om3 ordered maxitive minitive and modular aggregation operators axiomatic and probabilistic properties in an arity monotonic setting the recently introduced om3 aggregation operators fulfill three appealing properties they are simultaneously minitive maxitive and modular among the instances of om3 operators we find e g owmax and owmin operators the famous hirsch h index and all its natural generalizations in this paper the basic axiomatic and probabilistic properties of extended i e in an arity dependent setting om3 aggregation operators are studied we illustrate the di culties one is inevitably faced with when trying to combine the quality and quantity of numeric items into a single number the discussion on such aggregation methods is particularly important in the information resources producers assessment problem which aims to reduce the negative e ects of information overload it turns out that the hirsch like indices of impact do not fulfill a set of very important properties which puts the sensibility of their practical usage into question moreover thanks to the probabilistic analysis of the operators in an i i d model we may better understand the relationship between the aggregated items quality and their producers productivity

fuzzy interpolative reasoning via scale and move transformations interpolative reasoning does not only help reduce the complexity of fuzzy models but also makes inference in sparse rule based systems possible this paper presents an interpolative reasoning method by means of scale and move transformations it can be used to interpolate fuzzy rules involving complex polygon gaussian or other bell shaped fuzzy membership functions the method works by first constructing a new inference rule via manipulating two given adjacent rules and then by using scale and move transformations to convert the intermediate inference results into the final derived conclusions this method has three advantages thanks to the proposed transformations 1 it can handle interpolation of multiple antecedent variables with simple computation 2 it guarantees the uniqueness as well as normality and convexity of the resulting interpolated fuzzy sets and 3 it suggests a variety of definitions for representative values providing a degree of freedom to meet different requirements comparative experimental studies are provided to demonstrate the potential of this method

on the 2 tuples based genetic tuning performance for fuzzy rule based classification systems in imbalanced data sets when performing a classification task we may find some data sets with a different class distribution among their patterns this problem is known as classification with imbalanced data sets and it appears in many real application areas for this reason it has recently become a relevant topic in the area of machine learning the aim of this work is to improve the behaviour of fuzzy rule based classification systems frbcss in the framework of imbalanced data sets by means of a tuning step specifically we adapt the 2 tuples based genetic tuning approach to classification problems showing the good synergy between this method and some frbcss our empirical results show that the 2 tuples based genetic tuning increases the performance of frbcss in all types of imbalanced data furthermore when the initial rule base built by a fuzzy rule learning methodology obtains a good behaviour in terms of accuracy we achieve a higher improvement in performance for the whole model when applying the genetic 2 tuples post processing step this enhancement is also obtained in the case of cooperation with a preprocessing stage proving the necessity of rebalancing the training set before the learning phase when dealing with imbalanced data

aggregation functions and capacities abstract inspired by earlier results of bayes and benvenuti et al 3 we introduce and study some construction methods and transformations for capacities first we introduce constructions of capacities based on n ary aggregation functions and implications from fuzzy set theory parameterized by vectors x 0 1 n later implication based transforms of capacities parameterized by subsets b 1 2 n are given exemplified and discussed

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

owa generation function and some adjustment methods for owa operators with application we propose the concept of ordered weighted averaging owa generation function with some properties illustrative examples and usages a number of new properties of owa operators and relations between some well known owa operators are proposed and proved using owa generation functions we discuss some orness andness adjustment methods for a predetermined owa operator a practical application about investment prediction problem is given with detailed illustration and analysis which can show the advantages of the adjustment methods proposed in this paper in particular the concept consistent adjustment matrix is proposed and the interests and advantages of it can be shown by its special properties

capacities and overlap indexes with an application in fuzzy rule based classification systems in this work we introduce a method for constructing capacities using overlap indexes between the fuzzy sets which are generated from the inputs of the considered problem we also use these capacities to aggregate information by means of the choquet integral in a fuzzy rule based classifier we observe that with these capacities the obtained results are better than those obtained with other measures

an integer programming approach for fuzzy rule based classification systems abstract fuzzy rule based classification systems frbcss have been successfully employed as a data mining technique where the goal is to discover the hidden knowledge in a data set in the form of interpretable rules and develop an accurate classification model in this paper we propose an exact approach to learn fuzzy rules from a data set for a frbcs first we propose a mixed integer programming model that extracts optimal fuzzy rules from a data set the model s embedded feature selection allows absence of insignificant features in a fuzzy rule in order to enhance its accuracy and coverage in order to build a comprehensive rule base rb we use this model in an iterative procedure that finds multiple rules by converting the obtained optimal solutions into a set of taboo constraints that prevents the model from re finding the previously obtained rules furthermore it changes the search direction by temporarily removing the correctly predicted patterns from the training set aiming to find the optimal rules that predict uncovered patterns in the training set this procedure ensures that most of the patterns in the training set are covered by the rb next another mixed integer programming model is developed to maximize predictive accuracy of the classifier by pruning the rb and removing redundant rules the predictive accuracy of the proposed model is tested on the benchmark data sets and compared with the state of the art algorithms from the literature by non parametric statistical tests

