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

an iterative algorithm learning the maximal margin classifier abstract a simple learning algorithm for maximal margin classifiers also support vector machines with quadratic cost function is proposed we build our iterative algorithm on top of the schlesinger kozinec algorithm s k algorithm from 1981 which finds a maximal margin hyperplane with a given precision for separable data we suggest a generalization of the s k algorithm i to the non linear case using kernel functions and ii for non separable data the requirement in memory storage is linear to the data this property allows the proposed algorithm to be used for large training problems the resulting algorithm is simple to implement and as the experiments showed competitive to the state of the art algorithms the implementation of the algorithm in matlab is available we tested the algorithm on the problem aiming at recognition poor quality numerals

personalized mode transductive spanning svm classification tree personalized transductive learning ptl builds a unique local model for classification of individual test samples and is therefore practically neighborhood dependant i e a specific model is built in a subspace spanned by a set of samples adjacent to the test sample while existing ptl methods usually define the neighborhood by a predefined dis similarity measure this paper introduces a new concept of a knowledgeable neighborhood and a transductive support vector machine svm classification tree t svmt for ptl the neighborhood of a test sample is constructed over the classification knowledge modelled by regional svms and a set of such svms adjacent to the test sample is systematically aggregated into a t svmt compared to a regular svm and other svmts a t svmt by virtue of the aggregation of svms has an inherent superiority in classifying class imbalanced datasets the t svmt has also solved the over fitting problem of all previous svmts since it aggregates neighborhood knowledge and thus significantly reduces the size of the svm tree the properties of the t svmt are evaluated through experiments on a synthetic dataset eight bench mark cancer diagnosis datasets as well as a case study of face membership authentication

the continuous ordered weighted geometric operator and its application to decision making the aim of this paper is to develop a continuous ordered weighted geometric c owg operator which is based on the continuous ordered weighted averaging c owa operator recently introduced by the author and the geometric mean we study some desirable properties of the c owg operator and present its application to decision making with interval multiplicative preference relation and finally an illustrative example is pointed out

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

a pruning method of refining recursive reduced least squares support vector regression in this paper a pruning method is proposed to refine the recursive reduced least squares support vector regression rrlssvr and its improved version irrlssvr and thus two novel algorithms prurrlssvr and pruirrlssvr are yielded this pruning method ranks support vectors by defining a contribution function to the objective function and then the support vector with the least contribution is pruned unless it is the most recently selected support vector consequently prurrlssvr and pruirrlssvr outperform rrlssvr and irrlssvr respectively in terms of the number of support vectors while not impairing the generalization performance in addition a speedup scheme is presented that reduces the computational burden of computing the contribution function to show the effectiveness and feasibility of the proposed prurrlssvr and pruirrlssvr experiments are performed on ten benchmark data sets and a gas furnace instance

an optimization based approach to adjusting unbalanced linguistic preference relations to obtain a required consistency level in certain real decision making situations decision makers often feel more comfortable providing their knowledge and preferences in linguistic terms unbalanced linguistic term sets may be used in decision problems with preference relations however the lack of consistency in decision making with linguistic preference relations can lead to inconsistent conclusions based on the consistency measure of unbalanced linguistic preference relations this paper proposes an optimization based approach to improving the consistency level of unbalanced linguistic preference relations this consistency improving model preserves the utmost original knowledge and preferences in the process of improving consistency furthermore it guarantees that the elements in the optimal adjusted unbalanced linguistic preference relation are all simple unbalanced linguistic terms finally we propose a mixed 0 1 linear programming aimed to obtain the optimum solution to the proposed consistency improving model and to demonstrate its practicability

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 new approach to the detection of moving objects abstract in this paper the application of an edge detection algorithm based on homogeneous tests is extended to the detection of moving objects in this new detection algorithm dynamic regions occupied by moving objects on a motion sequence are located by a series of homogeneous tests operating on consecutive frames of the motion sequence upon locating the dynamic regions on a frame further processing is carried out to pinpoint the locations of the moving objects in general the new moving object displacement difference based detector is implemented by a two sample sign test two morphological operators a new object labeling algorithm two edge detectors and some simple operators the versatility of the proposed detector is demonstrated by the fact that it is made up of distribution free detection components the simulation results confirm that the detector performs well in gaussian and nongaussian salt and pepper noise environments

combined 5 2 cv f test for comparing supervised classification learning algorithms dietterich 1998 reviews five statistical tests and proposes the 5 2 cv t test for determining whether there is a significant difference between the error rates of two classifiers in our experiments we noticed that the 5 2 cv t test result may vary depending on factors that should not affect the test and we propose a variant the combined 5 2 cv f test that combines multiple statistics to get a more robust test simulation results show that this combined version of the test has lower type i error and higher power than 5 2 cv proper

