a fusion approach for managing multi granularity linguistic term sets in decision making the aim of this paper is to present a fusion approach of multi granularity linguistic information for managing information assessed in different linguistic term sets multi granularity linguistic term sets together with its application in a decision making problem with multiple information sources assuming that the linguistic performance values given to the alternatives by the different sources are represented in linguistic term sets with different granularity and or semantic in this context a decision process based on two steps is proposed with a view to obtaining the solution set of alternatives first the fusion of the multi granularity linguistic performance values is carried out in order to obtain collective performance evaluations in this step on the one hand the multi granularity linguistic information is made uniform using a linguistic term set as the uniform representation base the basic linguistic term set on the other hand the collective performance evaluations of the alternatives are obtained by means of an aggregation operator being fuzzy sets on the basic linguistic term set second the choice of the best alternative s from the collective performance evaluations is performed to do that a fuzzy preference relation is computed from the collective performance evaluations using a ranking method of pairs of fuzzy sets in the setting of possibility theory applied to fuzzy sets on the basic linguistic term set then a choice degree may be applied on the preference relation in order to rank the alternatives

optimal estimation of a general regression function let e be a convex subset of rd and for each 0 e e let f 0 dt be a probability on the line for any vector an an an2 ann where anl e e let xn1 xnn be independent observations the distribution of xn being f an dt the main results give a method of estimating the unknown regression function an based on a minimum distance recipe under regularity assumptions the proposed estimators are shown in an appropriate framework to be asymptotically normal locally asymptotically minimax and robust the abstract results are illustrated by application to the linear model and to exponential response models in general nothing at all is assumed about the form of the regression function accordingly this forces the limiting normal distributions of the proposed estimators to be located on infinite dimensional linear spaces

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

a robust surveillance scheme for stochastically ordered alternatives we sequentially observe independent observations x 1 x 2 such that initially they have distribution g 0 at some unknown time v they become stochastically larger having distribution g 1 neither g 0 nor g 1 is fully specified we wish to detect that a change has taken place as soon as possible after its occurrence subject to a constraint on the rate of false alarms we derive a family of nonparametric sequential procedures based on ranks with noncontiguous alternatives in mind large sample approximations to the operating characteristics are obtained analytically the proposed procedures all possess robustness of validity because they are based on ranks near optimal sensitivity can be obtained for specific alternatives by choosing an appropriate procedure for example when observations are normally distributed with one standard deviation shift in mean postchange an appropriate nonparametric surveillance scheme yields 97 asymptotic relative efficiency as compared to the optimal procedure when all distributional parameters are known our procedures are computationally feasible monte carlo experiments confirm the applicability of the asymptotic calculations including high levels of efficiency for sample sizes met in practice

benchmarking in linguistic importance weighted aggregations in this work we concentrate on the issue of weighted aggregations and provide a possibilistic approach to the process of importance weighted transformation when both the importances interpreted as benchmarks and the ratings are given by symmetric triangular fuzzy numbers we will show that using the possibilistic approach i small changes in the membership function of the importances can cause only small variations in the weighted aggregate ii the weighted aggregate of fuzzy ratings remains stable under small changes in the nonfuzzy importances iii the weighted aggregate of crisp ratings still remains stable under small changes in the crisp importances whenever we use a continuous implication operator for the importance weighted transformation we illustrate the proposed method by some simple examples

homology computations for complex braid groups ii abstract we complete the computation of the integral homology of the generalized braid group b associated to an arbitrary irreducible complex reflection group w of exceptional type in order to do this we explicitly computed the recursively defined differential of a resolution of z as a z b module using parallel computing we also deduce from this general computation the rational homology of the milnor fiber of the singularity attached to most of these reflection groups