universality of efficiency of an unsteady state heat engine at maximum instantaneous power abstract in 1975 curzon and ahlborn 2 showed that the efficiency of the finite time carnot cycle at maximum power is universal this raises the issue of universality of the efficiency at maximum power in 2005 van den broeck 3 demonstrated that in the linear regime the efficiency of a steady state heat engine at maximum power is universal further studies indicated that the values of the linear and quadratic coefficients of the efficiency at maximum power are universal for several strong coupling steady state models and for an overdamped brownian particle in a time dependent harmonic potential m esposito k lindenberg c van den broeck phys rev lett 102 2009 130602 in this paper we demonstrate that in the linear regime the efficiency of an unsteady state heat engine at maximum instantaneous power is universal

voting in fuzzy rule based systems for pattern classification problems in this paper we examine two kinds of voting schemes in fuzzy rule based systems for pattern classification problems one is the voting by multiple fuzzy if then rules in a single fuzzy rule based classification system the other is the voting by multiple fuzzy rule based classification systems first we discuss the voting by multiple fuzzy if then rules which is used as a fuzzy reasoning method for classifying input patterns in a single fuzzy rule based classification system the performance of the voting by multiple fuzzy if then rules is examined by computer simulations on the iris data next we discuss the voting by multiple fuzzy rule based classification systems three voting methods i e a perfect unison rule a majority rule and a weighted voting rule are used for combining classification results by multiple fuzzy rule based classification systems finally we compare the performance of fuzzy rule based classification systems with that of other classification methods such as neural networks and statistical techniques by computer simulations on some well known test problems

the tanh method for a reliable treatment of the k n n and the kp n n equations and its variants abstract in this work the nonlinear k n n and kp n n equations and its variants are analytically studied we show that these equations may exhibit compactons solitons or periodic solutions by using the tanh method the analysis reveals the change of the physical structure of the solutions as a result of the exponents and the coefficients of the derivatives

compacton solutions in a class of generalized fifth order korteweg de vries equations solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations such as the korteweg de vries kdv nonlinear schrodinger and the kadomtsev petviashvili equations these integrable equations have linear dispersion and the solitons have infinite support we have derived and investigate a new kdv like hamiltonian partial differential equation from a four parameter lagrangian where the nonlinear dispersion gives rise to solitons with compact support compactons the new equation does not seem to be integrable and only mass momentum and energy seem to be conserved yet the solitons display almost the same modal decompositions and structural stability observed in integrable partial differential equations the compactons formed from arbitrary initial data are nonlinearly self stabilizing and maintain their coherence after multiple collisions the robustness of these compactons and the inapplicability of the inverse scattering tools that worked so well for the kdv equation make it clear that there is a fundamental mechanism underlying the processes beyond integrability we have found explicit formulas for multiple classes of compact traveling wave solutions when there are more than one compacton solution for a particular set of parameters the wider compacton is the minimum of a reduced hamiltonian and is the only one that is stable

some quantities represented by the choquet integral this paper shows that the choquet integral can represent some useful quantities such as supremum infimum essential supremum essential infimum mean median quantile 100 percentile and l estimators including trimmed mean

generalized ordered modular averaging operator and its application to group decision making in this paper we propose a new class of operators called the ordered quasi modular averaging oqma operators based on the ordered modular averaging oma operators it is shown that the oqma operators are monotonic bounded idempotent commutative and quasi comonotone modular moreover we introduce the generalized ordered modular averaging goma operator which is a special case of the oqma operator some special cases of the goma operator are discussed an orness measure to reflect the or like degree of the goma operator is proposed we further extend the goma operator to the generalized ordered hybrid modular gohm operator which focuses not only on the degree of importance with respect to input arguments but also their serial positions finally a new method based on the gohm operator for multi attribute group decision making is presented and a numerical example shows that the developed approach is feasible

continuity issues of the implicational interpretation of fuzzy rules the implicational interpretation of fuzzy rules has received little attention in real world applications so far this is largely due to the fact that ensuring continuity of the resulting function is not a straightforward task this paper targets this subject departing from consistent linguistic descriptions rule bases we introduce sufficient conditions for the continuity of the implicational interpretation with mean of maximum defuzzification we demonstrate that continuity can be achieved under practically feasible conditions regardless of the dimensionality of the input

