a fuzzy extension of the silhouette width criterion for cluster analysis the present paper proposes a new cluster validity measure as an additional criterion to help the decision making process in fuzzy cluster analysis this measure named fuzzy silhouette is a generalization to the fuzzy case of the average silhouette width criterion originally conceived to assess crisp non fuzzy data partitions the fuzzy silhouette is more appealing than its crisp counterpart in the context of fuzzy cluster analysis since it makes explicit use of the fuzzy partition matrix provided by the clustering algorithm in addition it has been designed to improve performance of the original silhouette criterion in detecting regions with higher data density when the data set involves overlapping clusters the performance of the fuzzy silhouette is evaluated and compared to that of five well known cluster validity measures six data sets are used to illustrate different scenarios in which the proposed fuzzy silhouette performs similar to or better than these other criteria thus becoming eligible to join a pool of measures to be used all together in fuzzy cluster analysis

fuzzy clustering for symbolic data most of the techniques used in the literature in clustering symbolic data are based on the hierarchical methodology which utilizes the concept of agglomerative or divisive methods as the core of the algorithm the main contribution of this paper is to show how to apply the concept of fuzziness on a data set of symbolic objects and how to use this concept in formulating the clustering problem of symbolic objects as a partitioning problem finally a fuzzy symbolic c means algorithm is introduced as an application of applying and testing the proposed algorithm on real and synthetic data sets the results of the application of the new algorithm show that the new technique is quite efficient and in many respects superior to traditional methods of hierarchical nature

a class of fuzzy clusterwise regression models in this paper we introduce a class of fuzzy clusterwise regression models with lr fuzzy response variable and numeric explanatory variables which embodies fuzzy clustering into a fuzzy regression framework the model bypasses the heterogeneity problem that could arise in fuzzy regression by subdividing the dataset into homogeneous clusters and performing separate fuzzy regression on each cluster the integration of the clustering model into the regression framework allows us to simultaneously estimate the regression parameters and the membership degree of each observation to each cluster by optimizing a single objective function the class of models proposed here includes as special cases the fuzzy clusterwise linear regression model and the fuzzy clusterwise polynomial regression model we also introduce a set of goodness of fit indices to evaluate the fit of the regression model within each cluster as well as in the whole dataset finally we consider some cluster validity criteria that are useful in identifying the optimal number of clusters several applications are provided in order to illustrate the approach

a new upper bound on the ml decoding error probability of linear binary block codes in awgn interference performance evaluation of maximum likelihood ml soft decision decoded binary block codes is usually carried out using bounding techniques many tight upper bounds on the error probability of binary codes are based on the so called gallager s first bounding technique gfbt the tangential sphere bound tsb of poltyrev which has been believed for many years to offer the tightest bound developed for binary block codes is an example within the framework of the tsb and gfbt we apply a new method referred to as the added hyper plane ahp technique to the decomposition of the error probability this results in a bound developed upon the application of two stages of the gfbt with two different gallager regions culminating in a tightened upper bound beyond the tsb the proposed bound is simple and only requires the spectrum of the binary code

a fuzzy algorithm for color quantization of images in this paper we review a number of techniques for fuzzy color quantization we show that the fuzzy membership paradigm is particularly suited to color quantization where color cluster boundaries are not well defined we propose a new fuzzy color quantization technique which incorporates a term for partition index this algorithm produces better results than fuzzy c means at a reduced computational cost we test the results of the fuzzy algorithms using quality metrics which model the perception of the human visual system and illustrate that substantial quality improvements are achieved

fuzzy radicals and prime fuzzy ideals of ordered semigroups let s be an ordered semigroup a fuzzy subset of s is by definition an arbitrary mapping f s 0 1 where 0 1 is the usual interval of real numbers motivated by studying prime fuzzy ideals in rings semigroups and ordered semigroups and as a continuation of kehayopulu and tsingelis s works in ordered semigroups in terms of fuzzy subsets in this paper we introduce the notion of ordered fuzzy points of an ordered semigroup s and give a characterization of prime fuzzy ideals of an ordered semigroup s we also introduce the concepts of weakly prime fuzzy ideals completely prime fuzzy ideals completely semiprime fuzzy ideals and weakly completely prime fuzzy ideals of an ordered semigroup s and establish the relationship between the five classes of ideals furthermore we characterize weakly prime fuzzy ideals completely semiprime fuzzy ideals and weakly completely prime fuzzy ideals of s by their level ideals finally we introduce and investigate the fuzzy radicals of ordered semigroups by means of ordered fuzzy points and prove that the fuzzy radical of every completely semiprime fuzzy ideal of an ordered semigroup s can be expressed as the intersection of all weakly completely prime fuzzy ideals containing it as an application of the results of this paper the corresponding results of semigroups without order are also obtained