on viscosity solutions of path dependent pdes in this paper we propose a notion of viscosity solutions for path dependent semi linear parabolic pdes this can also be viewed as viscosity solutions of non markovian backward sdes and thus extends the well known nonlinear feynman kac formula to non markovian case we shall prove the existence uniqueness stability and comparison principle for the viscosity solutions the key ingredient of our approach is a functional ito calculus recently introduced by dupire functional ito calculus 2009 preprint

a retinex model based on absorbing markov chains the retinex algorithm developed by land and mccann provides an abstract model of the mechanism of color sensation in the human vision system at the basis of model lies the fact that the color appearance of a point does not depend only on its color value but rather on the comparison among itself and other pixels according to the model separately for each chromatic channel an image pixel receives suitably filtered information about the brightness of other image regions based on which its own brightness is eventually re scaled the original formulation land and mccann 1971 uses a path based sampling approach the information is transported by memoryless random walks starting from randomly chosen points along the path the information is filtered based on the brightness of the travelled regions by a specific path function computed through chains of ratios of pixel intensities such a function is path dependent and retains the value of the brightest point found along the path the overall correction to a pixel depends on the specific realizations of two sampling processes the starting point sampling process and the path sampling process as a consequence of the sampling this algorithm is known to be intrinsically noisy this draw back can be overcome by passing from the path sampling algorithm to the probabilistic representation of the corresponding diffusion process in this paper we start from the random path simulative model of retinex we respell the standard path based sampling process representation of the retinex model as formalized in provenzi et al 2005 and we show that despite the overall path dependence the model can be given a representation in terms of absorbing markov chains by means of the embedding into a suitable state space we derive the corresponding analytic model accounting for the combined effects of path function path sampling process and starting point sampling process finally we provide a numerical algorithm for working out its solution using such a model the output brightness of a pixel can be computed based on the solution of a simple sparse linear system we show that the output of the random walk sampling algorithm and the markov chain based algorithm agree to an extent that can be controlled by few model parameters we have found also that the markov chain based algorithm is more efficient than the basic random path sampling in obtaining noise free images those analytic probabilistic models and simulative models can be used as complementary tools for studying the retinex mechanism and for identifying and comparing variants

support function machine for set based classification with application to water quality evaluation in some applications measurement errors and multiple repeated measurements often lead to a set based classification task where objects are represented with a set of samples and the traditional support vector machines svms do not work in these settings to deal with this problem we construct a new classifier called support function machine sfm in this work first sets in d dimensional euclidean space r d are mapped into an infinite dimensional banach space c s whose elements are functions via support functions and then set based classification in r d is converted into function based classification in c s second we define the hyperplane via the riesz representation theorem in banach space and discuss the hausdorff distance of hyperpalnes and maximum margin principle mmp in c s based on mmp we construct an optimal problem and discuss some of its properties thereafter we establish an sfm to solve set based classification experiments about water quality evaluation and set valued data classifications show the superiority of sfm

issues about retinex theory and contrast enhancement we present an interpretation of land s retinex theory that we show to be consistent with the original formulation the proposed model relies on the computation of the expectation value of a suitable random variable weighted with a kernel function thus the name kernel based retinex kbr for the corresponding algorithm kbr shares the same intrinsic characteristics of the original retinex it can reduce the effect of a color cast and enhance details in low key images but since it can only increase pixel intensities it is not able to enhance over exposed pictures comparing the analytical structure of kbr with that of a recent variational model of color image enhancement we are able to perform an analysis of the action of kbr on contrast showing the need to anti symmetrize its equation in order to produce a two sided contrast modification able to enhance both under and over exposed pictures the anti symmetrized kbr equations show clear correspondences with other existing color correction models in particular ace whose relationship with retinex has always been difficult to clarify finally from an image processing point of view we mention that both kbr and its antisymmetric version are free from the chromatic noise due to the use of paths in the original retinex implementation and that they can be suitably approximated in order to reduce their computational complexity from mathcal o n 2 to mathcal o n log n being n the number of input pixels

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

fusion of multichannel local and global structural cues for photo aesthetics evaluation photo aesthetic quality evaluation is a fundamental yet under addressed task in computer vision and image processing fields conventional approaches are frustrated by the following two drawbacks first both the local and global spatial arrangements of image regions play an important role in photo aesthetics however existing rules e g visual balance heuristically define which spatial distribution among the salient regions of a photo is aesthetically pleasing second it is difficult to adjust visual cues from multiple channels automatically in photo aesthetics assessment to solve these problems we propose a new photo aesthetics evaluation framework focusing on learning the image descriptors that characterize local and global structural aesthetics from multiple visual channels in particular to describe the spatial structure of the image local regions we construct graphlets small sized connected graphs by connecting spatially adjacent atomic regions since spatially adjacent graphlets distribute closely in their feature space we project them onto a manifold and subsequently propose an embedding algorithm the embedding algorithm encodes the photo global spatial layout into graphlets simultaneously the importance of graphlets from multiple visual channels are dynamically adjusted finally these post embedding graphlets are integrated for photo aesthetics evaluation using a probabilistic model experimental results show that 1 the visualized graphlets explicitly capture the aesthetically arranged atomic regions 2 the proposed approach generalizes and improves four prominent aesthetic rules and 3 our approach significantly outperforms state of the art algorithms in photo aesthetics prediction