including a simplicity criterion in the selection of the best rule in a genetic fuzzy learning algorithm learning algorithms can obtain very useful descriptions of several problems many different alternative descriptions can be generated in many cases a simple description is preferable since it has a higher possibility of being valid in unseen cases and also it is usually easier to understand by a human expert thus the main idea of this paper is to propose simplicity criteria and to include them in a learning algorithm in this case the learning algorithm will reward the simplest descriptions we study simplicity criteria in the selection of fuzzy rules in the genetic fuzzy learning algorithm called slave

compactons and solitary patterns structures for variants of the kdv and the kp equations in this paper we discuss mathematical variants in higher dimensions of the kdv and the kp equations it is shown that the focusing branches of these variants exhibit compactons solitons with finite wavelength whereas the defocusing branches support solitary patterns solutions with infinite slopes or cusps the study presents a fairly complete understanding of the compact and noncompact dispersive structures

a computational approach to soliton solutions of the kadomtsev petviashvili equation in this paper we present a computational approach to develop soliton solutions of the nonlinear kadomtsev petviashvili equation our approach rests mainly on the adomian decomposition method to include few components of the decomposition series the proposed framework is presented in a general way so that it can be used in nonlinear evolution equations of the same type numerical examples are tested to illustrate the proposed scheme

generalizations of owa operators owa operators can be seen as symmetrized weighted arithmetic means as choquet integrals with respect to symmetric measures or as comonotone additive functionals following these three different looks on owas we discuss several already known generalizations of owa operators including gowa iowa oma operators as well as we propose new types of such generalizations

effect of rule weights in fuzzy rule based classification systems this paper examines the effect of rule weights in fuzzy rule based classification systems each fuzzy if then rule in our classification system has antecedent linguistic values and a single consequent class we use a fuzzy reasoning method based on a single winner rule in the classification phase the winner rule for a new pattern is the fuzzy if then rule that has the maximum compatibility grade with the new pattern when we use fuzzy if then rules with certainty grades the winner is determined as the rule with the maximum product of the compatibility grade and the certainty grade in this paper the effect of rule weights is illustrated by drawing classification boundaries using fuzzy if then rules with without certainty grades it is also shown that certainty grades play an important role when a fuzzy rule based classification system is a mixture of general rules and specific rules through computer simulations we show that comprehensible fuzzy rule based systems with high classification performance can be designed without modifying the membership functions of antecedent linguistic values when we use fuzzy if then rules with certainty grades

generalized cf1f2 integrals from choquet like aggregation to ordered directionally monotone functions abstract this paper introduces the theoretical framework for a generalization of c f 1 f 2 integrals a family of choquet like integrals used successfully in the aggregation process of the fuzzy reasoning mechanisms of fuzzy rule based classification systems the proposed generalization called by g c f 1 f 2 integrals is based on the so called pseudo pre aggregation function pairs f 1 f 2 which are pairs of fusion functions satisfying a minimal set of requirements in order to guarantee that the g c f 1 f 2 integrals to be either an aggregation function or just an ordered directionally increasing function satisfying the appropriate boundary conditions we propose a dimension reduction of the input space in order to deal with repeated elements in the input avoiding ambiguities in the definition of g c f 1 f 2 integrals we study several properties of g c f 1 f 2 integrals considering different constraints for the functions f 1 and f 2 and state under which conditions g c f 1 f 2 integrals present or not averaging behaviors several examples of g c f 1 f 2 integrals are presented considering different pseudo pre aggregation function pairs defined on e g t norms overlap functions copulas that are neither t norms nor overlap functions and other functions that are not even pre aggregation functions

tri hamiltonian duality between solitons and solitary wave solutions having compact support a simple scaling argument shows that most integrable evolutionary systems which are known to admit a bi hamiltonian structure are in fact governed by a compatible trio of hamiltonian structures we demonstrate how their recombination leads to integrable hierarchies endowed with nonlinear dispersion that supports compactons solitary wave solutions having compact support or cusped and or peaked solitons a general algorithm for effecting this duality between classical solitons and their nonsmooth counterparts is illustrated by the construction of dual versions of the modified korteweg de vries equation the nonlinear schr odinger equation the integrable boussinesq system used to model the two way propagation of shallow water waves and the ito system of coupled nonlinear wave equations these hierarchies include a remarkable variety of interesting integrable nonlinear differential equations textcopyright 1996 the american physical society

