an evidential reasoning based consensus model for multiple attribute group decision analysis problems with interval valued group consensus requirements abstract with the aim of modeling multiple attribute group decision analysis problems with group consensus gc requirements a gc based evidential reasoning approach and further an attribute weight based feedback model are sequentially developed based on an evidential reasoning er approach in real situations however giving precise crisp assessments for alternatives is often too restrictive and difficult for experts due to incompleteness or lack of information experts may also find it difficult to give appropriate assessments on specific attributes due to limitation or lack of knowledge experience and provided data about the problem domain in this paper an er based consensus model ercm is proposed to deal with these situations in which experts assessments are interval valued rather than precise correspondingly predefined interval valued gc igc requirements need to be reached after group analysis and discussion within specified times also the process of reaching igc is accelerated by a feedback mechanism including identification rules at three levels consisting of the attribute alternative and global levels and a suggestion rule particularly recommendations on assessments in the suggestion rule are constructed based on recommendations on their lower and upper bounds detected by the identification rule at a specific level a preferentially developed industry selection problem is solved by the ercm to demonstrate its detailed implementation process validity and applicability

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

group preference aggregation methods employed in ahp an evaluation and an intrinsic process for deriving members weightages abstract the analytic hierarchy process ahp is one of the popular and powerful techniques for decision making a detailed survey of the literature has revealed that there exists no formal evaluation of the group preference aggregation methods currently employed in ahp this paper provides such an evaluation using well established social choice axioms which govern the process of combining individual opinions to obtain a single group opinion the geometric mean method gmm and the weighted arithmetic mean method wamm are the two methods evaluated it is shown using counter examples that the gmm does not always satisfy the pareto optimality axiom which is one of the prominent and widely accepted social choice axioms this finding is significant as the gmm has been the most commonly used method in ahp for combining individual opinions to form a group opinion the other method viz wamm has satisfied all the axioms except the independence of irrelevant alternatives axiom in order to use the wamm one has to find the weightages importance to be assigned to the members of the group this is often a difficult task especially so if the group is large as in the case of public policy decisions and when judgements are elicited through the use of questionnaires these situations need an objective method to derive members weightages but only a few studies are available in the literature to address such a situation we propose a simple and intuitively appealing eigenvector based method to intrinsically determine the weightages for group members using their own subjective opinions the superiority of the proposed method over the previous methods is brought out in the paper

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

algorithms for improving consistency or consensus of reciprocal 0 1 valued preference relations we investigate the consistency and consensus of reciprocal 0 1 valued preference relations also called fuzzy preference relations by many authors based on the multiplicative consistency property which is an important issue in fuzzy set theory an algorithm is first developed to improve the consistency level of a reciprocal 0 1 valued preference relation and the corresponding algorithm for the incomplete reciprocal 0 1 valued preference relation is also developed we further propose the consensus improving algorithms for individual reciprocal 0 1 valued preference relations or incomplete ones the convergence and robustness of the algorithms are proven and some important conclusions are obtained in addition the proposed algorithms can improve the consistency or consensus of reciprocal 0 1 valued preference relations with less interactions with the decision makers which can save a lot of time and obtain the results quickly

stochastic group preference modelling in the multiplicative ahp a model of group consensus this paper proposes a model for the representation of a consensus seeking group decision making process under the multiplicative variant of the analytic hierarchy process ahp in particular it proposes a group preference model which expresses the group s preference intensity judgements as random variables with associated probability distributions and the structure of the multiplicative ahp is exploited to derive interval judgements for the alternatives final impact scores as perceived by the group these interval judgements can be used to determine the probability that a rank reversal may occur amongst alternatives due to the group preference uncertainty i e to assess the stability of the final impact score vector which in turn offers information about the degree of consensus within the group about the decision