fuzzy multiplication semigroup the notion of fuzzy multiplication semigroup is introduced using fuzzy ideal in a fuzzy multiplication semigroup with identity i every fuzzy ideal with sup property whose radical is prime is primary and ii every primary fuzzy ideal with sup property is some power of its fuzzy radical conditions i and ii are also found to be sufficient for a commutative semigroup with identity and satisfying some other conditions to be a fuzzy multiplication semigroup

prime fuzzy ideals in rings abstract in this paper give a characterization of prime fuzzy ideals we introduce weakly completely prime fuzzy ideals and establish a relation between completely prime fuzzy ideals and weakly completely prime fuzzy ideals

fuzzy clustering algorithms and their cluster validity abstract a non metric clustering algorithm based on a fuzzy objective function which reflects proximity based on some global dissimilarity measure is proposed the global optimal solution is shown to be difficult to obtain and an alternative iterative procedure is presented this procedure is easily implemented and converges to a local optimum some validity functionals which measure the effectiveness with which cluster structure has been identified are compared in relation with the iterative procedures described in the paper

a lower bound on the error probability for signals in white gaussian noise the performance of specific signal constellations in digital communications problems is often described through use of the union bound an upper bound which is asymptotically tight with respect to the signal to noise ratio it is not unnatural to ask how tight this result is for small to medium values of signal to noise ratio one way to answer this question is to develop an asymptotically tight lower bound such is the goal of the present paper

comparing som neural network with fuzzy c means k means and traditional hierarchical clustering algorithms in this paper we present a comparison among some nonhierarchical and hierarchical clustering algorithms including som self organization map neural network and fuzzy c means methods data were simulated considering correlated and uncorrelated variables nonoverlapping and overlapping clusters with and without outliers a total of 2530 data sets were simulated the results showed that fuzzy c means had a very good performance in all cases being very stable even in the presence of outliers and overlapping all other clustering algorithms were very affected by the amount of overlapping and outliers som neural network did not perform well in almost all cases being very affected by the number of variables and clusters the traditional hierarchical clustering and k means methods presented similar performance

interval type 2 credibilistic clustering for pattern recognition this paper presents a new approach to interval type 2 fuzzy clustering in order to consider compactness within the clusters and separation of them simultaneously the objective function of this paper is designed such that it generates both degrees of membership and non membership of each data in each cluster and integrates them using credibility concept also a new approach to separation of clusters is proposed and utilized in designing the objective function in this approach the borders of clusters and therefore their compactness contribute in attaining their separation so the separation of clusters is not assessed only by the distance of their centers the credibility degrees are transformed to interval type 2 form to handle different sources of uncertainty finally a new validity index to characterize the number of clusters based on proposed approach to separation of clusters and choquet integrals are proposed the advantages of paper contributions are illustrated using several examples a new objective function based fuzzy clustering is introduced using credibility concept a new approach to separation of clusters is presented a new validity index is designed by proposed approach to separation and choquet integral the obtained results show that proposed model can handle different types of clusters

on fuzzy ideals and fuzzy quotient rings of a ring abstract in this paper we define fuzzy quotient rings induced by fuzzy ideals and give the notion of fuzzy nilpotent ideals we give also a characterization of semiprime rings in terms of fuzzy ideals

bounds on the decoding error probability of binary linear codes via their spectra bounds on the error probability of maximum likelihood decoding of a binary linear code are considered the bounds derived use the weight spectrum of the code and they are tighter than the conventional union bound in the case of large noise in the channel the bounds derived are applied to a code with an average spectrum and the result is compared to the random coding exponent the author shows that the bound considered for the binary symmetrical channel case coincides asymptotically with the random coding bound for the case of awgn channel the author shows that berlekamp s 1980 tangential bound can be improved but even this improved bound does not coincide with the random coding bound although it can be very close to it