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

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

a theoretical analysis of bagging as a linear combination of classifiers we apply an analytical framework for the analysis of linearly combined classifiers to ensembles generated by bagging this provides an analytical model of bagging misclassification probability as a function of the ensemble size which is a novel result in the literature experimental results on real data sets confirm the theoretical predictions this allows us to derive a novel and theoretically grounded guideline for choosing bagging ensemble size furthermore our results are consistent with explanations of bagging in terms of classifier instability and variance reduction support the optimality of the simple average over the weighted average combining rule for ensembles generated by bagging and apply to other randomization based methods for constructing classifier ensembles although our results do not allow to compare bagging misclassification probability with the one of an individual classifier trained on the original training set we discuss how the considered theoretical framework could be exploited to this aim

a perceptually inspired variational framework for color enhancement basic phenomenology of human color vision has been widely taken as an inspiration to devise explicit color correction algorithms the behavior of these models in terms of significative image features such as e g contrast and dispersion can be difficult to characterize to cope with this we propose to use a variational formulation of color contrast enhancement that is inspired by the basic phenomenology of color perception in particular we devise a set of basic requirements to be fulfilled by an energy to be considered as perceptually inspired showing that there is an explicit class of functionals satisfying all of them we single out three explicit functionals that we consider of basic interest showing similarities and differences with existing models the minima of such functionals is computed using a gradient descent approach we also present a general methodology to reduce the computational cost of the algorithms under analysis from o n2 to o n logn being n the number of pixels of the input image

self similarity of brownian motion and a large deviation principle for random fields on a binary tree using self similarity of brownian motion and its representation as a product measure on a binary tree we construct a random sequence of probability measures which converges to the distribution of the brownian bridge we establish a large deviation principle for random fields on a binary tree this leads to a class of probability measures with a certain self similarity property the same construction can be carried out forc 0 1 valued processes and we can describe for instance ac 0 1 valued ornstein uhlenbeck process as a large deviation of brownian sheet

a note on a goal programming model for incomplete interval multiplicative preference relations and its application in group decision making abstract in a recently published paper by liu et al liu f zhang w g wang z x 2012 a goal programming model for incomplete interval multiplicative preference relations and its application in group decision making european journal of operational research 218 747 754 two equations are introduced to define consistency of incomplete interval multiplicative preference relations imprs and employed to develop a goal programming model for estimating missing values this note illustrates that such consistency definition and estimation model are technically incorrect new transitivity conditions are proposed to define consistent imprs and a two stage goal programming approach is devised to estimate missing values for incomplete imprs

dominance degrees for intervals and their application in multiple attribute decision making abstract since intervals are used to express decision information in various decision making problems it is necessary to give a feasible method to rank them the most commonly used method is to employ the possibility degree to compare intervals in pairs then construct a fuzzy preference relation generally the constructed fuzzy preference relation does not keep additive multiplicative consistency in order to ensure the consistency of decision information optimization models are constructed by using the logical relationship between the elements of the consistent fuzzy preference relation and their weights then by solving the optimization models consistent fuzzy preference relations are obtained the consistent fuzzy preference relations are the proxy of the original inconsistent fuzzy preference relation constructed by the possibility degree however such treatment is flawed the inconsistent fuzzy preference relation generated from the possibility degree can t guarantee the reliability of the result while the proxy consistent fuzzy preference relation would cause bias to solve this problem the additive dominance degree and multiplicative dominance degree for intervals are proposed as a result of indirect comparison the fuzzy preference relations are constructed from the dominance degrees of intervals to ensure the consistency of decision information in the process of ranking intervals this can avoid decision making bias furthermore a new approach to interval multiple attribute decision making is proposed based on the dominance degrees

uncertainty and rank order in the analytic hierarchy process abstract the analytic hierarchy process uses paired comparisons to derive a scale of relative importance for alternatives we investigate the effect of uncertainty in judgment on the stability of the rank order of alternatives the uncertainty experienced by decision makers in making comparisons is measured by associating with each judgment an interval of numerical values the approach leads to estimating the probability that an alternative or project exchanges rank with other projects these probabilities are then used to calculate the probability that project would change rank at all we combine the priority of importance of each project with the probability that it does not change rank to obtain the final ranking