on the complexity of sphere decoding in digital communications sphere decoding has been suggested by a number of authors as an efficient algorithm to solve various detection problems in digital communications in some cases the algorithm is referred to as an algorithm of polynomial complexity without clearly specifying what assumptions are made about the problem structure another claim is that although worst case complexity is exponential the expected complexity of the algorithm is polynomial herein we study the expected complexity where the problem size is defined to be the number of symbols jointly detected and our main result is that the expected complexity is exponential for fixed signal to noise ratio snr contrary to previous claims the sphere radius which is a parameter of the algorithm must be chosen to ensure a nonvanishing probability of solving the detection problem this causes the exponential complexity since the squared radius must grow linearly with problem size the rate of linear increase is however dependent on the noise variance and thus the rate of the exponential function is strongly dependent on the snr therefore sphere decoding can be efficient for some snr and problems of moderate size even though the number of operations required by the algorithm strictly speaking always grows as an exponential function of the problem size

relationships between l 1 metrics on linear ranking spaces in this paper we examine various l 1 distance measures on linear ranking spaces beginning with the absolute position measure of blin we construct two offspring measures one based on relative rank positioning the other on relative object positioning the first is shown to be equivalent to the permutation vector method of cook and seiford the other is equivalent to the preference matrix method of kemeny and snell we also prove that the kemeny and snell method can be formulated as a quadratic assignment problem

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

a novel group ranking model for revealing sequence and quantity knowledge abstract the aggregation of individuals preferences into a consensus ranking is a group ranking problem which has been widely utilized in various applications such as decision support systems recommendation systems and voting systems gathering the comparison of preferences and aggregate them to gain consensuses is a conventional issue for example b c d a indicates that b is favorable to c and c d is somewhat favorable but not fully favorable to d a where and are comparators and a b c and d are items recently a new type of ranking model was proposed to provide temporal orders of items the order b c a means that b and c can occur simultaneously and are also before a although this model can derive the order ranking of items the knowledge about quantity related items is also of importance to approach more real life circumstances for example when enterprises or individuals handle their portfolios in financial management two considerations the sequences and the amount of money for investment objects should be raised initially in this study we propose a model for discovering consensus sequential patterns with quantitative linguistic terms experiments using synthetic and real datasets showed the model s computational efficiency scalability and effectiveness

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

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

a new generic maximum likelihood metric expression for space time block codes with applications to decoding the metric expression for a generic linear space time block code stbc is studied using a different approach to vectorization and a new representation of the metric the new representation lends itself to a simple measure of reliability based on the sum of inner products and provides a quantifiable definition for minimum distance of a stbc this provides the framework for a new family of near maximum likelihood ml and ml decoding algorithms it also has applications in the development of optimality test criteria for stbcs as well as in the design of stbcs with low decoding complexity

a soft measure of consensus in the setting of partial fuzzy preferences abstract consensus as traditionally meant to be a full and unanimous agreement is often not reachable in practice a degree of consensus for indicating how far a particular group of individuals is from consensus may be therefore very useful we propose a new measure degree of consensus which is more human consistent in the sense that it better reflects a real human perception of the essence of consensus in practice basically our consensus measure expresses the degree to which say most of the important individuals agree as to their testimonies concerning almost all of the relevant options the point of departure is the set of individual testimonies which are here the individual fuzzy preference relations as a formal tool we use a fuzzy logic based calculus of linguistically quantified propositions

real valued maximum likelihood decoder for quasi orthogonal space time block codes in this letter we propose a low complexity maximum likelihood ml decoding algorithm for quasi orthogonal space time block codes qostbcs based on the real valued lattice representation and qr decomposition we show that for a system with rate r ns t where ns is the number of transmitted symbols per t time slots the proposed algorithm decomposes the original complex valued system into a parallel system with ns 2 times 2 real valued components thus allowing for a simple joint decoding of two real symbols for a square qam constellation with l points l qam this algorithm achieves full diversity by properly incorporating two dimensional rotation using the optimal rotation angle and the same rotating matrix for any number of transmit antennas n ges 4 we show that the complexity gain becomes greater when n or l becomes larger the complexity of the proposed algorithm is shown to be linear with the number of transmitted symbols ns