time series smoothing and owa aggregation in this paper an overview of the time series smoothing problem is provided and the role of data aggregation is described using a weighted average of the past observations two important features associated with this smoothing process are introduced one is the average age of the data and other is the expected variance it is noted how both of these are defined in terms of the associated weights we show the fundamental conflict between trying to keep the variance small while simultaneously using the freshest data we study the moving average and exponential smoothing methods focusing on the aggregation aspect of the data smoothing problem allows us to draw upon the work done with the ordered weighted averaging aggregation operators to suggest new methods for developing smoothing techniques a new class of smoothing operators based on the use of linearly decaying weights is introduced and is shown to have some better features than either exponential smoothing or the moving average other classes of smoothing operators are introduced we introduce the idea of an operational estimate that involves adjusting a smoothed value by other considerations

ga fuzzy modeling and classification complexity and performance the use of genetic algorithms gas and other evolutionary optimization methods to design fuzzy rules for systems modeling and data classification have received much attention in recent literature authors have focused on various aspects of these randomized techniques and a whole scale of algorithms have been proposed we comment on some recent work and describe a new and efficient two step approach that leads to good results for function approximation dynamic systems modeling and data classification problems first fuzzy clustering is applied to obtain a compact initial rule based model then this model is optimized by a real coded ga subjected to constraints that maintain the semantic properties of the rules we consider four examples from the literature a synthetic nonlinear dynamic systems model the iris data classification problem the wine data classification problem and the dynamic modeling of a diesel engine turbocharger the obtained results are compared to other recently proposed methods

adaptability interpretability and rule weights in fuzzy rule based systems this paper discusses interpretability in two main categories of fuzzy systems fuzzy rule based classifiers and interpolative fuzzy systems our goal is to show that the aspect of high level interpretability is more relevant to fuzzy classifiers whereas fuzzy systems employed in modeling and control benefit more from low level interpretability we also discuss the interpretability accuracy tradeoff and observe why various rule weighting schemes that have been brought into play to increase adaptability of fuzzy systems rather just increase computational overhead and seriously compromise interpretability of fuzzy systems

measure based aggregation operators in analogy to the representation of the standard probabilistic average as an expected value of a random variable a geometric approach to aggregation is proposed generalizing imaoka s integral based on copulas several properties of such aggregation operators are investigated and the relationship with distinguished classes of aggregation operators is discussed

fuzzy rule based models with interactive rules and their granular generalization abstract processing realized in fuzzy rule based models is associated with matching individual rules with the existing input data and aggregation of the levels of matching and conclusions of the rules rules are processed as individual entities in this study we introduce an augmentation of fuzzy models by facilitating interaction among the rules leading to more flexible type membership functions of fuzzy sets forming conditions of the rules thus resulting in substantially advanced topology of the partition of the input space different ways of realizing interaction among the rules are studied in the sequel we develop a granular fuzzy model implied by the rule based model showing how granular parameters of the original rule based model enhance its quality expressed in terms of coverage of experimental data the two evaluation criteria of the constructed granular model namely coverage and specificity are studied experimental results are reported for a series of publicly available data

distributed representation of fuzzy rules and its application to pattern classification abstract this paper introduces the concept of distributed representation of fuzzy rules and applies it to classification problems distributed representation is implemented by superimposing many fuzzy rules corresponding to different fuzzy partitions of a pattern space this means that we simulatenously employ many fuzzy rule tables corresponding to different fuzzy partitions in fuzzy inference in order to apply distributed representation of fuzzy rules to pattern classification problems we first propose an algorithm to generate fuzzy rules from numerical data next we propose a fuzzy inference method using the generated fuzzy rules the classification power of distributed representation is compared with that of ordinary fuzzy rules which can be viewed as local representation

rule weight specification in fuzzy rule based classification systems this paper shows how the rule weight of each fuzzy rule can be specified in fuzzy rule based classification systems first we propose two heuristic methods for rule weight specification next the proposed methods are compared with existing ones through computer simulations on artificial numerical examples and real world pattern classification problems simulation results show that the proposed methods outperform the existing ones in the case of multiclass pattern classification problems with many classes

gp coach genetic programming based learning of compact and accurate fuzzy rule based classification systems for high dimensional problems in this paper we propose gp coach a genetic programming based method for the learning of compact and accurate fuzzy rule based classification systems for high dimensional problems gp coach learns disjunctive normal form rules generated by means of a context free grammar coded as one rule per tree the population constitutes the rule base so it is a genetic cooperative competitive learning approach gp coach uses a token competition mechanism to maintain the diversity of the population and this obliges the rules to compete and cooperate among themselves and allows the obtaining of a compact set of fuzzy rules the results obtained have been validated by the use of non parametric statistical tests showing a good performance in terms of accuracy and interpretability