active learning based on locally linear reconstruction we consider the active learning problem which aims to select the most representative points out of many existing active learning techniques optimum experimental design oed has received considerable attention recently the typical oed criteria minimize the variance of the parameter estimates or predicted value however these methods see only global euclidean structure while the local manifold structure is ignored for example i optimal design selects those data points such that other data points can be best approximated by linear combinations of all the selected points in this paper we propose a novel active learning algorithm which takes into account the local structure of the data space that is each data point should be approximated by the linear combination of only its neighbors given the local reconstruction coefficients for every data point and the coordinates of the selected points a transductive learning algorithm called locally linear reconstruction llr is proposed to reconstruct every other point the most representative points are thus defined as those whose coordinates can be used to best reconstruct the whole data set the sequential and convex optimization schemes are also introduced to solve the optimization problem the experimental results have demonstrated the effectiveness of our proposed method

a simple generalization of the o brien and fleming group sequential test procedure to more than two treatment groups as a modification of a fixed single sample trial o brien and fleming 1979 proposed a group sequential test procedure for clinical trials for comparing only two treatments the purpose of this paper is to provide a direct generalization of this procedure to accomodate more than two treatment groups on the basis of monte carlo simulations a table that summarizes the critical values for levels equal to 05 and 10 in the situation where the number of treatment groups ranges from 2 to 10 and the number of sequential tests ranges from 1 to 10 has been derived as well

slic superpixels compared to state of the art superpixel methods computer vision applications have come to rely increasingly on superpixels in recent years but it is not always clear what constitutes a good superpixel algorithm in an effort to understand the benefits and drawbacks of existing methods we empirically compare five state of the art superpixel algorithms for their ability to adhere to image boundaries speed memory efficiency and their impact on segmentation performance we then introduce a new superpixel algorithm simple linear iterative clustering slic which adapts a k means clustering approach to efficiently generate superpixels despite its simplicity slic adheres to boundaries as well as or better than previous methods at the same time it is faster and more memory efficient improves segmentation performance and is straightforward to extend to supervoxel generation

further results on a multiple testing procedure for clinical trials o brien and fleming 1979 biometrics 35 549 556 proposed a procedure for multiple testing in clinical trials for acute disease we evaluated their procedure for chronic disease models and found that it can be used without modification type i errors are unaltered and no loss of power is seen in comparison with single sample procedures however average savings in sample size are less for the chronic disease models than for the acute model finally it is shown that for any specific disease model and fixed maximum number of inspections of the data the percentage reduction in sample size can be readily predicted from the power

the performance of the o brien fleming multiple testing procedure in the presence of intraclass correlation assuming that all subject responses were independent o brien and fleming 1979 biometrics 35 549 556 proposed a simple and useful multiple testing procedure for clinical trials for comparing two treatments with dichotomous data differences in the methods of evaluating subject responses at each evaluation time however may induce an intraclass correlation among these responses used in calculating the o brien fleming multiple testing procedure on the basis of monte carlo simulations we note that even a small intraclass correlation among subject responses in the same analysis can substantially inflate the type i error of the o brien fleming multiple testing procedure furthermore this inflation generally increases as either the number of analyses or the underlying response probability increases we also have demonstrated that if we were able to maintain a uniform medical test procedure between the two treatments for each analysis the actual type i error of the o brien fleming multiple testing procedure may conversely become conservative

building sparse twin support vector machine classifiers in primal space abstract twin support vector machines tsvm obtain faster training speeds than classical support vector machines svm however tsvm augmented vectors lose sparsity in this paper a rapid sparse twin support vector machine stsvm classifier in primal space is proposed to improve the sparsity and robustness of tsvm based on a simple back fitting strategy the stsvm iteratively builds each nonparallel hyperplanes by adding one support vector sv from the corresponding class at one time this process is terminated using an adaptive and stable stopping criterion stsvm learning is implemented by linear equation computing systems through introducing a quadratic function to approximate the empirical risk the computational results on several synthetic and benchmark datasets indicate that the stsvm obtains a sparse separating hyperplane at a low cost without sacrificing its generalization performance

image signature highlighting sparse salient regions we introduce a simple image descriptor referred to as the image signature we show within the theoretical framework of sparse signal mixing that this quantity spatially approximates the foreground of an image we experimentally investigate whether this approximate foreground overlaps with visually conspicuous image locations by developing a saliency algorithm based on the image signature this saliency algorithm predicts human fixation points best among competitors on the bruce and tsotsos 1 benchmark data set and does so in much shorter running time in a related experiment we demonstrate with a change blindness data set that the distance between images induced by the image signature is closer to human perceptual distance than can be achieved using other saliency algorithms pixel wise or gist 2 descriptor methods

