logic based fuzzy networks a study in system modeling with triangular norms and uninorms the ultimate challenges of system modeling concern designing accurate yet highly transparent and user centric models we have witnessed a plethora of neurofuzzy architectures which are aimed at addressing these two highly conflicting requirements this study is concerned with the design and the development of transparent logic networks realized with the aid of fuzzy neurons and fuzzy unineurons the construction of networks of this form requires a formation of efficient interfaces that constitute a conceptually appealing bridge between the model and the real world experimental environment in which the model is to be used in general the interfaces are constructed by invoking some form of granulation of information and binary boolean discretization in particular we introduce a new discretization environment that is realized by means of particle swarm optimization pso and data clustering implemented by the k means algorithm the underlying structure of the network is optimized by invoking a combination of the pso and the mechanisms of conventional gradient based learning we discuss various optimization strategies by considering boolean as well as fuzzy data coming as the result of discretization of original experimental data and then involving several learning strategies we elaborate on the interpretation aspects of the network and show how those could be strengthened through efficient pruning we also show how the interpreted network leads to a simpler and more accurate logic description of the experimental data a number of experimental studies are included

expectation consistent approximate inference we propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation the approximation can be understood as replacing an average over the original intractable distribution with a tractable one it requires two tractable probability distributions which are made consistent on a set of moments and encode different features of the original intractable distribution in this way we are able to use gaussian approximations for models with discrete or bounded variables which allow us to include non trivial correlations these are neglected in many other methods we test the framework on toy benchmark problems for binary variables on fully connected graphs and 2d grids and compare with other methods such as loopy belief propagation good performance is already achieved by using single nodes as tractable substructures significant improvements are obtained when a spanning tree is used instead

the fractional fourier transform and time frequency representations the functional fourier transform frft which is a generalization of the classical fourier transform was introduced a number of years ago in the mathematics literature but appears to have remained largely unknown to the signal processing community to which it may however be potentially useful the frft depends on a parameter spl alpha and can be interpreted as a rotation by an angle spl alpha in the time frequency plane an frft with spl alpha spl pi 2 corresponds to the classical fourier transform and an frft with spl alpha 0 corresponds to the identity operator on the other hand the angles of successively performed frfts simply add up as do the angles of successive rotations the frft of a signal can also be interpreted as a decomposition of the signal in terms of chirps the authors briefly introduce the frft and a number of its properties and then present some new results the interpretation as a rotation in the time frequency plane and the frft s relationships with time frequency representations such as the wigner distribution the ambiguity function the short time fourier transform and the spectrogram these relationships have a very simple and natural form and support the frft s interpretation as a rotation operator examples of frfts of some simple signals are given an example of the application of the frft is also given

new family of triangular norms for decreasing generators in the form of a logarithm of a linear fractional function abstract the purpose of this paper is to establish restrictions on the parameters under which a function in the form of a natural logarithm of a linear fractional function is a decreasing generator in addition to the general case all special cases of generators of this type are considered a triangular norm is constructed for each generator in fact a new parametric class of decreasing generators that generalizes and systematizes known generators is proposed such generators generate triangular norms represented by rational functions the results of this paper can be used to construct aggregation operations

support recovery with sparsely sampled free random matrices consider a bernoulli gaussian complex n vector whose components are vi xibi with xi c n 0 px and binary bi mutually independent and iid across i this random q sparse vector is multiplied by a square random matrix u and a randomly chosen subset of average size n p p 0 1 of the resulting vector components is then observed in additive gaussian noise we extend the scope of conventional noisy compressive sampling models where u is typically a matrix with iid components to allow u satisfying a certain freeness condition this class of matrices encompasses haar matrices and other unitarily invariant matrices we use the replica method and the decoupling principle of guo and verdu as well as a number of information theoretic bounds to study the input output mutual information and the support recovery error rate in the limit of n we also extend the scope of the large deviation approach of rangan and characterize the performance of a class of estimators encompassing thresholded linear mmse and l1 relaxation

kernel design for reduced interference distributions the authors present a class of time frequency signal representations tfrs called the reduced interference distribution rid an overview of commonly used tfrs is given and desirable distribution properties are introduced particular attention is paid to the interpretation of cohen s class of time frequency distributions of tfrs in the ambiguity temporal correlation spectral correlation and time frequency domains based on the desirable kernel requirements the rid is discussed and further defined a systematic procedure to create rid kernels or equivalently compute rids is proposed some aspects and properties of the rid are discussed the authors estimate design considerations for rids and compare various selections of the primitive window some experimental results demonstrating the performance of the rid are presented

on the universality of noiseless linear estimation with respect to the measurement matrix in a noiseless linear estimation problem one aims to reconstruct a vector x from the knowledge of its linear projections y x there have been many theoretical works concentrating on the case where the matrix is a random i i d one but a number of heuristic evidence suggests that many of these results are universal and extend well beyond this restricted case here we revisit this problematic through the prism of development of message passing methods and consider not only the universality of the l1 transition but also the one of the optimal bayesian reconstruction we observed that the universality extends to the bayes optimal minimum mean squared mmse error and to complicated matrices such as those appearing in randomly statistical retrieval problems

generalized medians distance aggregation operators are introduced in the case of singleton based distance a well known class of k medians is recovered for interval based distance characterization of p r distance aggregation operators is given in general as well as for idempotent operators based on the triangle of median factors medians are introduced owa operators are shown to be a linear convex combination of special j medians