robust estimation via minimum distance methods given a fixed parametric family p it is desired to estimate however due to contaminations of various sorts the data actually collected by the statistician follow a distribution that is close to but possibly distinct from thep s it is proved that under these conditions and in an appropriate asymptotic framework the minimum distance estimators of the cramer von mises type are robust specification of a cramer von mises weight functionh defines a notion of distance each such choice ofh then delineates the kind of contamination possible and leads to an estimator which defends optimally against it when the theory is specialized to location models various choices ofh lead to estimators asymptotically equivalent to such familiar ones as trimmed mean median hodges lehmann estimator and so forth the framework developed herein provides some guidelines for choosing among the possible estimators and suggests that the standard cramer von mises estimator of location is probably as good a robust estimator as any

fuzzy linguistic pert a model for program evaluation and review technique pert under fuzzy linguistic contexts is introduced in this fuzzy linguistic pert network model each activity duration is represented by a fuzzy linguistic description aggregation and comparison of the estimated linguistic expectations of activity durations are manipulated by the techniques of computing with words cw to provide suitable contexts for this purpose we first introduce several variations of basic linguistic labels of a linguistic variable such as weighted linguistic labels generalized linguistic labels and weighted generalized linguistic labels etc and then based on the notion of canonical characteristic value ccv function of a linguistic variable we develop some related cw techniques for aggregation and comparison of these linguistic labels afterward using a computing technique of linguistic probability introduced by zadeh and based on the new developed cw techniques for weighted generalized linguistic labels we investigate the associated linguistic expectation pert network of a fuzzy linguistic pert network also throughout the paper several examples are used to illustrate related notions and applications

complex reflection groups braid groups hecke algebras presentations a la coxeter are given for all irreducible nite com plex re ection groups they provide presentations for the corresponding generalized braid groups for all but six cases which allow us to generalize some of the known properties of nite coxeter groups and their associated braid groups such as the computation of the center of the braid group and the construction of deformations of the nite group algebra hecke algebras we introduce monodromy representations of the braid groups which factorize through the hecke algebras extending results of cherednik opdam kohno and others summary introduction complex re ection groups and their presentations a background from complex re ection groups b presentations braid groups and their diagrams a generalities about hyperplane complements b generalities about the braid groups c the braid diagrams proofs of the main theorems for the braid groups b de e r a notation and prerequisites b computation of b de e r and of its center for d c computation of b e e r and of its center hecke algebras a background from di erential equations and monodromy b a family of monodromy representations of the braid group c hecke algebras diagrams and tables appendix generators of the monodromy around a divisor appendix tables to mathematics subject classi cation primary g we thank jean michel peter orlik pierre vogel for useful conversations and the isaac newton institute for its hospitality while the last version of this manuscript was written up the second named author gratefully acknowledges nancial support by the fondation alexander von humboldt for his stays in paris michel brou e gunter malle raphael rouquier

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

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

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

minimax robust decentralized detection decentralized detection problems are studied where the sensor distributions are not specified completely the sensor distributions are assumed to belong to known uncertainty classes it is shown for a broad class of such problems that a set of least favorable distributions exists for minimax robust testing between the hypotheses it is hence established that the corresponding minimax robust tests are solutions to simple decentralized detection problems for which the sensor distributions are specified to be the least favorable distributions

decomposition numbers for finite coxeter groups and generalised non crossing partitions given a finite irreducible coxeter group w a positive integer d and types t 1 t 2 t d in the sense of the classification of finite coxeter groups we compute the number of decompositions c 1 2 d of a coxeter element c of w such that i is a coxeter element in a subgroup of type t i in w i 1 2 d and such that the factorisation is minimal in the sense that the sum of the ranks of the t i s i 1 2 d equals the rank of w for the exceptional types these decomposition numbers have been computed by the first author in tropics in discrete mathematics m klazar et al eds springer verlag berlin new york 2006 pp 93 126 and seminaire lotharingien combin 54 2006 article b541 the type a n decomposition numbers have been computed by goulden and jackson in europ j combin 13 1992 357 365 albeit using a somewhat different language we explain how to extract the type b n decomposition numbers from results of bona bousquet labelle and leroux adv appl math 24 2000 22 56 on map enumeration our formula for the type d n decomposition numbers is new these results are then used to determine for a fixed positive integer l and fixed integers r 1 r 2 r l the number of multi chains 1 2 l in armstrong s generalised non crossing partitions poset where the poset rank of i equals r i and where the block structure of 1 is prescribed we demonstrate that this result implies all known enumerative results on ordinary and generalised non crossing partitions via appropriate summations surprisingly this result on multi chain enumeration is new even for the original non crossing partitions of kreweras moreover the result allows one to solve the problem of rank selected chain enumeration in the type d n generalised non crossing partitions poset which in turn leads to a proof of armstrong s f m conjecture in type d n thus completing a computational proof of the f m conjecture for all types it also allows one to address another conjecture of armstrong on maximal intervals containing a random multi chain in the generalised non crossing partitions poset