membership margin based feature selection for mixed type and high dimensional data definition of membership margin based objective function weighting the antecedents of fuzzy if then rules to improve classification performance evaluate the feature importance within membership margin framework feature selection algorithm for mixed type and high dimensional data the effectiveness of the approach is proved through an extensive experimental study the present paper describes a new feature weighting method based on a membership margin distinctive properties of the proposed method include its capability to process problems characterized by mixed type data quantitative qualitative and interval as well as a huge number of features the key idea is to map simultaneously all the features of different types into a common space the membership space once all features are represented in a homogeneous space a feature weighting task can be performed in unified way this weighting approach is integrated here within a fuzzy classifier through a fuzzy rule weighted concept in order to improve its performance each antecedent fuzzy set in the fuzzy if then rule is weighted to characterize the importance of each proposition and therefore its corresponding feature weight estimation process is based on membership margin maximization to estimate a fuzzy weight of each feature in the membership space experiments on low and high dimensional real world datasets demonstrate that the proposed approach can improve significantly the performance of the fuzzy rule based as well as other state of the art classifiers and can even outperform classical feature weighting approaches in particular we show that this approach can yield meaningful results on two real world applications for cancer prognosis and industrial process diagnosis

two classes of variants of the generalized kdv equations with compact and noncompact solutions in this paper we study compact and noncompact solutions for two classes of new variants of the generalized kdv equations the study is conducted on the focusing and the defocusing structures of genuinely nonlinear dispersive equations the results emphasize the different physical structures of the compact and the noncompact solutions

a note on cc integral abstract recently choquet like copula based aggregation functions were introduced and discussed by lucca et al afterwards cmin integral i e a choquet like minimum based operator was examined by dimuro et al we show the link of these aggregation functions with universal integrals of klement et al in particular cmin integral is shown to be an alternative approach to the sugeno integral assuming symmetry an axiomatic characterization of the discussed aggregation functions is given and their coincidence with ordered modular averages in short oma operators is shown

general solutions with solitary patterns for the defocusing branch of the nonlinear dispersive k n n equations in higher dimensional spaces in this work the defocusing branch of the genuinely nonlinear dispersive k n n equation that exhibits solutions with solitary patterns is investigated the equation with constant coefficients to the derivatives is examined in one two and three dimensional spaces general formulas for solutions with solitary patterns are developed for all positive integers n n 1 two sets of entirely new formulas one set produces solutions for even integers n whereas the second set produces solutions in opposite directions for odd integers n n 1 are established

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

interpolative reasoning with insufficient evidence in sparse fuzzy rule bases abstract rule based fuzzy approximate reasoning uses various techniques of modified modus ponens the observation is in most cases not identical with any of the antecedents in the rules however a conclusion still can be computed by using some combination of all consequents where an overlapping of observation and antecedent is present if the rule base is sparse i e it contains insufficient information on the total state space it might occur that an observation has absolutely no overlapping with any of the antecedents and so not even a single rule is fired i e no conclusion can be computed on the basis of modus ponens in such a case interpolative reasoning in the strict sense can be applied some kind of weighted average of the flanking rules is calculated this technique can be extended to a form of extrapolation when the observation is not flanked from both sides linear interpolation and extrapolation is presented and then the idea is extended to arbitrary approximation

using stress functions to obtain owa operators the ordered weighted averaging operator attempts to provide a user friendly class of mean type aggregation operators by allowing a user to easily and naturally go from a mental model of a desired type of aggregation to its formal realization our objective in this paper is to support this agenda by providing a new methodology to help a user describe the type of aggregation they desire using the idea of a stress function with this stress function a user can stress which argument values they want to give more weight in the aggregation an important feature of this stress function is that it is only required to be nonnegative function on the unit interval this allows a user to completely focus on the issue of where to put the stress in the aggregation without having to consider satisfaction of any other requirements

fuzzy integral in multicriteria decision making abstract this paper presents a synthesis on the use of fuzzy integral as an aggregation operator in multicriteria decision making definitions essential properties are given and compared to those of usual aggregation operators a quick survey on applications is given

the ordered modular averages ordered modular averages omas generalize ordered weighted averages operators with the replacement of the additivity property by the modularity omas can be seen as a symmetrized idempotent modular aggregation functions characterized by comonotone modularity each oma can be seen also as a copula based integral with respect to a symmetric capacity special omas are characterized such as associative operators operators with neutral element or operators with an annihilator some construction methods for omas are also discussed