a new consensus ranking approach for correlated ordinal information based on mahalanobis distance the cohesiveness among experts opinions is addressed from a global point of view a new procedure to codify ordinal information is provided and characterized a measurement of the degree of dissensus designed for possibly correlated alternatives is defined a procedure to obtain a social consensus solution based on the mahalanobis distance is investigated we investigate from a global point of view the existence of cohesiveness among experts opinions we address this general issue from three basic essentials the management of experts opinions when they are expressed by ordinal information the measurement of the degree of dissensus among such opinions and the achievement of a group solution that conveys the minimum dissensus to the experts group accordingly we propose and characterize a new procedure to codify ordinal information we also define a new measurement of the degree of dissensus among individual preferences based on the mahalanobis distance it is especially designed for the case of possibly correlated alternatives finally we investigate a procedure to obtain a social consensus solution that also includes the possibility of alternatives that are correlated in addition we examine the main traits of the dissensus measurement as well as the social solution proposed the operational character and intuitive interpretation of our approaches are illustrated by an explanatory example

heuristic aggregation of individual judgments in ahp group decision making using simulated annealing algorithm sa algorithm is used as aggregation procedure in ahp group decision making the group priority vector is obtained by minimization of the euclidean distance objective search for maximum consensus between individuals within the group proposed procedure is invariant to any prioritization method proposed procedure performs better or at least equally to several other procedures there are various aggregation procedures for obtaining a group priority vector within analytic hierarchy process ahp supported decision making processes this paper will introduce a heuristic aggregation procedure based on simulated annealing sa algorithm to be used for the purposes of obtaining a group priority vector at any node of an ahp hierarchy the proposed procedure performs its aggregation process by minimizing the group euclidean distance ged consensus measure across group weights and judgments and the group vector obtained in this way is invariant to any prioritization method in other words there is no need to have individual priority vectors as is required by some other aggregation procedures along with sa minimization of the ged the group rank reversal minimum violation criterion is implemented as a control mechanism as well as the consensus measure based on the ranks of alternatives the presented procedure is compared with several reported combinations of different prioritization methods and group aggregation procedures five examples from literature are used to show that the proposed procedure performs better or at least equally to several other well known combinations of prioritization and aggregation in ahp group decision making frameworks

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

on the borda kendall consensus method for priority ranking problems this paper investigates the borda kendall method for the determination of a consensus ranking it is shown that in the case of ties the method does not perform as claimed a minimum variance method for determining the consensus ranking is proposed and its properties examined it is shown to be equivalent to the borda kendall method if ties are not allowed an algorithm to determine the minimum variance consensus ranking in the case of ties is described results obtained from the solution of problems of various sizes are discussed

low complexity sphere decoding algorithm for quasi orthogonal space time block codes space time codes can be decoded by the sphere decoding sd algorithm to reduce the complexity and retain maximum likelihood ml performance in this letter the ml metric of quasi orthogonal space time block codes is written into two independent euclidean norms thus sd can be applied to each function independently the new scheme reduces the complexity by at least 85 for systems with four or more transmit antennas compared with the conventional sd algorithm

accurate algorithms for identifying the median ranking when dealing with weak and partial rankings under the kemeny axiomatic approach abstract preference rankings virtually appear in all fields of science political sciences behavioral sciences machine learning decision making and so on the well known social choice problem consists in trying to find a reasonable procedure to use the aggregate preferences or rankings expressed by subjects to reach a collective decision this turns out to be equivalent to estimate the consensus central ranking from data and it is known to be a np hard problem a useful solution has been proposed by emond and mason in 2002 through the branch and bound algorithm bb within the kemeny and snell axiomatic framework as a matter of fact bb is a time demanding procedure when the complexity of the problem becomes untractable i e a large number of objects with weak and partial rankings in presence of a low degree of consensus as an alternative we propose an accurate heuristic algorithm called fast that finds at least one of the consensus ranking solutions found by bb saving a lot of computational time in addition we show that the building block of fast is an algorithm called quick that finds already one of the bb solutions so that it can be fruitfully considered to speed up even more the overall searching procedure if the number of objects is low simulation studies and applications on real data allows to show the accuracy and the computational efficiency of our proposal