on fuzzy quotient rings induced by fuzzy ideals abstract in this paper we define fuzzy quotient rings induced by fuzzy ideals and study the relation between fuzzy quotient rings and fuzzy ideals

t fuzzy prime ideals abstract the purpose of this paper is to define study and characterize the t fuzzy prime ideals t fuzzy strongly prime ideals and t s fuzzy weakly prime ideals proving the inclusion relationships that are satisfied among them the t fuzzy comaximal ideals and fuzzy maximal ideals are also investigated

fuzzy sets in pattern recognition methodology and methods abstract an objective of the paper is to discuss a state of the art of methodology and algorithms of fuzzy sets in the field of pattern recognition in real world recognition and classification problems we are faced with fuzziness that is connected with diverse facets of cognitive activity of the human being an origin of sources of fuzziness is related to labels expressed in feature space as well as to labels of classes taken into account in classification procedures an evident difference between a way of information processing by means of probability and fuzzy set theory and a way of interpretation of results is explained in detail in sequel methods of pattern recognition are studied in two main streams namely supervised and unsupervised learning different approaches to designing of classification schemes as e g relation calculus decision making approach etc are put into account a method of feature selection with the aid of fuzzy measure and fuzzy integral is introduced in clustering techniques methods relying on minimization of objective function are analyzed in detail also a problem of cluster validity expressed in terms of clustering indices is addressed numerical examples are also provided

unsupervised optimal fuzzy clustering this study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set assessment of cluster validity is based on performance measures using hypervolume and density criteria an algorithm is derived from a combination of the fuzzy k means algorithm and fuzzy maximum likelihood estimation the unsupervised fuzzy partition optimal number of classes algorithm performs well in situations of large variability of cluster shapes densities and number of data points in each cluster the algorithm was tested on different classes of simulated data and on a real data set derived from sleep eeg signal

a validity measure for fuzzy clustering the authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c partitions without assumptions as to the number of substructures inherent in the data this function depends on the data set geometric distance measure distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used the function is mathematically justified via its relationship to a well defined hard clustering validity function the separation index for which the condition of uniqueness has already been established the performance of this validity function compares favorably to that of several others the application of this validity function to color image segmentation in a computer color vision system for recognition of ic wafer defects which are otherwise impossible to detect using gray scale image processing is discussed

rank minimization over finite fields fundamental limits and coding theoretic interpretations this paper establishes information theoretic limits for estimating a finite field low rank matrix given random linear measurements of it these linear measurements are obtained by taking inner products of the low rank matrix with random sensing matrices necessary and sufficient conditions on the number of measurements required are provided it is shown that these conditions are sharp and the minimum rank decoder is asymptotically optimal the reliability function of this decoder is also derived by appealing to de caen s lower bound on the probability of a union the sufficient condition also holds when the sensing matrices are sparse a scenario that may be amenable to efficient decoding more precisely it is shown that if the n n sensing matrices contain on average nlog n entries the number of measurements required is the same as that when the sensing matrices are dense and contain entries drawn uniformly at random from the field analogies are drawn between the aforementioned results and rank metric codes in the coding theory literature in fact we are also strongly motivated by understanding when minimum rank distance decoding of random rank metric codes succeeds to this end we derive minimum distance properties of equiprobable and sparse rank metric codes these distance properties provide a precise geometric interpretation of the fact that the sparse ensemble requires as few measurements as the dense one

on fuzzy ideals of a ring 1 abstract the aim of this paper is to study fuzzy ideals of a ring to characterise regular rings and noetherian rings by fuzzy ideals and to determine all fuzzy prime ideals of the ring z of integers

fuzzy subrings and ideals redefined abstract v q fuzzy subrings and ideals of a ring are defined the concepts of v q fuzzy semiprime prime semi primary primary and maximal ideals are introduced and characterization of such fuzzy ideals are obtained v q fuzzy cosets determined by v q fuzzy ideals and v q fuzzy radicals of v q fuzzy ideals are discussed