sgerd a steady state genetic algorithm for extracting fuzzy classification rules from data this paper considers the automatic design of fuzzy rule based classification systems from labeled data the performance of classifiers and the interpretability of generated rules are of major importance in these systems in past research some genetic based algorithms have been used for the rule learning process these genetic fuzzy systems have utilized different approaches to encode rules in this paper we have proposed a novel steady state genetic algorithm to extract a compact set of good fuzzy rules from numerical data sgerd the selection mechanism of this algorithm is nonrandom and only the best individuals can survive our approach is very simple and fast and can be applied to high dimensional problems with numerical attributes to select the rules having high generalization capabilities our algorithm makes use of some rule and data dependent parameters we have also proposed an enhancing function that modifies the rule evaluation measures in order to assess the candidate rules more effectively before their selection experiments on some well known data sets are performed to show the performance of sgerd

tight coupling in thermal brownian motors we study analytically a thermal brownian motor model and calculate exactly the onsager coefficients we show how the reciprocity relation holds and that the determinant of the onsager matrix vanishes such a condition implies that the device is built with tight coupling this explains why carnot s efficiency can be achieved in the limit of infinitely slow velocities we also prove that the efficiency at maximum power has the maximum possible value which corresponds to the curzon alhborn bound finally we discuss the model acting as a brownian refrigerator

on distributive laws of uninorms over overlap and grouping functions overlap and grouping functions as two new classes of special binary aggregation functions have been investigated by several authors for applications in image processing decision making classification and fuzzy community detection problems on the other hand after aczel studied the distributive law between two operations the distributive laws among particular binary aggregation functions become an interesting and natural research area in this paper we continue to discuss this topic for uninorms and overlap and grouping functions first we give some basic properties for the distributive law of uninorms over overlap functions second we study this distributive law when the uninorms belong to one of the usual classes e g mathcal u min mathcal u max the family of idempotent uninorms representable uninorms or uninorms continuous on 0 1 2 finally we investigate the distributive law of uninorms over grouping functions by an analogous way

the owa aggregation with uncertain descriptions on weights and input arguments since the ordered weighted averaging owa operator was introduced by yager to provide a method for aggregating multiple inputs that lie between the max and min operators much research that deals with uncertain information on input arguments instead of numerical values has been conducted due to the fact that information provided by human beings is in fact often vague and imprecise in this paper the owa operators with uncertain weights such as interval or weak ordinal descriptions coupled with interval input arguments are presented in order to identify the superior course of action among a multitude of courses of action with the help of relaxation of information representation a burden of information specification imposed on decision maker can be to some extent relieved and thus with regard to the parameters we can obtain a less specific expression that renders human judgments readily available to perform the owa aggregation we take into account the strength of preference based on a probabilistic measure and present a way of ordering the input arguments specified by interval numbers as well as two heuristic algorithms to allocate uncertain weights to the ordered input arguments for prioritizing the courses of action

solving multi class problems with linguistic fuzzy rule based classification systems based on pairwise learning and preference relations this paper deals with multi class classification for linguistic fuzzy rule based classification systems the idea is to decompose the original data set into binary classification problems using the pairwise learning approach confronting all pair of classes and to obtain an independent fuzzy system for each one of them along the inference process each fuzzy rule based classification system generates an association degree for both of its corresponding classes and these values are encoded into a fuzzy preference relation our analysis is focused on the final step that returns the predicted class label specifically we propose to manage the fuzzy preference relation using a non dominance criterion on the different alternatives contrasting the behaviour of this model with both the classical weighted voting scheme and a decision rule that combines the fuzzy relations of preference conflict and ignorance by means of a voting strategy our experimental study is carried out using two different linguistic fuzzy rule learning methods for which we show that the non dominance criterion is a good alternative in comparison with the previously mentioned aggregation mechanisms this empirical analysis is supported through the corresponding statistical analysis using non parametrical tests

a universal integral as common frame for choquet and sugeno integral the choquet and the sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required however their applicability is restricted because of the special operations used in the construction of these integrals therefore we provide a concept of integrals generalizing both the choquet and the sugeno case for functions with values in the nonnegative real numbers universal integrals are introduced and investigated which can be defined on arbitrary measurable spaces and for arbitrary monotone measures for a fixed pseudo multiplication on the nonnegative real numbers the smallest and the greatest universal integrals are given finally another construction method for obtaining universal integrals is introduced and the restriction to the unit interval i e to fuzzy integrals is considered

