a new multiplicative consistency based method for decision making with triangular fuzzy reciprocal preference relations abstract triangular fuzzy reciprocal preference relations tfrprs are good choices to denote the decision makers fuzzy preferences consistency analysis is a very important topic to preference relations that can avoid the illogical ranking order however all previous multiplicative consistency concepts for tfrprs cannot well address this type of preference relations to address this issue this paper introduces a new multiplicative consistency concept for tfrprs which can be seen as a natural extension of tanino s multiplicative consistency concept for reciprocal preference relations based on the new consistency concept 0 1 mixed programming models for judging the multiplicative consistency of tfrprs are constructed and an approach for deriving multiplicative consistent tfrprs is provided considering the incomplete case programming models to determine missing values are constructed subsequently a multiplicative consistency based method for decision making with tfrprs is presented that can address the inconsistent and incomplete cases meanwhile illustrative examples are provided to show the concrete application of the proposed procedure and comparison analysis is also made

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

on angles and distances between subspaces abstract the angles and distances between two given subspaces of c n 1 are investigated on the basis of a joint decomposition of the corresponding orthogonal projectors several new results are established with the particular attention paid to the notions of inclinedness and minimal angle to demonstrate the usefulness of the approach utilized some results known to be valid in hilbert space are reestablished in c n 1 either in generalized form or with considerably shorter proofs than in the original sources

applications of high resolution time frequency transforms to attenuation estimation abstractattenuation estimates quantify the loss of energy of propagating seismic waves due to anelastic processes it is often carried out in the frequency domain the most well known methods for attenuation estimation such as the spectral ratio and frequency shift methods compare spectral shapes of waveforms along a given raypath they require broad spectra such as those obtained with the fourier transform and the continuous wavelet transform these methods are incompatible with high resolution time frequency transforms which drastically localize time frequency information on the other hand these transforms indicate stronger resistance to noise and can be used in combination with the peak frequency method to estimate attenuation we have applied high resolution transforms namely the synchrosqueezing transform basis pursuit and complete ensemble empirical mode decomposition to a synthetic wedge example and two seismic data set examples a seismic reflection profile and a vertical seismic profile

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

history and generality of the cs decomposition abstract it is almost a quarter of a century since chandler davis and william kahan brought together the key ideas of what stewart later completed and defined to be the cs decomposition csd of a partitioned unitary matrix this paper outlines some germane points in the history of the csd pointing out the contributions of jordan of davis and kahan and of stewart and the relationship of the csd to the direct rotation of davis and kato the paper provides an easy to memorize constructive proof of the csd reviews one of its important uses and suggests a motivation for the csd which emphasizes how generally useful it is it shows the relation between the csd and generalized singular value decompositions and points out some useful nullity properties one form of the csd trivially reveals finally it shows how via the qr factorization the csd can be used to obtain interesting results for partitioned nonsingular matrices we suggest the csd be taught in its most general form with no restrictions on the two by two partition and initially with no mention of angles between subspaces

pointwise gap metrics on transfer matrices a family of metrics pointwise gap metrics in the space of real rational matrices of fixed size is developed and used to study open loop and closed loop stability robustness of linear time invariant finite dimensional continuous time systems it is shown that pointwise gap metrics have the desired qualitative properties for the study of stability robustness necessary and sufficient conditions on the robustness are obtained in terms of the radii of the pointwise gap metric balls centered at the nominal plant and or the nominal controller comparison with the gap metric and the graph metric is made all of these metrics induce the same topology many of the quantitative properties of pointwise gap metrics are the same as those of the gap metric although they differ in value pointwise gap metrics in the scalar case have a very simple expression which is potentially useful for accessing the relationship between the uncertainty of physical parameters and uncertainty measured by pointwise gap metrics

aggregation of monotone reciprocal relations with application to group decision making this paper is composed of two complementary parts the first part is a formal investigation into the interplay of properties of reciprocal relations how monotonicity relates to some natural and intuitive properties including stochastic transitivity the goal is to aggregate monotone reciprocal relations on a given set of alternatives monotonicity is expressed w r t a linear order on the set of alternatives the second part is a practical protocol to both determine the best fitting linear order underlying the alternatives and construct a reciprocal relation monotone w r t it we formulate the problem as an optimization problem where the aggregated linear order is that for which the implied stochastic monotonicity conditions are closest to being satisfied by the distribution of the input monotone reciprocal relations we show that if stochastic monotonicity conditions are satisfied a monotone reciprocal relation is easily found on the basis of the possibly constructed stochastically monotone reciprocal distributional relation