a quasi orthogonal space time block code it has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space time block code is not possible for more than two antennas previous attempts have been concentrated in generalizing orthogonal designs which provide space time block codes with full diversity and a high transmission rate we design rate one codes which are quasi orthogonal and provide partial diversity the decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols

a generalized network formulation of the pairwise comparison consensus ranking model one of the best known and most widely referenced models for representing ordinal preferences is that due to kemeny and snell kemeny j g l j snell 1962 preference ranking an axiomatic approach mathematical models in the social sciences glnn new york 9 23 this model is designed to accommodate pairwise comparison data with an l1 norm used to measure voter disagreement while this model possesses many of the necessary properties for a social choice function solution procedures developed to date have been capable of handling only small problems due to the difficulty of modelling the transitivity requirements of an optimal consensus ranking this paper shows how the consensus formation problem for strict linear orderings can be modelled as a generalized network since efficient computer codes already exist for handling this special structure this approach will permit the solution of much larger problems than has been the case previously

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 numerical scheme for multi point special boundary value problems and application to fluid flow through porous layers abstract in this paper we propose a numerical scheme based on finite differences for the numerical solution of nonlinear multi point boundary value problems over adjacent domains in each subdomain the solution is governed by a different equation the solutions are required to be smooth across the interface nodes the approach is based on using finite difference approximation of the derivatives at the interface nodes smoothness across the interface nodes is imposed to produce an algebraic system of nonlinear equations a modified multi dimensional newton s method is proposed for solving the nonlinear system the accuracy of the proposed scheme is validated by examples whose exact solutions are known the proposed scheme is applied to solve for the velocity profile of fluid flow through multilayer porous media

improved integer linear programming formulations for the job sequencing and tool switching problem in this article we investigate the job sequencing and tool switching problem ssp a np hard combinatorial optimization problem arising from computer and manufacturing systems starting from the results described in tang and denardo 1987 crama et al 1994 and laporte et al 2004 we develop new integer linear programming formulations for the problem that are provably better than the alternative ones currently described in the literature computational experiments show that the lower bounds obtained by the linear relaxation of the considered formulations improve on average upon those currently described in the literature and suggest at the same time new directions for the development of future exact solution approaches

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

the group consensus based evidential reasoning approach for multiple attributive group decision analysis abstract many multiple attribute decision analysis problems include both quantitative and qualitative attributes with various kinds of uncertainties such as ignorance fuzziness interval data and interval belief degrees an evidential reasoning er approach developed in the 1990s and in recent years can be used to model these problems in this paper the er approach is extended to group consensus gc situations for multiple attributive group decision analysis problems in order to construct and check the gc a compatibility measure between two belief structures is developed first considering two experts utilities the compatibility between their assessments is naturally constructed using the compatibility measure based on the compatibility between two experts assessments the gc at a specific level that may be the attribute level the alternative level or the global level can be constructed and reached after the group analysis and discussion within specified times under the condition of gc we conduct a study on the forming of group assessments for alternatives the achievement of the aggregated utilities of assessment grades and the properties and procedure of the extended er approach an engineering project management software selection problem is solved by the extended er approach to demonstrate its detailed implementation process and its validity and applicability

a cardinal dissensus measure based on the mahalanobis distance abstract in this paper we address the problem of measuring the degree of consensus dissensus in a context where experts or agents express their opinions on alternatives or issues by means of cardinal evaluations to this end we propose a new class of distance based consensus model the family of the mahalanobis dissensus measures for profiles of cardinal values we set forth some meaningful properties of the mahalanobis dissensus measures finally an application over a real empirical example is presented and discussed