constrained epsilon minimax test for simultaneous detection and classification a constrained epsilon minimax test is proposed to detect and classify nonorthogonal vectors in gaussian noise with a general covariance matrix and in presence of linear interferences this test is epsilon minimax in the sense that it has a small loss of optimality with respect to the purely theoretical and incalculable constrained minimax test which minimizes the maximum classification error probability subject to a constraint on the false alarm probability this loss is even more negligible as the signal to noise ratio is large furthermore it is also an epsilon equalizer test since its classification error probabilities are equalized up to a negligible difference when the signal to noise ratio is sufficiently large an asymptotically equivalent test with a very simple form is proposed this equivalent test coincides with the generalized likelihood ratio test when the vectors to classify are strongly separated in term of euclidean distance numerical experiments on active user identification in a multiuser system confirm the theoretical findings

fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation ii shell clustering algorithms are ideally suited for computer vision tasks such as boundary detection and surface approximation particularly when the boundaries have jagged or scattered edges and when the range data is sparse this is because shell clustering is insensitive to local aberrations it can be performed directly in image space and unlike traditional approaches it does assume dense data and does not use additional features such as curvatures and surface normals the shell clustering algorithms introduced in part i of this paper assume that the number of clusters is known however which is not the case in many boundary detection and surface approximation applications this problem can be overcome by considering cluster validity we introduce a validity measure called surface density which is explicitly meant for the type of applications considered in this paper we show through theoretical derivations that surface density is relatively invariant to size and partiality incompleteness of the clusters we describe unsupervised clustering algorithms that use the surface density measure and other measures to determine the optimum number of shell clusters automatically and illustrate the application of the proposed algorithms to boundary detection in the case of intensity images and to surface approximation in the case of range images

on the meaning of dunn s partition coefficient for fuzzy clusters abstract a constantly recurring problem in cluster analysis is that of evaluating the number of clusters that are present in a data set the development of fuzzy clustering has brought no definite answer to this question although some new means have been provided offering new ways to tackle this problem one of the promising approaches was dunn s partition coefficient f k u that has been shown to vary between 1 for hard clusters and 1 k for completely fuzzy sets of objects hence the idea that f k u expresses a measure of how far a given fuzzy partition is from a hard one assuming moreover that an optimal partition in an optimal number of clusters will have a harder look than any other partition f k u could be considered as a cluster validity index that this procedure is unjustified is shown by the study of the d f diagram in which by analogy to the partition coefficient f a fuzziness coefficient d is defined an important result of this study is that a higher f k u value does not always correspond to a better allocation than a partition with a lower value this observation contradicts the role of the partition coefficient as cluster validity measurement these results are emply confirmed by various artificial and classical numerical examples

the lattice of fuzzy ideals of a ring the set of all fuzzy ideals of a ring r is partially ordered with respect to the natural ordering of fuzzy sets in r it has been shown that this is a lattice but not a sublattice of the lattice of all fuzzy sets in r this lattice of all fuzzy ideals of r is complete distributive and bounded and has neither atoms nor dual atoms

pseudo codeword analysis of tanner graphs from projective and euclidean planes we consider coded data transmission over a binary input output symmetric memoryless channel using a binary linear code in order to understand the performance of maximum likelihood ml decoding one studies the codewords in particular the minimal codewords and their hamming weights in the context of linear programming lp decoding one s attention needs to be shifted to the pseudo codewords in particular to the minimal pseudo codewords and their pseudo weights in this paper we investigate some families of codes that have good properties under lp decoding namely certain families of low density parity check ldpc codes that are derived from projective and euclidean planes we study the structure of their minimal pseudo codewords and give lower bounds on their pseudo weight besides this main focus we also present some results that hold for pseudo codewords and minimal pseudo codewords of any tanner graph and we highlight how the importance of minimal pseudo codewords under lp decoding varies depending on which binary input output symmetric memoryless channel is used