combining numerical and linguistic information in group decision making abstract people give information about their personal preferences in many different ways depending on their background this paper deals with group decision making problems in which the solution depends on information of a different nature i e assuming that the experts express their preferences with numerical or linguistic values the aim of this paper is to present a proposal for this problem we introduce a fusion operator for numerical and linguistic information this operator combines linguistic values assessed in the same label set with numerical ones assessed in the interval 0 1 it is based on two transformation methods between numerical and linguistic values which are defined using the concept of the characteristic values proposed in this paper its application to group decision making problems is illustrated by means of a particular fusion operator guided by fuzzy majority considering that the experts express their opinions by means of fuzzy or linguistic preference relations this operator is used to develop a choice process for the alternatives allowing solutions to be obtained in line with the majority of the experts opinions

information and asymptotic efficiency in parametric nonparametric models asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems for regular estimates and asymptotic minimax bounds the methods used involve i the notion of a hellinger differentiable root density where part of the differentiation is with respect to the nonparametric part of the model to obtain appropriate scores and ii calculation of the effective score for the real or vector finite dimensional parameter of interest as that component of the score function orthogonal to all nuisance parameter scores perhaps infinite dimensional the resulting asymptotic information for estimation of the parametric component of the model is just 4 times the squared l 2 norm of the effective score a corollary of these results is a simple necessary condition for adaptive estimation adaptation is possible only if the scores for the parameter of interest are orthogonal to the scores for the nuisance function or nonparametric part of the model examples considered include the one sample location model with and without symmetry mixture models the two sample shift model and cox s proportional hazards model

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

fudge fuzzy ontology building with consensuated fuzzy datatypes abstract an important problem in fuzzy owl 2 ontology building is the definition of fuzzy membership functions for real valued fuzzy sets so called fuzzy datatypes in fuzzy owl 2 terminology in this paper we present a tool called fudge whose aim is to support the consensual creation of fuzzy datatypes by aggregating the specifications given by a group of experts fudge is freeware and currently supports several linguistic aggregation strategies including the convex combination linguistic owa weighted mean and fuzzy owa and easily allows to build others in we also propose and have implemented two novel linguistic aggregation operators based on a left recursive form of the convex combination and of the linguistic owa

a new version of 2 tuple fuzzy linguistic representation model for computing with words in this paper we provide a new proportional 2 tuple fuzzy linguistic representation model for computing with words cw which is based on the concept of symbolic proportion this concept motivates us to represent the linguistic information by means of 2 tuples which are composed by two proportional linguistic terms for clarity and generality we first study proportional 2 tuples under ordinal contexts then under linguistic contexts and based on canonical characteristic values ccvs of linguistic labels we define many aggregation operators to handle proportional 2 tuple linguistic information in a computational stage for cw without any loss of information our approach for this proportional 2 tuple fuzzy linguistic representation model deals with linguistic labels which do not have to be symmetrically distributed around a medium label and without the traditional requirement of having equal distance between them moreover this new model not only provides a space to allow a continuous interpolation of a sequence of ordered linguistic labels but also provides an opportunity to describe the initial linguistic information by members of a continuous linguistic scale domain which does not necessarily require the ordered linguistic terms of a linguistic variable being equidistant meanwhile under the assumption of equally informative which is defined by a condition based on the concept of ccv we show that our model reduces to herrera and mart spl inodot spl acute nez s translational 2 tuple fuzzy linguistic representation model