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

single block coded modulation for mino systems this paper introduces a new class of space time codes that achieve coding gain without a trellis or any form of inter block dependency the construction of the new codes starts from an existing parent space time block code stbc then by increasing the constellation size followed by expurgation of the expanded codebook a better code is obtained at the original transmission rate this method can be applied to a wide variety of space time block codes including orthogonal codes and quasi orthogonal codes a multi stage design algorithm is presented and for orthogonal parent codes an efficient decoding algorithm is developed and its decoding complexity is analyzed despite altering the regular structure of the orthogonal code the decoding complexity is only affected by a constant factor

a multiple criteria decision model with ordinal preference data abstract this paper develops a model for aggregating ordinal preference ranking across multiple criteria criteria weights are developed as part of the optimization process the model utilizes three levels of ordinal priorities 1 preferences among alternatives on the basis of each criterion 2 preferences among the criteria to reflect the importance of those criteria and 3 preferences among the criteria which express the degree to which the respondent can clearly distinguish among the alternatives the model is based upon a data envelopment analysis structure which permits a flexible weighting mechanism for each alternative being ranked

rate one space time block codes with full diversity orthogonal space time block codes provide full diversity and maximum likelihood ml decoding for orthogonal codes can be realized on a symbol by symbol basis it has been shown that rate one complex orthogonal codes do not exist for systems with more than two transmit antennas for a general system with n transmit and m receive antennas it is very desirable to design rate one complex codes with full diversity in this letter we provide a systematic method of designing rate one codes real or complex for a general multiple input multiple output system full diversity of these codes is then achieved by constellation rotation a generalized reduced complexity decoding method for rate one codes is also provided

concordance and consensus this paper deals with the measurement of concordance and the construction of consensus in preference data either in the form of preference rankings or in the form of response distributions with likert items we propose a set of axioms of concordance in preference orderings and a new class of concordance measures the measures outperform classic measures like kendall s t and w and spearman s r in sensitivity and apply to large sets of orderings instead of just to pairs of orderings for sets of n orderings of n items we present very efficient and flexible algorithms that have a time complexity of only o nn 2 remarkably the algorithms also allow for fast calculation of all longest common subsequences of the full set of orderings we experimentally demonstrate the performance of the algorithms a new and simple measure for assessing concordance on likert items is proposed

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 method for measuring consensus within groups this paper presents a new index of disagreement or measure of consensus for comparison of data collected using likert items this new index which assesses the level of disagreement among group members exploits the conditional distribution of the variance for a given mean the variance is often used as a measure of disagreement with high variance seen as a high disagreement in a group however since the range of the variance is a function of the mean this implies that for a mean close to the end points of the scale the range of the variance is relatively small and for a mean at the center of the scale the range of the variance is larger the index of disagreement introduced in this paper takes into account both the mean and the variance and provides a way to compare two groups that is more meaningful than just considering the variance or other measures of disagreement or consensus that only depend on the variance

a general framework for distance based consensus in ordinal ranking models abstract the problem of aggregating a set of ordinal rankings of n alternatives has given rise to a number of consensus models among the most common of these models are those due to borda and kendall which amount to using average ranks and the l1 and l2 distance models a common criticism of these approaches is their use of ordinal rank position numbers directly as the values of being ranked at those levels this paper presents a general framework for associating value or worth with ordinal ranks and develops models for deriving a consensus based on this framework it is shown that the lp distance models using this framework are equivalent to the conventional ordinal models for any p 1 this observation can be seen as a form of validation of the practice of using ordinal data in a manner for which it was presumably not designed in particular it establishes the robustness of the simple borda kendall and median ranking models