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

microseismic and seismic denoising via ensemble empirical mode decomposition and adaptive thresholding random and coherent noise exists in microseismic and seismic data and suppressing noise is a crucial step in seismic processing we have developed a novel seismic denoising method based on ensemble empirical mode decomposition eemd combined with adaptive thresholding a signal was decomposed into individual components called intrinsic mode functions imfs each decomposed signal was then compared with those imfs resulting from a white noise realization to determine if the original signal contained structural features or white noise only a thresholding scheme then removed all nonstructured portions our scheme is very flexible and it is applicable in a variety of domains or in a diverse set of data for instance it can serve as an alternative for random noise removal by band pass filtering in the time domain or spatial prediction filtering in the frequency offset domain to enhance the lateral coherence of seismic sections we have determined its potential for microseismic and reflection seismic denoising by comparing its performance on synthetic and field data using a variety of methods including band pass filtering basis pursuit denoising frequency offset deconvolution and frequency offset empirical mode decomposition

on meaningfulness of means abstract we are concerned with the definition of means or averaging operators i e aggregators m x1 xi xm where xi r represent measures on the reals corresponding to a given type of scale ordinal interval or ratio scale the adequate mean which varies between min x1 xm and max x1 xm should correspond to some comparison meaningfulness property or some functional equation that induces invariance or stability we characterize the averaging operators which present some natural properties continuity monotonicity neutrality unanimity etc and comparison meaningfulness or invariance and we show that operators like order statistics and ordered weighted averaging operators can be used to rank elements defined by vectors x1 xm in a meaningful way in the spirit of measurement theory

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

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

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

optimal robustness in the gap metric the application of the gap metric to robust stabilization of feedback systems is considered in particular a solution to the problem of robustness optimization in the gap metric is presented the problem of robust stabilization under simultaneous plant controller perturbations is addressed and the least amount of combined plant controller uncertainty measured by the gap metric that can cause instability of a nominally stable feedback system is determined included are a detailed summary of the main properties of the gap metric and the introduction of a dual metric called the t gap metric a key contribution of this study is to show that the problem of robustness optimization in the gap metric is equivalent to robustness optimization for normalized coprime factor perturbations this settles the question as to whether maximizing allowable coprime factor uncertainty corresponds to tolerating the largest ball of uncertainty in a well defined metric

automatic noise removal signal removal based on general cross validation thresholding in synchrosqueezed domain and its application on earthquake data abstractrecorded seismic signals are often corrupted by noise we have developed an automatic noise attenuation method for single channel seismic data based upon high resolution time frequency analysis synchrosqueezing is a time frequency reassignment method aimed at sharpening a time frequency picture noise can be distinguished from the signal and attenuated more easily in this reassigned domain the threshold level is estimated using a general cross validation approach that does not rely on any prior knowledge about the noise level the efficiency of the thresholding has been improved by adding a preprocessing step based on kurtosis measurement and a postprocessing step based on adaptive hard thresholding the proposed algorithm can either attenuate the noise either white or colored and keep the signal or remove the signal and keep the noise hence it can be used in either normal denoising applications or preprocessing in ambient noise studies we tested the performance of the proposed method on s

fuzzy rationality measures fuzzy preference relations formalize intensity of individual preferences over fixed sets of alternatives it is therefore natural to extend to fuzzy preferences the notion of rationality or consistency with this goal in mind we address in this paper the problem of giving an axiomatic basis for defining the concept of fuzzy rationality specifically we establish a collection of conditions that any fuzzy rationality measure must satisfy some examples of fuzzy rationality measures are then given and analyzed