a note on continuity in scalarization for multicriteria optimization problems we establish sufficient conditions for solutions of scalarization replacements of multicriteria optimization problems to exhibit continuous dependence on scaling factors and other parameters

kernel design for time frequency signal analysis using the radon transform the authors present a kernel design technique based on using the radon transform of the modulus of the ambiguity function of the signal for determination of angles and distances of radially distributed contents of the autoterms in the ambiguity domain the proposed kernel effectively reduces the cross terms and noise for linear fm signals the result is a tool for high resolution time frequency representation of nonstationary primarily linear fm signals

signal recovery with cost constrained measurements we are concerned with the problem of optimally measuring an accessible signal under a total cost constraint in order to estimate a signal which is not directly accessible an important aspect of our formulation is the inclusion of a measurement device model where each device has a cost depending on the number of amplitude levels that the device can reliably distinguish we also assume that there is a cost budget so that it is not possible to make a high amplitude resolution measurement at every point we investigate the optimal allocation of cost budget to the measurement devices so as to minimize estimation error this problem differs from standard estimation problems in that we are allowed to design the number and noise levels of the measurement devices subject to the cost constraint our main results are presented in the form of tradeoff curves between the estimation error and the cost budget although our primary motivation and numerical examples come from wave propagation problems our formulation is also valid for other measurement problems with similar budget limitations where the observed variables are related to the unknown variables through a linear relation we discuss the effects of signal to noise ratio distance of propagation and the degree of coherence correlation of the waves on these tradeoffs and the optimum cost allocation our conclusions not only yield practical strategies for designing optimal measurement systems under cost constraints but also provide insights into measurement aspects of certain inverse problems

logic based fuzzy neurocomputing with unineurons in this paper we introduce a new category of logic neurons unineurons that are based on the concept of uninorms as uninorms form a certain generalization of the generic categories of fuzzy set operators such as t norms and t conorms the proposed unineurons inherit their logic processing capabilities which make them flexible and logically appealing we discuss several fundamental categories of uninorms such as uni or uni and and alike in particular we focus on the interpretability of networks composed of unineurons leading to several categories of rules to be exploited in rule based systems the learning aspects of the unineurons are presented along with detailed optimization schemes experimental results tackle two categories of problems such as a a logic approximation of fuzzy sets and b a design of associations between information granules where the ensuing development schemes directly relate to the fundamentals of granular fuzzy modeling

continuous generated associative aggregation operators continuous generated associative aggregation operators are discussed the only asymmetric solutions are the trivial operators of the projection to the first or the last coordinate respectively the only nontrivial convenient aggregation operators are necessarily symmetric and they are either continuous archimedean t norms and t conorms or generated nullnorms the latter may combine any nilpotent t conorm and any t norm with any prescribed annihilator k 0 1

the use of cone shaped kernels for generalized time frequency representations of nonstationary signals generalized time frequency representations gtfrs which use cone shaped kernels for nonstationary signal analysis are presented the cone shaped kernels are formulated for the gtfrs to produce good resolution simultaneously in time and frequency specifically for a gtfr with a cone shaped kernel finite time support is maintained in the time dimension along with an enhanced spectrum in the frequency dimension and the cross terms are smoothed out experimental results on simulated data and real speech show the advantages of the gtfrs with the cone shaped kernels through comparisons to the spectrogram and the pseudo wigner distribution

interference suppression in the wigner distribution using fractional fourier transformation and signal synthesis a novel method for the suppression of cross terms in the time frequency domain is introduced first interference is identified using a fractional fourier transform based technique then auto terms are detected synthesized and subtracted from the original signal the process is repeated until all signal components are extracted finally the wigner distributions of pure auto terms are superimposed to yield a high readability representation

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

digital computation of the fractional fourier transform an algorithm for efficient and accurate computation of the fractional fourier transform is given for signals with time bandwidth product n the presented algorithm computes the fractional transform in o nlogn time a definition for the discrete fractional fourier transform that emerges from our analysis is also discussed

time varying filtering and signal estimation using wigner distribution synthesis techniques the short time fourier transform stft the ambiguity function af and the wigner distribution wd are mixed time frequency signal representations that use fourier transform techniques to map a one dimensional function of time into a two dimensional function of time and frequency these mixed time frequency mappings have been used to analyze the local frequency characteristics of a variety of signals and systems although much work has also been done to develop stft and af synthesis algorithms that can be used to implement a variety of time varying signal processing operations no such synthesis techniques have thus far been developed for the wd in this paper a signal synthesis algorithm that works directly with the real valued high resolution wd will be derived examples of how this wd synthesis procedure can be used to perform time varying filtering operations or signal separation will be given

criteria importances in median like aggregation an axiomatization of criteria importances appearing in a given aggregation operator is proposed some distinguished examples are recalled for the class of k medians an integral based approach for inclusion of criteria importances is introduced several examples are given the case of ordinal scales is also discussed

triangular norm based iterative compensatory operators abstract aggregation operators based on a fixed t norm and on suitable transformations of processed data are introduced a special attention is paid to the class of iterative compensatory operators containing also the classical arithmetic geometric and harmonic means several properties of introduced operators are studied e g the symmetry the associativity the idempotency the anihilation etc several examples are given including continuous idempotent bisymmetric iterative compensatory operators with zero anihilator