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

a probabilistic associative model for segmenting weakly supervised images weakly supervised image segmentation is an important yet challenging task in image processing and pattern recognition fields it is defined as in the training stage semantic labels are only at the image level without regard to their specific object scene location within the image given a test image the goal is to predict the semantics of every pixel superpixel in this paper we propose a new weakly supervised image segmentation model focusing on learning the semantic associations between superpixel sets graphlets in this paper in particular we first extract graphlets from each image where a graphlet is a small sized graph measures the potential of multiple spatially neighboring superpixels i e the probability of these superpixels sharing a common semantic label such as the sky or the sea to compare different sized graphlets and to incorporate image level labels a manifold embedding algorithm is designed to transform all graphlets into equal length feature vectors finally we present a hierarchical bayesian network to capture the semantic associations between postembedding graphlets based on which the semantics of each superpixel is inferred accordingly experimental results demonstrate that 1 our approach performs competitively compared with the state of the art approaches on three public data sets and 2 considerable performance enhancement is achieved when using our approach on segmentation based photo cropping and image categorization

repeated significance testing for a general class of statistics used in censored survival analysis abstract the asymptotic joint distribution of a class of sequentially computed statistics used in survival analysis is derived when the individuals under study enter serially and are subject to random loss to follow up these results are used for constructing repeated significance tests over real time

the optimal group continuous logarithm compatibility measure for interval multiplicative preference relations based on the cowga operator the calculation of compatibility measures is an important technique employed in group decision making with interval multiplicative preference relations in this paper a new compatibility measure called the continuous logarithm compatibility which considers risk attitudes in decision making based on the continuous ordered weighted geometric averaging cowga operator is introduced we also develop a group continuous compatibility model gcc model by minimizing the group continuous logarithm compatibility measure between the synthetic interval multiplicative preference relation and the continuous characteristic preference relation furthermore theoretical foundations are established for the proposed model such as the sufficient and necessary conditions for the existence of an optimal solution the conditions for the existence of a superior optimal solution and the conditions for the existence of redundant preference relations in addition we investigate certain conditions for which the optimal objective function of the gcc model guarantees its efficiency as the number of decision makers increases finally practical illustrative examples are examined to demonstrate the model and compare it with previous methods

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

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

a pde formalization of retinex theory in 1964 edwin h land formulated the retinex theory the first attempt to simulate and explain how the human visual system perceives color his theory and an extension the reset retinex were further formalized by land and mccann several retinex algorithms have been developed ever since these color constancy algorithms modify the rgb values at each pixel to give an estimate of the color sensation without a priori information on the illumination unfortunately the retinex land mccann original algorithm is both complex and not fully specified indeed this algorithm computes at each pixel an average of a very large set of paths on the image for this reason retinex has received several interpretations and implementations which among other aims attempt to tune down its excessive complexity in this paper it is proved that if the paths are assumed to be symmetric random walks the retinex solutions satisfy a discrete poisson equation this formalization yields an exact and fast implementation using only two ffts several experiments on color images illustrate the effectiveness of the retinex original theory

the random subspace method for constructing decision forests much of previous attention on decision trees focuses on the splitting criteria and optimization of tree sizes the dilemma between overfitting and achieving maximum accuracy is seldom resolved a method to construct a decision tree based classifier is proposed that maintains highest accuracy on training data and improves on generalization accuracy as it grows in complexity the classifier consists of multiple trees constructed systematically by pseudorandomly selecting subsets of components of the feature vector that is trees constructed in randomly chosen subspaces the subspace method is compared to single tree classifiers and other forest construction methods by experiments on publicly available datasets where the method s superiority is demonstrated we also discuss independence between trees in a forest and relate that to the combined classification accuracy

a ν twin support vector machine ν tsvm classifier and its geometric algorithms in this paper a n twin support vector machine n tsvm is presented improving upon the recently proposed twin support vector machine tsvm this n tsvm introduces a pair of parameters n to control the bounds of the fractions of the support vectors and the error margins the theoretical analysis shows that this n tsvm can be interpreted as a pair of minimum generalized mahalanobis norm problems on two reduced convex hulls rchs based on the well known gilbert s algorithm a geometric algorithm for tsvm ga tsvm and its probabilistic speed up version named pga tsvm are presented computational results on several synthetic as well as benchmark datasets demonstrate the significant advantages of the proposed algorithms in terms of both computation complexity and classification accuracy

