induction of fuzzy rules and membership functions from training examples abstract most fuzzy controllers and fuzzy expert systems must predefine membership functions and fuzzy inference rules to map numeric data into linguistic variable terms and to make fuzzy reasoning work in this paper we propose a general learning method as a framework for automatically deriving membership functions and fuzzy if then rules from a set of given training examples to rapidly build a prototype fuzzy expert system based on the membership functions and the fuzzy rules derived a corresponding fuzzy inference procedure to process inputs is also developed

implementing dempster s rule for hierarchial evidence this article gives an algorithm for the exact implementation of dempster s rule in the case of hierarchical evidence this algorithm is computationally efficient and it makes the approximation suggested by gordon and shortliffe unnecessary the algorithm itself is simple but its derivation depends on a detailed understanding of the interaction of hierarchical evidence

second chern class of fano manifolds and anti canonical geometry let x be a fano manifold of picard number one we establish a lower bound for the second chern class of x in terms of its index and degree as an application if y is a n dimensional fano manifold with k y n 3 h for some ample divisor h we prove that h 0 y h ge n 2 moreover we show that the rational map defined by vert mh vert is birational for m ge 5 and the linear system vert mh vert is basepoint free for m ge 7 as a by product the pluri anti canonical systems of singular weak fano varieties of dimension at most 4 are also investigated

effective algorithms for the nearest neighbor method in the clustering problem abstract two effective algorithms are presented for the nearest neighbor method in the hierarchical agglomerative clustering procedures one is effective when the number of clusters into which a data set should be classified is already known the other is effective to search for several probable clustering solutions when the number of clusters to be obtained is not known in advance the computation times of the algorithms are shown to be o n 2 for clustering of n objects therefore the algorithms are very powerful for the nearest neighbor method to classify a large data set

on fano manifolds of large pseudoindex abstract we describe fano manifolds of large pseudoindex that are rationally connected with respect to some numerically independent families of rational curves

finding relevant attributes and membership functions fuzzy systems that automatically derive fuzzy if then rules from numeric data have been developed most have to predefine membership functions in order to learn hong and lee proposed a general learning method that automatically derives fuzzy if then rules and membership functions from a set of given training examples using a decision table all available attributes were included in the decision table and the initial membership functions for each attribute were built according to the predefined smallest unit although hong and lee s method accurately derives the fuzzy if then rules and final membership functions the decision table and the initial membership functions are complex if there are many attributes or if the predefined unit is small we improve hong and lee s method by first selecting relevant attributes and building appropriate initial membership functions these attributes and membership functions are then used in a decision table to derive final fuzzy if then rules and membership functions experimental results on iris data show that the proposed method effectively induces membership functions and fuzzy if then rules

strategies to identify fuzzy rules directly from certainty degrees a comparison and a proposal with identification methods that learn fuzzy rules directly from certainty degrees we refer to methods that select the most promising rules from the training examples in only one pass in order to do that these methods employ a certainty measure to assess the goodness of each rule this paper aims to analyze in depth the behaviors and features of two different strategies for identifying fuzzy models from certainty degrees each of both combined with one of two well known alternatives for measuring the certainty degrees of the rules with this aim the advantages and drawbacks of each method are analyzed experimentally by considering the model error when applied to several systems besides the robustness of the results is investigated by applying the methods to noisy data as a conclusion a new method combining the best components of the previously considered methods is proposed and its results are analyzed the achieved performance in accuracy and computational cost shows the benefit of this new method

a recursive rule base adjustment algorithm for a fuzzy logic controller this paper introduces a recursive rule base adjustment to enhance the performance of fuzzy logic controllers here the fuzzy controller is constructed on the basis of a decision table dt relying on membership functions and fuzzy rules that incorporate heuristic knowledge and operator experience if the controller performance is not satisfactory it has previously been suggested that the rule base be altered by combined tuning of membership functions and controller scaling factors the alternative approach proposed here entails alteration of the fuzzy rule base the recursive rule base adjustment algorithm proposed in this paper has the benefit that it is computationally more efficient for the generation of a dt and advantage for online realization simulation results are presented to support this thesis

self organized fuzzy system generation from training examples in the synthesis of a fuzzy system two steps are generally employed the identification of a structure and the optimization of the parameters defining it the paper presents a methodology to automatically perform these two steps in conjunction using a three phase approach to construct a fuzzy system from numerical data phase 1 outlines the membership functions and system rules for a specific structure starting from a very simple initial topology phase 2 decides a new and more suitable topology with the information received from the previous step it determines for which variable the number of fuzzy sets used to discretize the domain must be increased and where these new fuzzy sets should be located this in turn decides in a dynamic way in which part of the input space the number of fuzzy rules should be increased phase 3 selects from the different structures obtained to construct a fuzzy system the one providing the best compromise between the accuracy of the approximation and the complexity of the rule set the accuracy and complexity of the fuzzy system derived by the proposed self organized fuzzy rule generation procedure sofrg are studied for the problem of function approximation simulation results are compared with other methodologies such as artificial neural networks neuro fuzzy systems and genetic algorithms