the tanh coth method for new compactons and solitons solutions for the k n n and the k n 1 n 1 equations abstract the nonlinear k n n and the k n 1 n 1 equations are analytically studied the tanh coth method the rational hyperbolic functions method and the rational exponential function method are applied for this analytic study we show that these equations exhibit new compactons solitons and periodic solutions the change of the physical structure of the solutions is caused by variation of the exponents and the coefficients of the derivatives

general compactons solutions for the focusing branch of the nonlinear dispersive k n n equations in higher dimensional spaces in this paper we will study the focusing branch of the genuinely nonlinear dispersive k n n equation that exhibits compactons solitons with finite wavelengths the equation will be studied in one two and three dimensional spaces general formulas for compactons solutions are developed for all positive integers n n 1 two sets of entirely new formulas one set produces compactons for even integers n whereas the second set produces compactons and anticompactons for odd integers n n 1 are established

overlap indices construction of and application to interpolative fuzzy systems in this paper we analyze the minimal set of axioms that overlap indices between fuzzy sets must fulfill we also present a method to build overlap indices using overlap functions and we carry on a theoretical study about the continuity the invariance and some general properties of such indices we present a generalization of the inference algorithm for interpolative fuzzy systems using overlap indices we also propose an algorithm for choosing among a set of overlap indices the best one for a considered problem

generalized adaptive fuzzy rule interpolation as a substantial extension to fuzzy rule interpolation that works based on two neighboring rules flanking an observation adaptive fuzzy rule interpolation is able to restore system consistency when contradictory results are reached during interpolation the approach first identifies the exhaustive sets of candidates with each candidate consisting of a set of interpolation procedures which may jointly be responsible for the system inconsistency then individual candidates are modified such that all contradictions are removed and thus interpolation consistency is restored it has been developed on the assumption that contradictions may only be resulted from the underlying interpolation mechanism and that all the identified candidates are not distinguishable in terms of their likelihood to be the real culprit however this assumption may not hold for real world situations this paper therefore further develops the adaptive method by taking into account observations rules and interpolation procedures all as diagnosable and modifiable system components in addition given the common practice in fuzzy systems that observations and rules are often associated with certainty degrees the identified candidates are ranked by examining the certainty degrees of its components and their derivatives from this the candidate modification is carried out based on such ranking this study significantly improves the efficacy of the existing adaptive system by exploiting more information during both the diagnosis and modification processes

axiomatizations of lovasz extensions of pseudo boolean functions three important properties in aggregation theory are investigated namely horizontal min additivity horizontal max additivity and comonotonic additivity which are defined by certain relaxations of the cauchy functional equation in several variables we show that these properties are equivalent and we completely describe the functions characterized by them by adding some regularity conditions these functions coincide with the lovasz extensions vanishing at the origin which subsume the discrete choquet integrals we also propose a simultaneous generalization of horizontal min additivity and horizontal max additivity called horizontal median additivity and we describe the corresponding function class additional conditions then reduce this class to that of symmetric lovasz extensions which includes the discrete symmetric choquet integrals

optimal potentials for temperature ratchets in a spatially periodic temperature profile directed transport of an overdamped brownian particle can be induced along a periodic potential with a load force applied to the particle this setup can perform as a heat engine for a given load the optimal potential maximizes the current and thus the power output of the heat engine we calculate the optimal potential for different temperature profiles and show that in the limit of a periodic piecewise constant temperature profile alternating between two temperatures the optimal potential leads to a divergent current this divergence being an effect of both the overdamped limit and the infinite temperature gradient at the interface would be cut off in any real experiment

comparison of fuzzy reasoning methods l a zadeh e h mamdani and m mizumoto et al have proposed methods for fuzzy reasoning in which the antecedent involves a fuzzy conditional proposition if x is a then y is b with a and b being fuzzy concepts mizumoto et al have investigated the properties of their methods in the case of generalized modus ponens this paper deals with the properties of their methods in the case of generalized modus tollens and investigates the other new fuzzy reasoning methods obtained by introducing the implication rules of many valued logic systems finally the properties of syllogism and contrapositive are investigated under each fuzzy reasoning method