minimax robust quickest change detection the popular criteria of optimality for quickest change detection procedures are the lorden criterion the pollak criterion and the bayesian criterion in this paper a robust version of these quickest change detection problems is considered when the pre change and post change distributions are not known exactly but belong to known uncertainty classes of distributions for uncertainty classes that satisfy a specific condition it is shown that one can identify least favorable distributions lfds from the uncertainty classes such that the detection rule designed for the lfds is optimal for the robust problem in a minimax sense the condition is similar to that required for the identification of lfds for the robust hypothesis testing problem originally studied by huber an upper bound on the delay incurred by the robust test is also obtained in the asymptotic setting under the lorden criterion of optimality this bound quantifies the delay penalty incurred to guarantee robustness when the lfds can be identified the proposed test is easier to implement than the cusum test based on the generalized likelihood ratio glr statistic which is a popular approach for such robust change detection problems the proposed test is also shown to give better performance than the glr test in simulations for some parameter values

applicability of the fuzzy operators in the design of fuzzy logic controllers a study of the different roles played by the fuzzy operators in fuzzy control is developed in this paper the behavior of a very large amount of fuzzy operators is analyzed and a comparison of the accuracy of many fuzzy logic controllers designed by means of these operators is carried out in order to do that a comparison methodology is defined and two fuzzy control applications are selected the inverted pendulum problem and the fuzzy modeling of the real curve y x

optimal stopping times for detecting changes in distributions it is shown that page s stopping time is optimal for the detection of changes in distributions in a well defined sense this work is a generalization of an existing result where it was shown that page s stopping time is optimal asymptotically

a multiple attributes decision making method using individual and collaborative attribute data in a fuzzy environment although multiple attribute decision making madm problems with both individual attribute data of a single alternative and collaborative attribute data of pairwise alternatives exist in the real world they have seldom been a focus of research this paper proposes a madm method using individual and collaborative attribute data in a fuzzy environment in which experts use linguistic variables to express their opinions in the method first the evaluation matrix of individual attributes date and the judgment matrix of collaborative attributes data are constructed then the central dominance of one alternative outranking other all alternatives is defined for aggregating the collaborative data from this an integrated decision matrix incorporating individual and collaborative attribute data is constructed further based on an extended topsis the fuzzy positive ideal solution fpis and the fuzzy negative ideal solution fnis are determined and the relative closeness of each alternative to the fpis and fnis is calculated to determine the ranking order of all alternatives finally two examples are used to illustrate the applicability of the proposed method

non crossing partitions of type e e r abstract we investigate a new lattice of generalised non crossing partitions constructed using the geometry of the complex reflection group g e e r for the particular case e 2 resp r 2 our lattice coincides with the lattice of simple elements for the type d n resp i 2 e dual braid monoid using this lattice we construct a garside structure for the braid group b e e r as a corollary one may solve the word and conjugacy problems in this group

a fuzzy rough set approach for incremental feature selection on hybrid information systems in real applications there may exist many kinds of data e g boolean categorical real valued and set valued data and missing data in an information system which is called as a hybrid information system his a new hybrid distance hd in his is developed based on the value difference metric and a novel fuzzy rough set is constructed by combining the hd distance and the gaussian kernel considering the information systems often vary with time the updating mechanisms for attribute reduction feature selection are analyzed with the variation of the attribute set fuzzy rough set approaches for incremental feature selection on his are presented then two corresponding incremental algorithms are proposed respectively finally extensive experiments on eight datasets from uci and an artificial dataset show that the incremental approaches significantly outperform non incremental approaches with feature selection in the computational time

finite complex reflection arrangements are k pi 1 let v be a finite dimensional complex vector space and w gl v be a finite complex reflection group let v reg be the complement in v of the reflecting hyperplanes we prove that v reg is a k 1 space this was predicted by a classical conjecture originally stated by brieskorn for complexified real reflection groups the complexified real case follows from a theorem of deligne and after contributions by nakamura and orliksolomon only six exceptional cases remained open in addition to solving these six cases our approach is applicable to most previously known cases including complexified real groups for which we obtain a new proof based on new geometric objects we also address a number of questions about 1 w v the braid group of w this includes a description of periodic elements in terms of a braid analog of springer s theory of regular elements