validity guided re clustering with applications to image segmentation when clustering algorithms are applied to image segmentation the goal is to solve a classification problem however these algorithms do not directly optimize classification duality as a result they are susceptible to two problems 1 the criterion they optimize may not be a good estimator of true classification quality and 2 they often admit many suboptimal solutions this paper introduces an algorithm that uses cluster validity to mitigate problems 1 and 2 the validity guided re clustering vgc algorithm uses cluster validity information to guide a fuzzy re clustering process toward better solutions it starts with a partition generated by a soft or fuzzy clustering algorithm then it iteratively alters the partition by applying novel split and merge operations to the clusters partition modifications that result in improved partition validity are retained vgc is tested on both synthetic and real world data for magnetic resonance image mri segmentation evaluations by radiologists show that vgc outperforms the unsupervised fuzzy c means algorithm and vgc s performance approaches that of the supervised k nearest neighbors algorithm

a new learning strategy for stereo matching derived from a fuzzy clustering method this paper presents an approach to the local stereo correspondence problem the primitives or features used are groups of collinear connected edge points called segments each segment has several associated attributes or properties we have verified that the differences of the attributes for the true matches cluster in a cloud around a center then for each current pair of primitives we compute a distance between the difference of its attributes and the cluster center the correspondence is established in the basis of the minimum distance criterion similarity constraint we have designed an image understanding system to learn the best representative cluster center for such purpose a new learning method is derived from the fuzzy c means fcm algorithm where the dispersion of the true samples in the cluster is taken into account through the mahalanobis distance this is the main contribution of this paper a better performance of the proposed local stereo matching learning method is illustrated with a comparative analysis between classical local methods without learning

the structural clustering and analysis of metric based on granular space in this paper the research on granular space theory and structural clusters of metric based on granular space is introduced and a comprehensive of theoretical and analyzing methodologies is developed the granular space theory is established based on normalized equicrural metric and the consistent cluster characteristics of ordered granular spaces are derived details are shared for some related subject such as the granular representation of structural cluster from normalized metric the optimal cluster determination the fusion of structural cluster and the structural clustering analysis of metric space based on granular space etc theories and methodologies are established for structural clustering based on metric space and developed a series of mathematical models and formal description tools for the research on its potential applications direct and geometric interpretations for structural clustering analysis are provided to assist deeper understanding the essence of clustering or classifying procedure

fuzzy k ideals of semirings the aim of this paper is to introduce the notions of fuzzy k ideals prime fuzzy k ideals and semiregularity of semirings and to characterize prime fuzzy k ideals semiregular semirings noetherian semirings and artinian semirings by fuzzy k ideals

sphere packing bounds revisited for moderate block lengths the main reference of this paper is the sphere packing bound of 1967 sp67 derived by shannon gallager and berlekamp it offers a lower bound on the decoding error probability over a very large variety of channels if it has failed so far to provide any usable material in practical implementation of telecommunication systems it is due to an original focus on asymptotic results making it inapplicable for moderate code lengths and to the difficulty of the involved methods which makes the derivation of sp67 quite hermetic and uninspiring for further research the purpose of this paper is two fold 1 to stir up some renewed interest in the topic on which shannon concluded his career in information theory thanks to a qualitative rather than technical review of the derivation of sp67 introduced by a review of the simpler sphere packing bound derived by shannon in 1959 2 to prove the practical interest of sp67 by extending its field of application to continuous output channels and particularly the additive white gaussian noise awgn channel used with any particular modulation scheme and by improving its lower bound for the moderate code length case so that it becomes the best lower bound for most iteratively decodable codes turbo codes low density parity check ldpc codes repeat accumulate ra codes etc of usual lengths

a fuzzy algebraic system based on the theory of falling shadows abstract based on the concept of a falling shadow a theoretical approach of the fuzzy algebraic system is established a fuzzy subalgebraic system of an algebraic system is considered as a falling shadow of the cloud of the subalgebraic systems when an algebraic system is a ring fuzzy subrings fuzzy ideas fuzzy prime ideas of a ring are seen as falling shadows of the cloud of subrings cloud of ideas cloud of prime ideas we shall show that fuzzy algebraic systems defined int norms are consequences of our definition under certain conditions

on fuzzy ideals and fuzzy bi ideals in semigroups abstract in this paper we give some properties of fuzzy ideals and fuzzy bi ideals of semigroups and characterize semigroups that are left duo left simple and semilattices of subsemigroups in terms of fuzzy ideals and fuzzy bi ideals

