than does the concept of fg transitivity

global existence in critical spaces for compressible navier stokes equations we investigate global strong solutions for isentropic compressible fluids with initial data close to a stable equilibrium we obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations more precisely the initial velocity has the same critical regularity index as for the incompressible homogeneous navier stokes equations and one more derivative is needed for the density we point out a smoothing effect on the velocity and a l 1 decay on the difference between the density and the constant reference state the proof lies on uniform estimates for a mixed hyperbolic parabolic linear system with a convection term

visualizing and rectifying different inconsistencies for fuzzy reciprocal preference relations abstract consistency is related with reasonableness this paper proposes a graphical method to visualize and rectify different inconsistencies for fuzzy reciprocal preference relations fprs and the consistency includes the ordinal and cardinal consistencies ordinal inconsistency implies cardinal inconsistency but not vice versa and cardinal consistency of fprs includes additive consistency and multiplicative consistency therefore there are four types of inconsistencies includes 1 the additive inconsistency 2 the multiplicative inconsistency 3 the ordinal and additive inconsistencies and 4 the ordinal and multiplicative inconsistencies first gower plots are proposed to visualize the ordinal and cardinal inconsistencies on a two dimensional plane then some optimization models are formulated to rectify the four different types of inconsistences respectively some examples are illustrated to show how the models work and comparisons with the existing methods are also offered to show the advantages of the proposed methods

global well posedness for compressible navier stokes equations with highly oscillating initial velocity in this paper we prove global well posedness for compressible navier stokes equations in the critical functional framework with the initial data close to a stable equilibrium this result allows us to construct global solutions for the highly oscillating initial velocity the proof relies on a new estimate for the hyperbolic parabolic system with convection terms 2010 wiley periodicals inc

deviation square priority method for distinct preference structures based on generalized multiplicative consistency preference structures such as fuzzy preference relations incomplete fuzzy preference relations utility values and preference orderings are very useful in depicting the decision makers preferences over the considered objects in group decision making they have been attracting great interest from both researchers and practitioners in recent decades an important issue on these preference structures is to investigate the techniques of deriving priority weights of the objects from them in this paper based on generalized multiplicative consistency we establish a general nonlinear optimization model with fuzzy preference relations incomplete fuzzy preference relations utility values and preference orderings by solving the model we get a system of nonlinear equations and prove the uniqueness of its solution then a convergent iterative algorithm is devised to derive the priority weights from this system of equations the model and the algorithm include a variety of special cases suitable for group decision making with one or several of the aforementioned preference structures a practical case illustration concerning a manufacturing company that is searching for the best compression ignition engine design is provided and the numerical results of the developed models and the algorithm and the existing ones are also compared and analyzed in order to demonstrate the advantages and practicality of our models and algorithm

monotonicity based ranking on the basis of multiple partially specified reciprocal relations abstract the aggregation of rankings is a recurrent task in several fields of application in a recent work by rademaker and de baets a ranking rule based on a natural monotonicity property was proposed in the context of social choice theory this rule is built on the premise that for a ranking a b c to represent a group s opinion it would be natural that the strength with which a c is supported should not be less than both the strength with which a b and the strength with which b c are supported a first approach to this ranking rule considering totally specified monotone reciprocal relations on a bipolar qualitative scale has already been taken in this paper a more general setting is considered each voter is allowed to provide a partially specified reciprocal relation that may not be monotone on the unit interval additionally new ways of measuring the cost of imposing monotonicity are introduced

a fuzzy approach for modelling visual texture properties abstract in this paper we address the problem of simulating the human perception of texture properties in images in particular we have focused our study on the properties of coarseness contrast and directionality that play a fundamental role in the human perception of texture the objective is not to precisely identify classify or discriminate between different textures as a whole but to be able to assess the presence of each texture property in the image for this purpose fuzzy sets defined on the domain of different groups of measures are employed in order to model each property by using parametric membership functions the corresponding parameters are obtained by learning a functional relationship between the computational values given by the measures and the human perception the performance of each fuzzy set is analyzed and tested with the human assessments and a ranking of subsets of measures is obtained according to their ability to represent the perception of the property allowing us to identify the most suitable combination of measures

the w reciprocity rule abstract given a small number of choices a matrix is a convenient way to represent a fuzzy preference relation usually this matrix is reciprocal the w reciprocity rule is presented here as a way to relax the rigidity of the reciprocal assumption and to embody linguistic meanings for indifference and for the representation of the converse preference

consistency analysis and group decision making based on triangular fuzzy additive reciprocal preference relations a positive triangular fuzzy number is expressed by a cross ratio expressed triplet operational laws are established for cross ratio expressed triangular fuzzy numbers cretfns multiplicative consistency is analyzed for triangular fuzzy additive reciprocal preference relations a triangular fuzzy weighted geometric operator is developed to aggregate cretfnsa novel method is put forward for comparing two cretfns triangular fuzzy numbers are effective in modeling imprecise and uncertain information and have been widely applied in decision making this paper uses a cross ratio expressed triplet to characterize a positive triangular fuzzy number and introduces notions of cross ratio expressed triangular fuzzy numbers cretfns and triangular fuzzy additive reciprocal preference relations tfarprs we present transformation methods between tfarprs and triangular fuzzy multiplicative reciprocal preference relations and develop operational laws of cretfns such as complement addition multiplication and power a cross ratio expressed triangular fuzzy multiplication based transitivity equation is established to define multiplicative consistency of tfarprs the new consistency captures tanino s multiplicative consistency among the cross ratio expressed modal values and geometric consistency of the interval fuzzy preference relation constructed from lower and upper support values of cross ratio expressed triangular fuzzy judgments some desirable properties are furnished for multiplicatively consistent tfarprs we propose a cross ratio expressed triangular fuzzy weighted geometric operator to aggregate cretfns and extend it to fuse tfarprs score and uncertainty index functions are defined and employed to devise a novel comparison method for cretfns a detailed procedure is put forward to solve group decision making problems with tfarprs six numerical examples are provided to illustrate the validity and applicability of the proposed models