optimal detection of a change in distribution abstract document discusses a stopping rule that is a limit of bayes rules derived then an almost minimax rule is presented

a normal form for a class of monoids including the singular braid monoids abstract the first part of this paper investigates a class of homogeneously presented monoids constructions which enable division and multiplication to be computed are described the word problem and the division problem are solved and a unique normal form is given for monoids in this class the second part deals with the motivating examples of this class the positive singular artin monoids finally the singular artin monoids are introduced the word and division problems are solved for all singular artin monoids of finite type including for example the singular braid monoids introduced by baez and birman

a goal programming approach to group decision making based on multiplicative preference relations and fuzzy preference relations abstract this paper proposes a goal programming approach to solve group decision making gdm problems where the preference information on alternatives provided by decision makers is represented in two different formats i e multiplicative preference relations and fuzzy preference relations in order to narrow the gap between the collective opinion and each decision maker s opinion a linear goal programming model is constructed to integrate the two different formats of preference relations and to compute the collective ranking values of the alternatives thus the ranking of alternatives or selection of the most desirable alternative s is obtained directly from the computed collective ranking values a numerical example is also used to illustrate the applicability of the proposed approach

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

a new approach to the word and conjugacy problems in the braid groups abstract a new presentation of the n string braid group b n is studied using it a new solution to the word problem in b n is obtained which retains most of the desirable features of the garside thurston solution and at the same time makes possible certain computational improvements we also give a related solution to the conjugacy problem but the improvements in its complexity are not clear at this writing

an approach to computing with words based on canonical characteristic values of linguistic labels herrera and martinez initiated a 2 tuple fuzzy linguistic representation model for computing with words cw which offers a computationally feasible method for aggregating linguistic information that are represented by linguistic variables with equidistant labels through counting indexes of the corresponding linguistic labels lawry introduced an alternative approach to cw based on mass assignment theory that takes into account the underlying definitions of the words recently we provided a new proportional 2 tuple fuzzy linguistic representation model for cw that is an extension of herrera and martinez s model and takes into account the underlying definitions of linguistic labels of linguistic variables in the process of aggregating linguistic information by assigning canonical characteristic values ccvs of the corresponding linguistic labels in this paper we study further into cw based on ccvs of linguistic labels to provide a unifying link between lawry s framework and herrera and martinez s 2 tuple framework as well as allowing for computationally feasible cw our approach is based on a formal definition of ccv functions of a linguistic variable which is introduced under the context of its proportional 2 tuple linguistic representation model as continuation of our earlier works and on a group voting model that is for the probabilistic interpretation of the whole semantics of the ordered linguistic terms set of an arbitrary linguistic variable after the general framework developed in the former part of this paper we focus on a particular linguistic variable probability we show that for a linguistic probability description the expectation of its posterior conditional probability is a canonical characteristic value of the linguistic probability description then a calculus for reasoning with linguistic syllogisms and inference from linguistic information is introduced it is investigated under the context that linguistic quantifiers in such linguistic syllogisms can be arbitrary linguistic probability description and that the related linguistic information can be linguistic facts overfacts or underfacts intrinsically our approach to this calculus is with computing with words based on canonical characteristic values of linguistic labels

a dual braid monoid for the free group abstract we construct a quasi garside monoid structure for the free group this monoid should be thought of as a dual braid monoid for the free group generalising the constructions by birman ko lee and by the author of new garside monoids for artin groups of spherical type

qualitative robustness of rank tests an asymptotic notion of robust tests is studied which is based on the requirement of equicontinuous error probabilities if the test statistics are consistent their robustness in hampel s sense and robustness of the associated tests turn out to be equivalent uniform extensions are considered moreover test breakdown points are defined the main applications are on rank statistics they are generally robust under a slight condition even uniformly so their points of final breakdown coincide with the breakdown points of the corresponding r estimators