applications of the synchrosqueezing transform in seismic time frequency analysis abstracttime frequency representation of seismic signals provides a source of information that is usually hidden in the fourier spectrum the short time fourier transform and the wavelet transform are the principal approaches to simultaneously decompose a signal into time and frequency components known limitations such as trade offs between time and frequency resolution may be overcome by alternative techniques that extract instantaneous modal components empirical mode decomposition aims to decompose a signal into components that are well separated in the time frequency plane allowing the reconstruction of these components on the other hand a recently proposed method called the synchrosqueezing transform sst is an extension of the wavelet transform incorporating elements of empirical mode decomposition and frequency reassignment techniques this new tool produces a well defined time frequency representation allowing the identification of instantaneous frequencies in seismic signals to highlight

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

group decision making using bilateral agreement matrix abstract group decision making based on a bilateral agreement matrix is investigated in this paper to derive a group decision from the opinions of individual decision makers pairs of decision makers are allowed to negotiate with one another and provide their bilateral negotiation values two algorithms are provided to help pairs of decision makers reach bilateral agreements which enables the construction of the bilateral agreement matrix the definition of a consistent bilateral agreement matrix is introduced to measure the credibility of the final result and its properties are investigated based on which a method is provided to construct a consistent bilateral agreement matrix from an inconsistent one models are then given to derive the weight vector from the bilateral agreement matrix based on which a consistency index of the matrix is defined two algorithms are then given to improve the level of consistency of the bilateral agreement matrix the final group decision is obtained by aggregating individual opinions using the weight vector the proposed methods are further extended to deal with the problem of incomplete bilateral agreement matrices several examples are also given to illustrate the proposed approach

frequency domain uncertainty and the graph topology a new metric on linear time invariant systems is defined this metric is no greater than the gap metric and is in fact the smallest metric for which a certain robust stabilization result holds unlike other known metrics which induce the graph topology it has a clear frequency response interpretation this allows questions regarding robustness in the face of parametric uncertainty to be considered in terms of this metric

canonical angles of unitary spaces and perturbations of direct complements abstract let n plane1d 4b2 be a given direct sum decomposition we determine the largest number r i such that all subspaces for which the gap between and plane1d 4b2 satisfies have the property dim plane1d 4b2 the problem involves angles between subspaces i e singular values of products of projections

multi criteria group decision making based on bilateral agreements abstract in multi criteria group decision making a key issue is aggregating individual preference into group one in this study we employ a bilateral agreement to conduct group evaluation of alternatives the bilateral agreement between a pair of individuals could be on the weight of a criterion a criterion evaluation function or willingness to pay any one of three types of bilateral agreements can derive the group utility to express the relationship between the bilateral agreement and individual evaluations the quasi arithmetic mean is used which can ensure the consistency property of the pairwise comparison matrices the minimum requirements are explored to obtain the group preference which shows that n 1 pairs of bilateral agreements are necessary finally several examples are provided to illustrate the proposed methods

on a subspace metric based on matrix rank abstract the metric between subspaces m n c n 1 defined by m n rk p m p n where rk denotes rank of a matrix argument and p m and p n are the orthogonal projectors onto the subspaces m and n respectively is investigated such a metric takes integer values only and is not induced by any vector norm by exploiting partitioned representations of the projectors several features of the metric m n are identified it turns out that the metric enjoys several properties possessed also by other measures used to characterize subspaces such as distance also called gap frobenius distance direct distance angle or minimal angle

feedback stability under simultaneous gap metric uncertainties in plant and controller abstract the stability robustness of a feedback system is studied in this paper by assuming that the plant and the controller are subject to independent uncertainties and that the uncertainties are measured by the gap metric a fairly complete solution is obtained by exploring the trigonometric structure of the graphs of the plant and the controller

development of emd based denoising methods inspired by wavelet thresholding one of the tasks for which empirical mode decomposition emd is potentially useful is nonparametric signal denoising an area for which wavelet thresholding has been the dominant technique for many years in this paper the wavelet thresholding principle is used in the decomposition modes resulting from applying emd to a signal we show that although a direct application of this principle is not feasible in the emd case it can be appropriately adapted by exploiting the special characteristics of the emd decomposition modes in the same manner inspired by the translation invariant wavelet thresholding a similar technique adapted to emd is developed leading to enhanced denoising performance