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

on a class of generalized takagi functions with linear pathwise quadratic variation abstract we consider a class x of continuous functions on 0 1 that is of interest from two different perspectives first it is closely related to sets of functions that have been studied as generalizations of the takagi function second each function in x admits a linear pathwise quadratic variation and can thus serve as an integrator in follmer s pathwise it calculus we derive several uniform properties of the class x for instance we compute the overall pointwise maximum the uniform maximal oscillation and the exact uniform modulus of continuity for all functions in x furthermore we give an example of a pair x y x for which the quadratic variation of the sum x y does not exist

a variational framework for retinex retinex theory addresses the problem of separating the illumination from the reflectance in a given image and thereby compensating for non uniform lighting this is in general an ill posed problem in this paper we propose a variational model for the retinex problem that unifies previous methods similar to previous algorithms it assumes spatial smoothness of the illumination field in addition knowledge of the limited dynamic range of the reflectance is used as a constraint in the recovery process a penalty term is also included exploiting a priori knowledge of the nature of the reflectance image the proposed formulation adopts a bayesian view point of the estimation problem which leads to an algebraic regularization term that contributes to better conditioning of the reconstruction problem based on the proposed variational model we show that the illumination estimation problem can be formulated as a quadratic programming optimization problem an efficient multi resolution algorithm is proposed it exploits the spatial correlation in the reflectance and illumination images applications of the algorithm to various color images yield promising results

image categorization by learning a propagated graphlet path spatial pyramid matching is a standard architecture for categorical image retrieval however its performance is largely limited by the prespecified rectangular spatial regions when pooling local descriptors in this paper we propose to learn object shaped and directional receptive fields for image categorization in particular different objects in an image are seamlessly constructed by superpixels while the direction captures human gaze shifting path by generating a number of superpixels in each image we construct graphlets to describe different objects they function as the object shaped receptive fields for image comparison due to the huge number of graphlets in an image a saliency guided graphlet selection algorithm is proposed a manifold embedding algorithm encodes graphlets with the semantics of training image tags then we derive a manifold propagation to calculate the postembedding graphlets by leveraging visual saliency maps the sequentially propagated graphlets constitute a path that mimics human gaze shifting finally we use the learned graphlet path as receptive fields for local image descriptor pooling the local descriptors from similar receptive fields of pairwise images more significantly contribute to the final image kernel thorough experiments demonstrate the advantage of our approach

a two stage logarithmic goal programming method for generating weights from interval comparison matrices a two stage logarithmic goal programming tlgp method is proposed to generate weights from interval comparison matrices which can be either consistent or inconsistent the first stage is devised to minimize the inconsistency of interval comparison matrices and the second stage is developed to generate priorities under the condition of minimal inconsistency the weights are assumed to be multiplicative rather than additive in the case of hierarchical structures a nonlinear programming method is used to aggregate local interval weights into global interval weights a simple yet practical preference ranking method is investigated to compare the interval weights of criteria or rank alternatives in a multiplicative aggregation process the proposed tlgp is also applicable to fuzzy comparison matrices when they are transformed into interval comparison matrices using a level sets and the extension principle six numerical examples including a group decision analysis problem with a group of comparison matrices a hierarchical decision problem and a fuzzy decision problem using fuzzy comparison matrix are examined to show the applications of the proposed methods comparisons with other existing procedures are made whenever possible

design of state estimator for bidirectional associative memory neural networks with leakage delays this paper considers the issue of state estimation for a class of bidirectional associative memory bam neural networks more precisely the bam model is considered with mixed delays which includes a constant delay in the leakage term time varying discrete delay and constant distributed delay by constructing a novel lyapunov krasovskii functional lkf together with free weighting matrix technique a new delay dependent sufficient condition is derived to estimate the neuron states through available output measurements such that for all admissible delay bounds the resulting estimation error system is globally asymptotically stable also it is assumed that the derivative of time delay is not necessarily zero or less than one further the derived conditions are formulated in terms of a set of linear matrix inequalities lmis which can be easily solved by using some standard numerical packages finally a numerical example with simulation result is presented to show the effectiveness of the proposed theory the result reveals that the leakage delays have a destabilizing influence on the system and they cannot be ignored

a rough margin based support vector machine by introducing the rough set theory into the support vector machine svm a rough margin based svm rmsvm is proposed to deal with the overfitting problem due to outliers similar to the classical svm the rmsvm searches for the separating hyper plane that maximizes the rough margin defined by the lower and upper margin in this way more data points are adaptively considered rather than the few extreme value points used in the classical svm in addition different support vectors may have different effects on the learning of the separating hyper plane depending on their positions in the rough margin points in the lower margin have more effects than those in the boundary of the rough margin from experimental results on six benchmark datasets the classification accuracy of this algorithm is improved without additional computational expense compared with the classical n svm

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

continuous generalized owa operator and its application to decision making in this paper we present a new class of operators called the continuous generalized ordered weighted averaging c gowa operators which extends the continuous ordered weighted averaging operator to adapt to uncertain and complex situations in decision making we use differentiated aggregation method and produce special forms of c gowa operator in addition we apply the c gowa operator to the aggregation of multiple interval arguments and obtain a wide range of aggregation operators we especially discuss the controlling parameter and the selection of basic unit interval monotonic function introduced in the information aggregation to make it more feasible we further generalize the previous approaches by using choquet integral and quasi arithmetic means obtaining the combined continuous generalized choquet integral aggregation operator and the combined continuous quasi arithmetic choquet integral aggregation operator we also present some further extension by using hierarchical aggregation rules obtaining the ordered hierarchies of the combined c gowa operator meanwhile some desirable properties of these operators are investigated finally we give a numerical example to illustrate the application of these operators to group decision making with interval arguments

