a characterization of a class of aggregation functions abstract the called aggregation functions are an important kind of binary operations used in fuzzy sets theory in this paper we characterize two special classes of aggregation functions by functional equations we also solve the same functional equations when the involving functions are t norms

or and neuron in modeling fuzzy set connectives the paper introduces a neural network based model of logical connectives the basic processing unit consists of two types of generic or and and neurons structured into a three layer topology due to the functional integrity we will be referring to it as an or and neuron the specificity of the logical connectives is captured by the or and neuron within its supervised learning further analysis of the connections of the neuron obtained in this way provides a better insight into the nature of the connectives applied in fuzzy sets by emphasizing their features of locality and interactivity afterward we will study several architectures of neural networks comprising these neurons treated as their basic functional components the numerical studies embrace both the structures formed by single or and neurons and aimed at modeling logical connectives including the zimmermann zysno data set 1980 and the networks representing various decision making architectures we will also propose a realization of a pseudo median filter in which the or and neurons play an ultimate role

generalized means as model of compensative connectives abstract empirical investigations have shown that instead of strong logical and and or connectives there is often some degree of compensation in between in this paper the generalized means are proposed as connective operators for fuzzy set theory which easily allow for modelling the degree of compensation in a natural manner including the arithmetic and geometric means as well as the maximum and minimum operators as special cases numerical examples with empirical data form an illustration of this concept some aspects of applications to decision making are discussed

semilinear copulas a family of copulas called semilinear is constructed starting with some assumptions about the linearity of the copulas along some segments of the unit square this family contains some other known families of copulas e g cuadras auge frechet and has a nice statistical interpretation several construction methods are provided especially concerning aggregation of semilinear copulas and a special form of ordinal sum construction is introduced some results about related families of quasi copulas and semicopulas are hence given

triangular norms position paper ii general constructions and parameterized families this second part out of three of a series of position papers on triangular norms for part i see triangular norms position paper i basic analytical and algebraic properties fuzzy sets and systems in press deals with general construction methods based on additive and multiplicative generators and on ordinal sums also included are some constructions leading to non continuous t norms and a presentation of some distinguished families of t norms

front speed enhancement by incompressible flows in three or higher dimensions we study in dimensions n 3 the family of first integrals of an incompressible flow these are h 1 rm loc functions whose level surfaces are tangential to the streamlines of the advective incompressible field one main motivation for this study comes from earlier results proving that the existence of nontrivial first integrals of an incompressible flow q is the main key that leads to a linear speed up by a large advection of pulsating traveling fronts solving a reaction advection diffusion equation in a periodic heterogeneous framework the family of first integrals is not well understood in dimensions n 3 due to the randomness of the trajectories of q and this is in contrast with the case n 2 by looking at the domain of propagation as a union of different components produced by the advective field we provide more information about first integrals and we give a class of incompressible flows which exhibit ergodic components of positive lebesgue measure and hence are not shear flows and which under certain sharp geometric conditions speed up the kpp fronts linearly with respect to the large amplitude in the proofs we establish a link between incompressibility ergodicity first integrals and the dimension to give a sharp condition about the asymptotic behavior of the minimal kpp speed in terms of the configuration of ergodic components

using fuzzy sets in operational research abstract during the last four decades a large number of mainly mathematical tools have been developed in and for operational research they are primarily devices to find optimal solutions after a problem has been modelled formally hardly any new tools have been developed for proper modelling of problems which are not well structured and which can not easily be cast into classical mathematical models fuzzy set theory as proposed by l zadeh in 1965 promises to bridge part of this gap it is much more adaptable to different problem structures and better suited to model human evaluation and decision making processes than classical mathematics this paper will primarily focus attention on four questions why fuzzy sets in or what are fuzzy sets where can they be used and how are they being used