a study of the characteristics of white noise using the empirical mode decomposition method based on numerical experiments on white noise using the empirical mode decomposition emd method we find empirically that the emd is effectively a dyadic filter the intrinsic mode function imf components are all normally distributed and the fourier spectra of the imf components are all identical and cover the same area on a semi logarithmic period scale expanding from these empirical findings we further deduce that the product of the energy density of imf and its corresponding averaged period is a constant and that the energy density function is chi squared distributed furthermore we derive the energy density spread function of the imf components through these results we establish a method of assigning statistical significance of information content for imf components from any noisy data southern oscillation index data are used to illustrate the methodology developed here

group decisions with multiple criteria we consider a decision problem where a group of individuals evaluates multiattribute alternatives we explore the minimal required agreements that are sufficient to specify the group utility function a surprising result is that under some conditions a bilateral agreement among pairs of individuals on a single attribute is sufficient to derive the multiattribute group utility the bilateral agreement between a pair of individuals could be on the weight of an attribute on an attribute evaluation function or on willingness to pay we focus on the case in which each individual s utility function is additive we show that the group utility can be represented as the weighted sum of group attribute weights and more remarkably of attribute evaluation functions these group attribute evaluation functions are in turn weighted sums of individual attribute evaluation functions

on the angular metrics between linear subspaces it has recently been shown that the symmetric gauge functions on the canonical principal angles give a family of unitarily invariant metrics between linear subspaces of the same dimension in this short paper we extend such metrics to subspaces of possibly different dimensions this extension is necessary in addressing some perturbation analysis problems involving subspaces with different dimensions examples of such perturbation analysis problems are also studied in this paper using the extended metrics

on training rbf neural networks using input output fuzzy clustering and particle swarm optimization this paper elaborates on the use of particle swarm optimization in training gaussian type radial basis function neural networks under the umbrella of input output fuzzy clustering the problem being investigated concerns the selection of basis function centers that contribute most in network s performance given that the clustering process in the input space is guided by the clustering in the output space to accomplish this task we quantify the effect of the input space fuzzy partition upon network s square error in terms of an objective function that describes the ability of the partition to accurately reconstruct the input training samples we then theoretically prove that the minimization of the above function acts to minimize an upper bound of the network s square error therefore the resulting solution corresponds to a minimal square error while at the same time it maintains the structure of the input data due to the peculiarity of the aforementioned objective function we treat it as the fitness function used by the particle swarm optimizer the proposed methodology encompasses three design steps the first step implements an independent fuzzy clustering in the output space to obtain a set of cluster centers in the second step unlike other approaches the above centers are directly involved in the estimation of the membership degrees in the input output space in the third step these membership degrees are used by the particle swarm optimizer in order to obtain optimal values for the centers to summarize the novelty of our contribution lies in a the way we handle the information flow from output to input space and b the way we handle the effect of the input space partition upon network s performance the experiments indicate that the fitness function decreases as the number of hidden node increases finally a comparison between the proposed method and other sophisticated approaches shows its statistically significant superiority

acceptable consistency analysis of interval reciprocal comparison matrices when a decision maker expresses his her opinions by means of an interval reciprocal comparison matrix the study of consistency becomes a very important aspect in decision making in order to avoid a misleading solution in the present paper an acceptably consistent interval reciprocal comparison matrix is defined which can be reduced to an acceptably consistent crisp reciprocal comparison matrix when the intervals become exact numbers an interval reciprocal comparison matrix with unacceptable consistency can be easily adjusted such that the revised matrix possesses acceptable consistency utilizing a convex combination method a family of crisp reciprocal comparison matrices with acceptable consistency can be obtained whose weights are further found to exhibit a style of convex combination and aggregated to obtain interval weights from an acceptably consistent interval reciprocal comparison matrix a novel simple yet effective formula of possibility degree is presented to rank interval weights numerical results are calculated to show the quality and quantity of the proposed approaches and compare with other existing procedures