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

discovering discriminative graphlets for aerial image categories recognition recognizing aerial image categories is useful for scene annotation and surveillance local features have been demonstrated to be robust to image transformations including occlusions and clutters however the geometric property of an aerial image i e the topology and relative displacement of local features which is key to discriminating aerial image categories cannot be effectively represented by state of the art generic visual descriptors to solve this problem we propose a recognition model that mines graphlets from aerial images where graphlets are small connected subgraphs reflecting both the geometric property and color texture distribution of an aerial image more specifically each aerial image is decomposed into a set of basic components e g road and playground and a region adjacency graph rag is accordingly constructed to model their spatial interactions aerial image categories recognition can subsequently be casted as rag to rag matching based on graph theory rag to rag matching is conducted by comparing all their respective graphlets because the number of graphlets is huge we derive a manifold embedding algorithm to measure different sized graphlets after which we select graphlets that have highly discriminative and low redundancy topologies through quantizing the selected graphlets from each aerial image into a feature vector we use support vector machine to discriminate aerial image categories experimental results indicate that our method outperforms several state of the art object scene recognition models and the visualized graphlets indicate that the discriminative patterns are discovered by our proposed approach

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

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

change of variable formulas for non anticipative functionals on path space we derive a change of variable formula for non anticipative functionals defined on the space of rd valued right continuous paths with left limits the functionals are only required to possess certain directional derivatives which may be computed pathwise our results lead to functional extensions of the ito formula for a large class of stochastic processes including semimartingales and dirichlet processes in particular we show the stability of the class of semimartingales under certain functional transformations

axiomatic property based consistency analysis and decision making with interval multiplicative reciprocal preference relations abstract this paper focuses on obtaining an interval extension of saaty s consistency and eliciting normalized interval weights in analytic form from interval multiplicative reciprocal preference relations imrprs as well as checking acceptability of imrprs four axiomatic properties are presented to characterize multiplicative consistency of imrprs the paper shows that six existing consistency definitions fail to satisfy all the four axiomatic properties a constrained interval multiplication based transitivity equation is devised and an interval matrix is constructed to capture original preferences and row uncertainty proportionalities of an imrpr based on the constructed interval matrix an ordinary interval multiplication based transitivity equation is developed to define consistency of imrprs a logarithmic least square model is established to find normalized interval weights from imrprs and its analytic solution is obtained by the lagrangian multiplier method the paper introduces an index to measure uniformity of row uncertainties in an imrpr and proposes a geometric consistency index to measure inconsistency of imrprs a novel method is put forward to determine acceptability of imrprs by checking acceptable consistency and acceptable uncertainty the proposed models are illustrated by eight numerical examples and a hierarchical multi criteria decision making problem dealing with recommending undergraduate students to graduate admission

functional ito calculus and stochastic integral representation of martingales we develop a non anticipative calculus for functionals of a continuous semimartingale using an extension of the ito formula to path dependent functionals which possess certain directional derivatives the construction is based on a pathwise derivative introduced by b dupire for functionals on the space of right continuous functions with left limits we show that this functional derivative admits a suitable extension to the space of square integrable martingales this extension denes a weak derivative which is shown to be the inverse of the ito integral and which may be viewed as a non anticipative lifting of the malliavin derivative these results lead to a constructive martingale representation formula for ito processes by contrast with the clark haussmann ocone formula this representation only involves nonanticipative quantities which may be computed pathwise

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

on signed takagi landsberg functions pth variation maximum and modulus of continuity abstract we study a class x h of signed takagi landsberg functions with hurst parameter h 0 1 we first show that the functions in x h admit a linear pth variation along the sequence of dyadic partitions of 0 1 where p 1 h the slope of the linear increase can be represented as the pth absolute moment of the infinite bernoulli convolution with parameter 2 h 1 the existence of a continuous pth variation enables the use of the functions in x h as test integrators for higher order pathwise ito calculus our next results concern the maximum the maximizers and the modulus of continuity of the classical takagi landsberg function for all 0 h 1 then we identify the uniform maximum the uniform maximal oscillation and a uniform modulus of continuity for the class x h