color image segmentation an innovative approach in this paper we describe a color image segmentation system that performs color clustering in a color space and then color region segmentation in the image domain for color segmentation we developed a fuzzy clustering algorithm that iteratively generates color clusters using a uniquely defined fuzzy membership function and an objective function for clustering optimization the fuzzy membership function represents belief value of a color belonging to a color cluster and the mutual interference of neighboring clusters the region segmentation algorithm merges clusters in the image domain based on color similarity and spatial adjacency we developed three different methods for merging regions in the image domain unlike many existing clustering algorithms the image segmentation system does not require the knowledge about the number of the color clusters to be generated at each stage and the resolution of the color regions can be controlled by one single parameter the radius of a cluster the color image segmentation system has been implemented and tested on a variety of color images including satellite images car and face images the experiment results are presented and the performance of each algorithm in the segmentation system is analyzed the system has shown to be both effective and efficient

fuzzy algorithms for combined quantization and dithering color quantization reduces the number of the colors in a color image while the subsequent dithering operation attempts to create the illusion of more colors with this reduced palette in quantization the palette is designed to minimize the mean squared error mse however the dithering that follows enhances the color appearance at the expense of increasing the mse we introduce three joint quantization and dithering algorithms to overcome this contradiction the basic idea is the same in two of the approaches introducing the dithering error to the quantizer in the training phase the fuzzy c means fcm and the fuzzy learning vector quantization flvq algorithms are used to develop two combined mechanisms in the third algorithm we minimize an objective function including an inter cluster separation ics term to obtain a color palette which is more suitable for dithering the goal is to enlarge the convex hull of the quantization colors to obtain the illusion of more colors after error diffusion the color contrasts of images are also enhanced with the proposed algorithm we test the results of these three new algorithms using quality metrics which model the perception of the human visual system and illustrate that substantial improvements are achieved after dithering

on radicals of fuzzy submodules and primary fuzzy submodules we define in this paper the concepts of the radical of fuzzy submodules and the primary fuzzy submodules and prove some of their properties

on the error probability of signals in additive white gaussian noise a new upper bound to the probability of error in detecting one of m equally probable signals in additive white gaussian noise is presented this bound is easy to calculate can be applied to any signal set it is always better than the union and minimum distance bounds examples demonstrate the use of the bound

lower bounds on the error probability of block codes based on improvements on de caen s inequality new lower bounds on the error probability of block codes with maximum likelihood decoding are proposed the bounds are obtained by applying a new lower bound on the probability of a union of events derived by improving on de caen s lower bound the new bound includes an arbitrary function to be optimized in order to achieve the tightest results since the optimal choice of this function is known but leads to a trivial and useless identity we find several useful approximations for it each resulting in a new lower bound for the additive white gaussian noise awgn channel and the binary symmetric channel bsc the optimal choice of the optimization function is stated and several approximations are proposed when the bounds are further specialized to linear codes the only knowledge on the code used is its weight enumeration the results are shown to be tighter than the latest bounds in the current literature such as those by seguin 1998 and by keren and litsyn 2001 moreover for the bsc the new bounds widen the range of rates for which the union bound analysis applies thus improving on the bound to the error exponent compared with the de caen based bounds

tight error bounds for nonuniform signaling over awgn channels we consider a bonferroni type lower bound due to kounias 1968 on the probability of a finite union the bound is expressed in terms of only the individual and pairwise event probabilities however it suffers from requiring an exponentially complex search for its direct implementation we address this problem by presenting a practical algorithm for its evaluation this bound is applied together with two other bounds a recent lower bound the kat bound and a greedy algorithm implementation of an upper bound due to hunter 1976 to examine the symbol error p sub a and bit error p sub b probabilities of an uncoded communication system used in conjunction with m ary phase shift keying psk quadrature amplitude qam psk qam modulations and maximum a posteriori map decoding over additive white gaussian noise awgn channels it is shown that the bounds which can be efficiently computed provide an excellent estimate of the error probabilities over the entire range of the signal to noise ratio snr e sub b n sub 0 the new algorithmic bound and the greedy bound are particularly impressive as they agree with the simulation results even during very severe channel conditions