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

fluid mechanics of the interface region between two porous layers flow through and over a fluid saturated porous layer is investigated the flow through a porous channel which is assumed to be governed by forchheimer equation is terminated by a porous layer possessing a different structure the flow through which is governed by the brinkman equation at the interface between the physical regions matching conditions on the velocity and shear stress are imposed the flow through this configuration admits solutions which are linear combinations of polynomial and exponential functions the effect of the reynolds number and the darcy numbers on the interface velocity is presented in this work

distance based and ad hoc consensus models in ordinal preference ranking abstract this paper examines the problem of aggregating ordinal preferences on a set of alternatives into a consensus this problem has been the subject of study for more than two centuries and many procedures have been developed to create a compromise or consensus we examine a variety of structures for preference specification and in each case review the related models for deriving a consensus two classes of consensus models are discussed namely ad hoc methods evolving primarily from parliamentary settings over the past 200 years and distance or axiomatic based methods we demonstrate the levels of complexity of the various distance based models by presenting the related mathematical programming formulations for them we also present conditions for equivalence that is for yielding the same consensus ranking for some of the methods finally we discuss various extensions of the basic ordinal ranking structures paying specific attention to partial ranking voting member weighted consensus ranking with intensity of preference and rank correlation methods as alternative approaches to deriving a consensus suggestions for future research directions are given

a dynamic consensus scheme based on a nonreciprocal fuzzy preference relation modeling in this paper we propose a dynamical consensus scheme which makes use of an index of comparability and of an index of concordance to regulate the information flow in the discussion among the experts in addition to the traditional use of a concordance index to identify the discordant expert who can be invited to review his opinion or to explain his judgment to the other experts here an index of comparability is utilized to identify the experts that have faced difficulties in expressing their preferences with this information at hand a moderator can invite the experts that are confident on their opinions to support the experts that are hesitating in the construction of the fuzzy preference relations

a new iterative technique for solving nonlinear second order multi point boundary value problems abstract we present a semi analytical iterative method for solving nonlinear second order multi point boundary value problems to demonstrate the working of the method we consider a particular example of this class of problems in this example we demonstrate the accuracy and convergence of the method to the solution we demonstrate clearly that the method is accurate fast and has a reasonable order of convergence

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

sphere decoding algorithms with improved radius search we start by identifying a relatively efficient version of sphere decoding algorithm sda that performs exact maximum likelihood ml decoding we develop novel algorithms based on an improved increasing radius search iirs which offer error performance and decoding complexity between two extremes the ml receiver and the nulling canceling nc receiver with detection ordering with appropriate choices of parameters our iirs offers the flexibility to trade error performance for complexity we provide design intuitions and guidelines analytical parameter specifications and a semianalytical error performance analysis simulations illustrate that iirs achieves considerable complexity reduction while maintaining performance close to ml

improved methods for calculating vectors of short length in a lattice including a complexity analysis the standard methods for calculating vectors of short length in a lattice use a reduction procedure followed by enumerating all vectors of z in a suitable box however it suffices to consider those x e z which lie in a suitable ellipsoid having a much smaller volume than the box we show in this paper that searching through that ellipsoid is in many cases much more efficient if combined with an appropriate reduction procedure our method allows to do computations in lattices of much higher dimensions several randomly constructed numerical examples illustrate the superiority of our new method over the known ones

measuring consensus and dissensus a generalized index of disagreement using conditional probability abstract we generalize an index of disagreement recently proposed by akiyama et al 2016 which can be applied only to surveys that measure opinions expressed using the standard 5 scale likert scale to a general case that uses any scale with more than five response levels as stated in the aforementioned study the variance alone computed from a survey that employs the likert scale is not an adequate indicator for measuring the disagreement within a group because the range of the variance is a function of the mean to overcome this limitation they define the disagreement index using a conditional probability density function which allows us to compare responses to questions having different means or between groups across different time periods however developing a measure that considers likert scales larger than five has not yet been developed and our work addresses this lacuna as an example we illustrate an advantage of our generalized measure by calculating the disagreement within consumers price expectations