incremental update of approximations in dominance based rough sets approach under the variation of attribute values dominance based rough sets approach drsa has received much attention since it is able to acquire knowledge from information with preference ordered attribute domains and decision classes in many real life applications the information systems may evolve over time dynamically in a dynamic information system the obtained knowledge e g approximations in drsa need to be updated for decision making and other related tasks as a useful technique the incremental update can be applied to process dynamic information with revising the obtained knowledge in this paper we propose an incremental approach for maintaining approximations of drsa when attribute values vary over time some numerical examples illustrate that the incremental approach can renew approximations of drsa without beginning from scratch experimental evaluations show that the incremental algorithm can effectively reduce the computational time in comparison with the non incremental one when the ratio of the attribute values varied is less than a threshold

non crossing cumulants of type b we establish connections between the lattices of non crossing partitions of type b introduced by v reiner and the framework of the free probability theory of d voiculescu lattices of non crossing partitions of type a up to now have played an important role in the combinatorics of free probability primarily via the non crossing cumulants of r speicher here we introduce the concept of non crossing cumulant of type b the inspiration for its definition is found by looking at an operation of restricted convolution of multiplicative functions studied in parallel for functions on symmetric groups in type a and on hyperoctahedral groups in type b the non crossing cumulants of type b live in an appropriate framework of non commutative probability space of type b and are closely related to a type b analogue for the r transform of voiculescu which is the free probabilistic counterpart of the fourier transform by starting from a condition of vanishing of mixed cumulants of type b we obtain an analogue of type b for the concept of free independence for random variables in a non commutative probability space

a sequential selection process in group decision making with a linguistic assessment approach in this paper a sequential selection process in group decision making under linguistic assessments is presented where a set of linguistic preference relations represents individuals preferences a collective linguistic preference is obtained by means of a defined linguistic ordered weighted averaging operator whose weights are chosen according to the concept of fuzzy majority specified by a fuzzy linguistic quantifier then we define the concepts of linguistic non dominance linguistic dominance and strict dominance degrees as parts of the sequential selection process the solution alternative s is obtained by applying these concepts

using classification as an aggregation tool in mcdm abstract in this paper we propose a method to obtain the set of best alternatives when data involved in mcdm are of different types e g numbers linguistic labels or truth values this method consists of a classification of the alternatives according to criteria and then an ordering of the classes obtained in this way we study each alternative in relation with the other ones the groups formed indicate that their members are equally prefered over the others otherwise we describe some specialized methods to be used in case that all criteria have the same type of values

on a canonical representation of fuzzy numbers abstract fuzzy numbers and more generally linguistic values are approximate assessments given by experts and accepted by decision makers when obtaining more accurate values is impossible or unnecessary to simplify the task of representing and handling fuzzy numbers several authors have introduced real indices in order to capture the information contained in a fuzzy number in this paper we propose two parameters value and ambiguity for this purpose we use these parameters to obtain canonical representations and to deal with fuzzy numbers in decision making problems several examples illustrate these ideas

the evaluation of service quality using generalized choquet integral in view of the compatibility between psychology and linguistic terms this study generalizes the standard choquet integral whose measurable evidence and fuzzy measures are real numbers the proposed generalization can deal with fuzzy number types of measurable evidence and fuzzy measures in comparison with the previous research on service quality and fuzzy sets this study integrates the three column format servqual into the generalized choquet integral a numerical example evaluating the overall service quality of e stores is provided to illustrate how the generalized choquet integral evaluates service quality in the three column format servqual this integral is also compared with the possibility necessity model when measuring service quality