a mixed integer programming approach to multi class data classification problem this paper presents a new data classification method based on mixed integer programming traditional approaches that are based on partitioning the data sets into two groups perform poorly for multi class data classification problems the proposed approach is based on the use of hyper boxes for defining boundaries of the classes that include all or some of the points in that set a mixed integer programming model is developed for representing existence of hyper boxes and their boundaries in addition the relationships among the discrete decisions in the model are represented using propositional logic and then converted to their equivalent integer constraints using boolean algebra the proposed approach for multi class data classification is illustrated on an example problem the efficiency of the proposed method is tested on the well known iris data set the computational results on the illustrative example and the iris data set show that the proposed method is accurate and efficient on multi class data classification problems

fuzzy data mining for interesting generalized association rules due to the increasing use of very large databases and data warehouses mining useful information and helpful knowledge from transactions is evolving into an important research area most conventional data mining algorithms identify the relationships among transactions using binary values and find rules at a single concept level transactions with quantitative values and items with hierarchy relation are however commonly seen in real world applications in this paper we thus introduce the problem of mining fuzzy generalized association rules from quantitative data a fuzzy mining algorithm based on srikant and agrawal s method is proposed for extracting implicit generalized knowledge from transactions stored as quantitative values it integrates fuzzy set concepts and generalized data mining technologies to achieve this purpose items in rules may be from any level of the given taxonomy the effect of numbers of fuzzy regions on the performance of the proposed algorithm is also discussed

processing individual fuzzy attributes for fuzzy rule induction fuzzy systems that can automatically derive fuzzy if then rules and membership functions from numeric data have recently been developed in this paper we propose two new fuzzy learning methods for automatically deriving membership functions and fuzzy if then rules from a set of given training examples the proposed methods first select relevant attributes and build appropriate initial membership functions they then simplify the intervals and the membership functions of each attribute before forming a decision table these attributes and membership functions are then used in a decision table to derive the final fuzzy if then rules and membership functions experimental results for the iris data show that our methods can achieve a high degree of accuracy the proposed methods are thus useful in constructing membership functions and in managing uncertainty and vagueness they can also reduce the time and effort needed to develop a fuzzy knowledge base

the singularity category of a nakayama algebra abstract let a be a nakayama algebra we give a description of the singularity category of a inside its stable module category which provides a new approach to the singularity category of a nakayama algebra we prove that there is a duality between the singularity category of a and the singularity category of its opposite algebra as a consequence the resolution quiver of a and the resolution quiver of its opposite algebra have the same number of cycles and the same number of cyclic vertices

a fast approach for automatic generation of fuzzy rules by generalized dynamic fuzzy neural networks a fast approach for automatically generating fuzzy rules from sample patterns using generalized dynamic fuzzy neural networks gd fnns is presented the gd fnn is built based on ellipsoidal basis functions and functionally is equivalent to a takagi sugeno kang fuzzy system the salient characteristics of the gd fnn are 1 structure identification and parameters estimation are performed automatically and simultaneously without partitioning input space and selecting initial parameters a priori 2 fuzzy rules can be recruited or deleted dynamically 3 fuzzy rules can be generated quickly without resorting to the backpropagation bp iteration learning a common approach adopted by many existing methods the gd fnn is employed in a wide range of applications ranging from static function approximation and nonlinear system identification to time varying drug delivery system and multilink robot control simulation results demonstrate that a compact and high performance fuzzy rule base can be constructed comprehensive comparisons with other latest approaches show that the proposed approach is superior in terms of learning efficiency and performance

induction of fuzzy decision trees abstract most decision tree induction methods used for extracting knowledge in classification problems do not deal with cognitive uncertainties such as vagueness and ambiguity associated with human thinking and perception in this paper cognitive uncertainties involved in classification problems are explicitly represented measured and incorporated into the knowledge induction process a fuzzy decision tree induction method which is based on the reduction of classification ambiguity with fuzzy evidence is developed fuzzy decision trees represent classification knowledge more naturally to the way of human thinking and are more robust in tolerating imprecise conflict and missing information

combining gp operators with sa search to evolve fuzzy rule based classifiers abstract the genotype phenotype encoding of fuzzy rule bases in ga along with their corresponding crossover and mutation operators can be used by other search schemes improving the behavior of these last ones as a practical consequence of this a simulated annealing based method for inducting both parameters and structure of a fuzzy classifier has been developed the adjacency operator in sa has been replaced with a macromutation taken from tree shaped genotype gas we will show that results of sa search are similar to those of gp in both the efficiency of the learned classifiers and in its linguistic interpretability while the memory consumption of the learning process is lower