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

priority ranking and consensus formation the case of ties this paper investigates the problem of obtaining a compromise consensus from a set of ordinal rankings of n objects supplied by m committee members earlier work by cook and seiford cook wade d lawrence m seiford 1978 priority ranking and consensus formation management sci 24 16 1721 1732 dealt with the problem of consensus when attention was restricted to complete rankings only that is no ties were permitted this paper examines the general problem which allows for tied preferences a convex polyhedral representation is given of the feasible solution space and a branch and bound procedure is developed for determining an optimal ranking computational results for various problem sizes are presented generalizations and directions for further research are discussed

a concise consensus support model for group decision making with reciprocal preference relations based on deviation measures supporting the process of consensus building has become a major research field in group decision making gdm the purpose of this paper is to present a consistency consensus based decision support model for gdm based on reciprocal preference relations inspired by the concept of a deviation measure between two matrices an individual consistency index and a group consensus index are presented in the support model a consistency control process is designed to make an inconsistent reciprocal preference relation one of acceptable consistency to achieve a predefined consensus level an interactive consensus reaching process is provided where the group reciprocal preference relation is seen as a reference when experts change their preferences theoretical foundations are then established for the proposed model the proposed model revises the original information in a simple and straightforward gradual way in the consensus process the individual rationality level in terms of consistency is maintained two examples are examined to demonstrate the model in practical problems

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

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

standard numerical schemes for coupled parallel flow over porous layers in this work we develop finite difference schemes of various orders of accuracy that are suitable for the simulation of flow through and over porous layers the flow through the porous layer is assumed to be governed by a brinkman type equation and that through free space by the navier stokes equations matching conditions at the interface between layers are invoked to derive numerical expressions for the velocity and shear stress results are compared with the exact solution of flow through a channel bounded by a porous layer

a universal lattice code decoder for fading channels we present a maximum likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver the decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point by judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment

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

fast ml detection for quasi orthogonal stbcs of rate 2 in under determined systems transactions papers a fast maximum likelihood ml detection scheme is proposed for the important quasi orthogonal space time block codes stbcs of symbol rate 2 for three and four transmission antennas in particular the proposed scheme is applicable even to the under determined system where the number of transmission antennas is larger than that of the receive antennas the half of the symbols of the transmission matrix are detected by two dependent double layer sphere decoders which are referred to as dual double layer sphere decoding in this paper the remaining half of the symbols are detected by single symbol detection of which complexity is extremely low numerical results demonstrate that the proposed new detection method improves the detection speed up to ten times depending on the signal to noise ratio snr compared to the state of the art scheme

minimizing adjusted simple terms in the consensus reaching process with hesitant linguistic assessments in group decision making in some real world decision processes decision makers may prefer to provide their opinions using linguistic expressions instead of a single linguistic term particularly they may hesitate between several linguistic terms in this paper we deal with the consensus issue in the hesitant linguistic group decision making gdm problem firstly a novel distance based consensus measure is proposed then using this consensus measure we develop an optimization based consensus model in the hesitant linguistic gdm which minimizes the number of adjusted simple terms in the consensus building furthermore a two stage model is displayed to further optimize the solutions to the proposed consensus model through which we obtain the unique optimal adjustment suggestion to support the consensus reaching process in the hesitant linguistic gdm finally several desirable properties are proposed to justify the proposal and two examples are used to demonstrate the validity of the models

an attribute weight based feedback model for multiple attributive group decision analysis problems with group consensus requirements in evidential reasoning context abstract in an evidential reasoning context a group consensus gc based approach can model multiple attributive group decision analysis problems with gc requirements the predefined gc is reached through several rounds of group analysis and discussion gad in the approach however the gad with no guidance may not be the most appropriate way to reach the predefined gc because several rounds of gad will spend a lot of time of all experts and yet cannot help them to effectively emphasize on the assessments which primarily damage the gc in this paper an attribute weight based feedback model is constructed to effectively identify the assessments primarily damaging the gc and accelerate the gc convergence considering important attributes with the weights more than or at least equal to the mean of the weights of all attributes the feedback model constructs identification rules to identify the assessments damaging the gc for the experts to renew in addition a suggestion rule is introduced to generate appropriate recommendations for the experts to renew their identified assessments the identification rules are constructed at three levels including the attribute alternative and global levels the feedback model is used to solve an engineering project management software selection problem to demonstrate its detailed implementation process its validity and applicability and its advantages compared with the gc based approach