gaussian groups and garside groups two generalisations of artin groups it is known that a number of algebraic properties of the braid groups extend to arbitrary finite coxeter type artin groups here we show how to extend the results to more general groups that we call garside groups define a gaussian monoid to be a finitely generated cancellative monoid where the expressions of a given element have bounded lengths and where left and right lowest common multiples exist a garside monoid is a gaussian monoid in which the left and right lowest common multiples satisfy an additional symmetry condition a gaussian group is the group of fractions of a gaussian monoid and a garside group is the group of fractions of a garside monoid braid groups and more generally finite coxeter type artin groups are garside groups we determine algorithmic criteria in terms of presentations for recognizing gaussian and garside monoids and groups and exhibit infinite families of such groups we describe simple algorithms that solve the word problem in a gaussian group show that these algorithms have a quadratic complexity if the group is a garside group and prove that garside groups have quadratic isoperimetric inequalities we construct normal forms for gaussian groups and prove that in the case of a garside group the language of normal forms is regular symmetric and geodesic has the 5 fellow traveller property and has the uniqueness property this shows in particular that garside groups are geodesically fully biautomatic finally we consider an automorphism of a finite coxeter type artin group derived from an automorphism of its defining coxeter graph and prove that the subgroup of elements fixed by this automorphism is also a finite coxeter type artin group that can be explicitly determined 1991 mathematics subject classification primary 20f05 20f36 secondary 20b40 20m05

using the generalized likelihood ratio statistic for sequential detection of a change point we study sequential detection of a change point using the generalized likelihood ratio statistic for the special case of detecting a change in a normal mean with known variance we give approximations to the average run lengths and compare our procedure to standard cusum tests and combined cusum shewhart tests several examples indicating extensions to problems involving multiple parameters are discussed

qualitative robustness of tests abstract a test is qualitatively robust by definition if its sequence of n 1 log transformed p values n being a measure of the sample size is continuous as a point function of the observations and weakly equicontinuous as a function of discrete probability measures this definition is applitable both to unconditional and to conditional tests under weak regularity conditions an unconditional test is qualitatively robust if and only if its test statistic is continuous a counterexample shows that conditional tests do not share this property the sample mean student s t and ybar xbar permutation tests are not qualitatively robust the sign wilcoxon huber censored likelihood and normal scores tests are qualitatively robust

efficient robust estimates in parametric models let p n an open subset ofr k be a regular parametric model for a sample ofn independent identically distributed observations this paper describes estimates t n n 1 of which are asymptotically efficient under the parametric model and are robust under small deviations from that model in essence the estimates are adaptively modified one step maximum likelihood estimates which adjust themselves according to how well the parametric model appears to fit the data when the fit seems poor t n discounts observations that would have large influence on the value of the usual one step mle the estimates t n are shown to be asymptotically minimax in the hajek lecam sense for a hellinger ball contamination model an alternative construction of robust asymptotically minimax estimates as modified mle s is described for canonical exponential families

algorithmic recognition of quasipositive braids of algebraic length two abstract we give an algorithm to decide if a given braid is a product of two factors which are conjugates of given powers of standard generators of the braid group the same problem is solved in a certain class of garside groups including artin tits groups of spherical type the solution is based on the garside theory and especially on the theory of cyclic sliding developed by gebhardt and gonzalez meneses we show that if a braid is of the required form then any cycling orbit in its sliding circuit set in the dual garside structure contains an element for which this fact is immediately seen from the left normal form

braid groups of imprimitive complex reflection groups abstract we obtain new presentations for the imprimitive complex reflection groups of type d e e r and their braid groups b d e e r for d r 2 diagrams for these presentations are proposed the presentations have much in common with coxeter presentations of real reflection groups they are positive and homogeneous and give rise to quasi garside structures diagram automorphisms correspond to group automorphisms the new presentation shows how the braid group b d e e r is a semidirect product of the braid group of affine type a r 1 and an infinite cyclic group elements of b d e e r are visualised as geometric braids on r 1 strings whose first string is pure and whose winding number is a multiple of e we classify periodic elements and show that the roots are unique up to conjugacy and that the braid group b d e e r is strongly translation discrete

complete positive group presentations abstract a combinatorial property of positive group presentations called completeness is introduced with an effective criterion for recognizing complete presentations and an iterative method for completing an incomplete presentation we show how to directly read several properties of the associated monoid and group from a complete presentation cancellativity or existence of common multiples in the case of the monoid or isoperimetric inequality in the case of the group in particular we obtain a new criterion for recognizing that a monoid embeds in a group of fractions typical presentations eligible for the current approach are the standard presentations of the artin tits groups and the heisenberg group