consistency analysis and priority derivation of triangular fuzzy preference relations based on modal value and geometric mean existing consistency notions of triangular fuzzy preference relations tfprs are illustrated to be non robust new consistency and acceptable consistency definitions are put forward for tfprs we propose a notion of normalized triangular fuzzy multiplicative weights ntfmws transformation formulae are provided to convert ntfmws into consistent tfprs a logarithmic least square model is developed to derive a ntfmw vector from a tfpr triangular fuzzy preference relation tfpr is an effective framework to model pairwise estimations with imprecision and vagueness in order to obtain a reliable and rational decision result it is important to investigate consistency and priority derivation of tfprs the paper analyzes existing definitions and properties of consistent tfprs and illustrates that they have no invariance with respect to permutations of decision alternatives a new triangular fuzzy arithmetic based transitivity equation is introduced to define consistent tfprs the new transitivity equation reflects multiplicative consistency of modal values and multiplicative consistency of geometric means of triangular fuzzy estimations some properties are presented for consistent tfprs and a notion of acceptable consistency is put forward for tfprs geometric mean and uncertainty ratio based transformation formulae are devised to convert normalized triangular fuzzy multiplicative weights into consistent tfprs a logarithmic least square model is further established for deriving a normalized triangular fuzzy multiplicative weight vector from a tfpr with acceptable consistency a geometric mean based method is developed to compare and rank triangular fuzzy multiplicative weights three numerical examples including a group decision making problem are examined to demonstrate validity and advantages of the proposed models

perceptual multi channel visual feature fusion for scene categorization abstract effectively recognizing sceneries from a variety of categories is an indispensable but challenging technique in computer vision and intelligent systems in this work we propose a novel image kernel based on human gaze shifting aiming at discovering the mechanism of humans perceiving visually semantically salient regions within a scenery more specifically we first design a weakly supervised embedding algorithm which projects the local image features i e graphlets in this work onto the pre defined semantic space thereby we describe each graphlet by multiple visual features at both low level and high level it is generally acknowledged that humans attend to only a few regions within a scenery thus we formulate a sparsity constrained graphlet ranking algorithm which incorporates visual clues at both the low level and the high level according to human visual perception these top ranked graphlets are either visually or semantically salient we sequentially connect them into a path which mimics human gaze shifting lastly a so called gaze shifting kernel gsk is calculated based on the learned paths from a collection of scene images and a kernel svm is employed for calculating the scene categories comprehensive experiments on a series of well known scene image sets shown the competitiveness and robustness of our gsk we also demonstrated the high consistency of the predicted path with real human gaze shifting path

a decision making model based on interval additive reciprocal matrices with additive approximation consistency abstract in order to capture the rationality experienced by decision makers in choosing the best alternative s of much interest is to study the consistency of preference relations in the analytic hierarchy process ahp when the typical ahp is extended by using fuzzy numbers to evaluate the opinions of decision makers the consistency of fuzzy judgments is worth to be considered in this paper we analyze some definitions of interval additive reciprocal matrices with additive consistency it is concluded that interval additive reciprocal matrices are inconsistent in essence the concept of additive approximation consistency of interval additive reciprocal matrices is proposed moreover a novel exchange method is designed to enumerate all permutations of alternatives for checking the approximation consistency by considering the randomness exhibited in pairwisely comparing alternatives a method of obtaining the interval weight vector is given a new algorithm of solving the decision making problem with interval additive reciprocal matrices is proposed finally two numerical examples are carried out to illustrate the new definition and some comparisons are offered

constructing functions with prescribed pathwise quadratic variation we construct rich vector spaces of continuous functions with prescribed curved or linear pathwise quadratic variations we also construct a class of functions whose quadratic variation may depend in a local and nonlinear way on the function value these functions can then be used as integrators in follmer s pathwise it calculus our construction of the latter class of functions relies on an extension of the doss sussman method to a class of nonlinear it differential equations for the follmer integral as an application we provide a deterministic variant of the support theorem for diffusions we also establish that many of the constructed functions are nowhere differentiable

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

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

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

random ordinality ensembles data with multi valued categorical attributes can cause major problems for decision trees the high branching factor can lead to data fragmentation where decisions have little or no statistical support in this paper we propose a new ensemble method random ordinality ensembles roe that reduces this problem and provides significantly improved accuracies over current ensemble methods we perform a random projection of the categorical data into a continuous space as the transformation to continuous data is a random process each dataset has a different imposed ordinality a decision tree that learns on this new continuous space is able to use binary splits hence reduces the data fragmentation problem generally these binary trees are accurate diverse training datasets ensure diverse decision trees in the ensemble we created two variants of the technique roe in the first variant we used decision trees as the base models for ensembles in the second variant we combined the attribute randomisation of random subspaces with random ordinality these methods match or outperform other popular ensemble methods different properties of these ensembles were studied the study suggests that random ordinality trees are generally more accurate and smaller than multi way split decision trees it is also shown that random ordinality attributes can be used to improve bagging and adaboost m1 ensemble methods