autoregressive time series prediction by means of fuzzy inference systems using nonparametric residual variance estimation we propose an automatic methodology framework for short and long term prediction of time series by means of fuzzy inference systems in this methodology fuzzy techniques and statistical techniques for nonparametric residual variance estimation are combined in order to build autoregressive predictive models implemented as fuzzy inference systems nonparametric residual variance estimation plays a key role in driving the identification and learning procedures concrete criteria and procedures within the proposed methodology framework are applied to a number of time series prediction problems the learn from examples method introduced by wang and mendel w m is used for identification the levenberg marquardt l m optimization method is then applied for tuning the w m method produces compact and potentially accurate inference systems when applied after a proper variable selection stage the l m method yields the best compromise between accuracy and interpretability of results among a set of alternatives delta test based residual variance estimations are used in order to select the best subset of inputs to the fuzzy inference systems as well as the number of linguistic labels for the inputs experiments on a diverse set of time series prediction benchmarks are compared against least squares support vector machines ls svm optimally pruned extreme learning machine op elm and k nn based autoregressors the advantages of the proposed methodology are shown in terms of linguistic interpretability generalization capability and computational cost furthermore fuzzy models are shown to be consistently more accurate for prediction in the case of time series coming from real world applications

upper bounds for the dominant dimension of nakayama and related algebras abstract optimal upper bounds are provided for the dominant dimensions of nakayama algebras and more general algebras a with an idempotent e such that there is a minimal faithful injective projective module ea and such that eae is a nakayama algebra this answers a question of abrar and proves a conjecture of yamagata for monomial algebras

the gorenstein projective modules for the nakayama algebras i abstract the aim of this paper is to outline the structure of the category of the gorenstein projective modules where is a nakayama algebra in addition we are going to introduce the resolution quiver of it provides a fast algorithm in order to obtain the gorenstein projective modules and to decide whether is a gorenstein algebra or not and whether it is cm free or not

fuzzy classification using pattern discovery rule based classifiers allow rationalization of classifications made this in turn improves understanding which is essential for effective decision support as a rule based classifier the pattern discovery pd algorithm functions well in discrete nominal and continuous data domains a drawback when using pd as a classifier for decision support is that it has an unbounded decision space that confounds the understanding of the degree of support for a decision incorporating pd into a fuzzy inference system fis allows the the degree of support for a decision to be expressed with intuitively understandable terms in addition using discrete algorithms in continuous domains can result in reduced accuracy due to quantization fuzzification reduces this ldquocost of quantizationrdquo and improves classification performance in this work the pd algorithm was used as a source of rules for a series of fiss implemented using different rule weighting and defuzzification schemes each providing a linguistic basis for rule description and a bounded space for expression of decision support the output of each fis consists of a suggested outcome a strong confidence metric describing suggestions within this space and a linguistic expression of the rules this constitutes a stronger basis for decision making than that provided by pd alone a variety of synthetic continuous class distributions with varying degrees of separation was used to evaluate the performance of fuzzy pd back propagation and bayesian classifiers overall the accuracy of the fuzzy system was found to be similar but slightly below that of the inherently continuous valued classifiers and was somewhat improved with respect to the pd classifiers for the difficult spiral class distributions studied the fuzzy classifiers were able to make more classifications than the pd classifiers the correct classification rates for the fuzzy classifiers were similar across the various rule weighting and defuzzification schemes demonstrating the strength of the statistical method for rule generation analysis of several real world data sets shows that a pd based fis has comparable performance to a neuro fuzzy system the use of a pd based fis however provides insight into the structure of the data analyzed not available through the other approaches

resolution quiver and cyclic homology criteria for nakayama algebras abstract if a nakayama algebra is not cyclic it has finite global dimension for a cyclic nakayama algebra there are many characterizations of when it has finite global dimension in 17 shen gave such a characterization using ringel s resolution quiver in 11 the second author with zacharia gave a cyclic homology characterization for when a monomial relation algebra has finite global dimension we show directly that these criteria are equivalent for all nakayama algebras our comparison result also reproves both characterizations in a separate paper we discuss an interesting example that came up in our attempt to generalize this comparison result to arbitrary monomial relation algebras 8

neuro fuzzy rule generation survey in soft computing framework the present article is a novel attempt in providing an exhaustive survey of neuro fuzzy rule generation algorithms rule generation from artificial neural networks is gaining in popularity in recent times due to its capability of providing some insight to the user about the symbolic knowledge embedded within the network fuzzy sets are an aid in providing this information in a more human comprehensible or natural form and can handle uncertainties at various levels the neuro fuzzy approach symbiotically combining the merits of connectionist and fuzzy approaches constitutes a key component of soft computing at this stage to date there has been no detailed and integrated categorization of the various neuro fuzzy models used for rule generation we propose to bring these together under a unified soft computing framework moreover we include both rule extraction and rule refinement in the broader perspective of rule generation rules learned and generated for fuzzy reasoning and fuzzy control are also considered from this wider viewpoint models are grouped on the basis of their level of neuro fuzzy synthesis use of other soft computing tools like genetic algorithms and rough sets are emphasized rule generation from fuzzy knowledge based networks which initially encode some crude domain knowledge are found to result in more refined rules finally real life application to medical diagnosis is provided

on the classification of higher auslander algebras for nakayama algebras abstract we give new improved bounds for the dominant dimension of nakayama algebras and use those bounds to give a classification of nakayama algebras with n simple modules that are higher auslander algebras with global dimension at least n the classification is then used to extend the results on the inequality for the global dimension of nakayama algebras obtained in 18