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

fuzzy semiprime ideals in semigroups abstract in this paper we shall introduce the notion of fuzzy semiprimality in a semigroup which is an extension of semiprimality in it and characterize a semigroup that is a semilattice of simple semigroups in terms of fuzzy semiprimality

distance distribution of binary codes and the error probability of decoding we address the problem of bounding below the probability of error under maximum likelihood decoding of a binary code with a known distance distribution used on a binary symmetric channel bsc an improved upper bound is given for the maximum attainable exponent of this probability the reliability function of the channel in particular we prove that the random coding exponent is the true value of the channel reliability for codes rate r in some interval immediately below the critical rate of the channel an analogous result is obtained for the gaussian channel

fuzzy cosets and some fuzzy radicals abstract an attempt is made to formulate fuzzy versions of jacobson and prime radicals of a ring certain basic results pertaining to the notions of jacobson and prime radicals of a ring are extended to the fuzzy setting in particular the following is obtained the jacobson radical prime radical of the ring of fuzzy cosets of in r is zero where r is a commutative ring with identity and is the fuzzy jacobson radical fuzzy prime radical of r

prime and primary l fuzzy ideals of l fuzzy rings the aim of this paper is to give a definition of prime l fuzzy ideal and primary l fuzzy ideal of a fuzzy ring and to give their first properties as well as the relationship of these concepts with the concept of l fuzzy radical

an efficient algorithmic lower bound for the error rate of linear block codes we present an efficient algorithmic lower bound for the block error rate of linear binary block codes under soft maximum likelihood decoding over binary phase shift keying modulated additive white gaussian noise channels we cast the problem of finding a lower bound on the probability of a union as an optimization problem that seeks to find the subset that maximizes a recent lower bound due to kuai alajaji and takahara that we will refer to as the kat bound the improved bound which is denoted by lb s is asymptotically tight as the signal to noise ratio snr grows to infinity and depends only on the code s weight enumeration function for its calculation the use of a subset of the codebook to evaluate the lb s lower bound not only significantly reduces computational complexity but also tightens the bound specially at low snrs numerical results for binary block codes indicate that at high snrs the lb s bound is tighter than other recent lower bounds in the literature which comprise the lower bound due to seguin the kat bound evaluated on the entire codebook and the dot product and norm bounds due to cohen and merhav

cluster validity for fuzzy clustering algorithms abstract the proportion exponent is introduced as a measure of the validity of the clustering obtained for a data set using a fuzzy clustering algorithm it is assumed that the output of an algorithm includes a fuzzy nembership function for each data point we show how to compute the proportion of possible memberships whose maximum entry exceeds the maximum entry of a given membership function and use these proportions to define the proportion exponent its use as a validity functional is illustrated with four numerical examples and its effectiveness compared to other validity functionals namely classification entropy and partition coefficient

cluster validity for the fuzzy c means clustering algorithrm the uniform data function is a function which assigns to the output of the fuzzy c means fc m or fuzzy isodata algorithm a number which measures the quality or validity of the clustering produced by the algorithm for the preselected number of cluster c the fc m algorithm produces c vectors in the space in which the data lie called cluster centers which represent points about which the data are concentrated it also produces for each data point c membership values numbers between zero and one which measure the similarity of the data points to each of the cluster centers it is these membership values which indicate how the point is classified they also indicate how well the point has been classified in that values close to one indicate that the point is close to a particular center but uniformly low memberships indicate that the point has not been classified clearly the uniform data functional udf combines the memberships in such a way as to indicate how well the data have been classified and is computed as follows for each data point compute the ratio of its smallest membership to its largest and then compute the probability that one could obtain a smaller ratio indicating better classification from a clustering of a standard data set in which there is no cluster structure these probabilities are then averaged over the data set to obtain the values of the udf

a lower bound on the error probability for signals in white gaussian noise in this correspondence we apply a recent inequality by de caen 1997 to derive a lower bound on the probability of error for m ary signals derived from a binary linear code and used on the additive white gaussian noise channel with a maximum likelihood decoder this bound depends only on the weight enumerator of the code and the signal to noise ratio e sub b n sub 0 we show that this bound converges to the union upper bound as e sub b n sub 0 goes to infinity finally by means of examples we compare our lower bound with those of shannon and swaszek and with poltyrev s upper bound