competitive interaction reasoning in designing fuzzy rule based classification systems frbcss complex fuzzy rule extraction techniques and tuning membership functions are frequently used to enhance classification accuracy however these approaches not only decrease system s transparency which is the hallmark of fizzy design but also are oftentimes computationally expensive and require multiple parameters to be optimized using a large amount of training data in this paper inspired by the so called competitive behavior of mini columns in the brain neuronal circuitry we proposed a new reasoning method for fuzzy classifiers referred to as competitive interaction reasoning cir that employs the cumulative information provided by all fuzzy rules and adjusts the decision boundaries as if the membership functions are directly modified this mechanism is mathematically implemented by a linear transformation and resembles the competitive interaction observed in brain neuronal columns cross rule competition weights are optimized using hebbian reinforcement learning using a large number of simulations on benchmark data sets we show that the proposed cir significantly improves classification accuracy without compromising interpretability of the fuzzy classifier in addition cir can further facilitate formation of the fuzzy rules and incorporation of the expert knowledge by confining the destructive effects of noisy rules or expert inconsistencies experiments on 23 well known benchmark data sets confirm high performance of cir in comparison with a number of popular classifiers

some new results on the migrativity of uninorms over overlap and grouping functions abstract in 2018 qiao and hu 48 studied the migrativity of uninorms over overlap and grouping functions when the uninorm u belongs to one certain class e g u min u max the family of idempotent uninorms representable uninorms or uninorms continuous on 0 1 2 in addition they obtained some equivalent characterizations of them this paper will continue to consider the characterizations of this kind of migrativity equations by means of the ordinal sum of overlap and grouping functions we give the necessary and sufficient conditions for the solutions of the o migrativity equation when the uninorm u becomes a t norm or a conjunctive uninorm locally internal on the boundary and the g migrativity equation when the uninorm u becomes a t conorm or a disjunctive uninorm locally internal on the boundary respectively

weighted fuzzy pattern matching the fuzzy pattern matching technique has been developed in the framework of fuzzy set and possibility theory in order to take into account the imprecision and the uncertainty pervading values which have to be compared in a matching process this technique has proved very useful for implementing patterns of approximate reasoning in expert system inference engines and for designing retrieval systems capable of managing incomplete and fuzzy information data bases and vague queries in this paper the fuzzy pattern matching procedure is improved by introducing weights assessing the relative importance of atoms in the pattern matching indices are obtained using weighted versions of the minimum and maximum operations of fuzzy set theory this approach is extended to the case of variable weights and is related to aggregation schemes proposed by yager when modeling soft quantified statements such as most of the criteria must be met a notion of soft partial matching is thus modelled

on the relationship between symmetric maxitive minitive and modular aggregation operators in this paper the relationship between symmetric minitive maxitive and modular aggregation operators is considered it is shown that the intersection between any two of the three discussed classes is the same moreover the intersection is explicitly characterized it turns out that the intersection contains families of aggregation operators such as owmax owmin and many generalizations of the widely known hirsch s h index often applied in scientific quality control

a neuro fuzzy method to learn fuzzy classification rules from data abstract neuro fuzzy systems have recently gained a lot of interest in research and application neuro fuzzy models as we understand them are fuzzy systems that use local learning strategies to learn fuzzy sets and fuzzy rules neuro fuzzy techniques have been developed to support the development of e g fuzzy controllers and fuzzy classifiers in this paper we discuss a learning method for fuzzy classification rules the learning algorithm is a simple heuristics that is able to derive fuzzy rules from a set of training data very quickly and tunes them by modifying parameters of membership functions our approach is based on nefclass a neuro fuzzy model for pattern classification we also discuss some results obtained by our software implementation of nefclass which is freely available on the internet

the relation between inference and interpolation in the framework of fuzzy systems abstract this papers aims at clarifying the meaning of different interpretations of the max min or more generally the max t norm rule in fuzzy systems it turns out that basically two distinct approaches play an important role in fuzzy logic and its applications fuzzy interpolation on the basis of an imprecisely known function and logical inference in the presence of fuzzy information

fuzzyfeaturerank bringing order into fuzzy classifiers through fuzzy expressions abstract this work presents fuzzyfeaturerank a new feature reduction method inspired on pagerank to reduce the dimensionality of the feature space in supervised classification problems more precisely as it relies on a weighted directed graph it is ultimately inspired on textrank a pagerank based method that adds weights to the edges to express the strength of the connections between nodes the method is based on dividing each original feature used to describe the data into a set of fuzzy predicates and then ranking all of them by their ability to differentiate among classes in the light of the training set in order to do that both the information gained by each predicate and their redundancy with other already selected predicates are taken into account the fuzzy predicates with the best scores can then be used as a reduced input to construct fuzzy classifiers that consider only the preselected predicates to build the antecedents of the fuzzy rules the novelty of the proposal relies on being an approach halfway between feature selection and feature extraction approaches being able to improve the discrimination ability of the original features but preserving the interpretability of the new features in the sense that they are fuzzy expressions the experimental results support the suitability of the proposal