modified fuzzy c means algorithm for cellular manufacturing several studies have used the fuzzy c means fcm algorithm for part machine grouping in cellular manufacturing however the application of the standard fcm algorithm to this problem has a number of drawbacks this paper proposes a modified fcm mfcm algorithm that groups components and machines in parallel and through an annealing process with the weighting exponent arrives at a crisp solution and an objective function value which can be interpreted in terms of the number of voids and intercellular movements of the part machine grouping obtained computational experiences show that although mfcm may sometimes require slightly more computing time than other methods not only is it able to find better solutions but also it has higher discriminating power for determining the number of cells

fuzzy partition models for fitting a set of partitions methodology is described for fitting a fuzzy consensus partition to a set of partitions of the same set of objects three models defining median partitions are described two of them are obtained from a least squares fit of a set of membership functions and the third proposed by pittau and vichi is acquired from a least squares fit of a set of joint membership functions the models are illustrated by application to both a set of hard partitions and a set of fuzzy partitions and comparisons are made between them and an alternative approach to obtaining a consensus fuzzy partition proposed by sato and sato a discussion is given of some interesting differences in the results

on fuzzy cluster validity indices cluster analysis aims at identifying groups of similar objects and helps to discover distribution of patterns and interesting correlations in large data sets especially fuzzy clustering has been widely studied and applied in a variety of key areas and fuzzy cluster validation plays a very important role in fuzzy clustering this paper introduces the fundamental concepts of cluster validity and presents a review of fuzzy cluster validity indices available in the literature we conducted extensive comparisons of the mentioned indices in conjunction with the fuzzy c means clustering algorithm on a number of widely used data sets and make a simple analysis of the experimental results

fuzzy c means clustering and internet portals a case study researchers in operational research have used fuzzy c means clustering ubiquitously in a wide range of areas it appears that internet portals can also benefit from this powerful methodology this paper tests the applicability of fuzzy c means clustering to internet portals and shows that there exist meaningful clusters among the potential users of an internet portal that offers business related information the results suggest that internet portals can use fuzzy c means clustering to determine homogenous groups of people and offer specific information to each group

fuzzy h ideals of hemirings a characterization of an h hemiregular hemiring in terms of a fuzzy h ideal is provided some properties of prime fuzzy h ideals of h hemiregular hemirings are investigated it is proved that a fuzzy subset z of a hemiring s is a prime fuzzy left right h ideal of s if and only if z is two valued z 0 1 and the set of all x in s such that z x 1 is a prime left right h ideal of s finally the similar properties for maximal fuzzy left right h ideals of hemirings are considered

a note on l fuzzy primary and semiprime ideals abstract in this note we introduce a definition for l fuzzy primary ideal in term of l fuzzy points and prove that this definition is equivalent to one of malik and mordeson 1991 where l 0 1 moreover l fuzzy semiprime ideals are introduced and some equivalent conditions of an l fuzzy semiprime ideal are proved

on prime quasi prime weakly quasi prime fuzzy left ideals of semigroups in this paper we introduce and study the prime quasi prime and weakly quasi prime fuzzy left ideals of a semigroup s we give characterizations of the largest fuzzy ideal i f contained in a fuzzy left ideal f of a semigroup s and the largest fuzzy subsemigroup i f such that f is a fuzzy ideal of i f finally strongly semisimple semigroups are characterized by quasi prime fuzzy left ideals

information ratios for validating mixture analyses abstract determining the number of components in a mixture of distributions is an important but difficult problem this article introduces a procedure called minimum information ratio estimation and validation mirev which is based on a ratio of fisher information matrices the smallest eigenvalue of the information ratio matrix is used to determine the number of components a measure of uncertainty may be obtained using a bootstrap technique simulations illustrate the effectiveness of the procedure for mixtures of exponential families an expression for the observed information ratio matrix provides insight to the success of the procedure cluster analysis attempts to identify and characterize subpopulations believed to be present in a population a wide variety of methods are available including criterion optimization hierarchical methods and various heuristic methods criterion optimization techniques such as mixture analysis fuzzy clustering and partitioning methods are popular because they