hierarchies consistency analysis for nontransitive problems abstract by assuming different hierarchies or different hierarchy structures for the same problem should yield the same aggregated performance index an approach can be developed for evaluating the performance of multiple level and multiple criteria problems this proposed approach has the advantage that it is completely based on a rational index and no requirement of transitivity is needed furthermore the analyses of different criteria structures give further insights about the problem being considered the disadvantage is of course we must assume that different hierarchies must yield the same aggregate performance index which is not generally true for all problems under all conditions

a triparametric family of cardinality based fuzzy similarity measures previously we introduced a biparametric family of cardinality based fuzzy similarity measures in this paper we generalize this family by adding a third parameter we also study the generalized family for specific values of the third parameter more precisely we show that for particular values of this parameter certain properties can be ensured by imposing constraints on the two remaining parameters to conclude we examine some members of the presented family of fuzzy similarity measures

diagonals of continuous triangular norms diagonals of continuous t norms are studied the characterization of all functions being diagonals of continuous t norms is given to a given diagonal the class of all continuous t norms with this diagonal is characterized

statistically grounded logic operators in fuzzy sets abstract in this study we are concerned with a category of logic operators for fuzzy sets that is inherently associated with underlying statistical properties of membership grades they operate on these constructs are referred to as statistically grounded logic operators namely statistically grounded ors sors for short and statistically grounded ands sands for short operators in essence they arise as a solution to the optimization problem of the following form arg min m 0 1 k 1 n w x k x k m where xk k 1 2 n are the corresponding membership grades to be combined the weight function w 0 1 0 1 captures the nature of the logic and and or aggregation respectively we show that the weight function could be induced by t norms and t conorms the weight functions could be also implied by some statistical characteristics of data membership grades the choice of the t norm t conorm depends upon the predefined form of the logic operators to be developed we demonstrate that sands and sors offer an efficient operational framework for constructing fuzzy rough sets lead to the increased sensitivity of computing possibility and necessity measures bring a new insight into fuzzy relational equations and deliver an interpretation vehicle for fuzzy clustering that is provided in the form of dependency analysis

combining fuzzy sets the geometric consensus function family this paper introduces the geometric consensus function gcf family a set of combination functions for triangular and trapezoidal fuzzy sets we give some examples of this family among them two defined as counterparts of two previously defined in the literature we observe in this case that a gcf returns a membership function easier to represent with less non derivable points two of the examples introduced are easy to compute and satisfy the independence of irrelevant alternative condition

a distributed model of fuzzy set connectives abstract the development of logical connectives operations on fuzzy sets constitute a central issue in the theoretical and applied pursuits of the area taking into account the semantics aspects of the logical connectives it is not surprising that they require a careful context dependent analysis we propose a new neural network model of these operations which address two of their new and important conceptual features such as i a compensatory character and ii spatial distributivity it is also shown that many of the real world problems exhibit a clear logical underlying skeleton whose structure lends directly into the discussed neural network model

an axiomatic approach to soft learning vector quantization and clustering this paper presents an axiomatic approach to soft learning vector quantization lvq and clustering based on reformulation the reformulation of the fuzzy c means fcm algorithm provides the basis for reformulating entropy constrained fuzzy clustering ecfc algorithms according to the proposed approach the development of specific algorithms reduces to the selection of a generator function linear generator functions lead to the fcm and fuzzy learning vector quantization algorithms while exponential generator functions lead to ecfc and entropy constrained learning vector quantization algorithms the reformulation of lvq and clustering algorithms also provides the basis for developing uncertainty measures that can identify feature vectors equidistant from all prototypes these measures are employed by a procedure developed to make soft lvq and clustering algorithms capable of identifying outliers in the data set this procedure is evaluated by testing the algorithms generated by linear and exponential generator functions on speech data

the fuzzy weighted average within a generalized means function the fuzzy weighted average is widely used to solve hierarchical evaluation problems including fuzzy consideration for the operations of scoring weighting and aggregating previous works considered the fuzziness of score and weight and used the additive function to aggregate these weighted scores this study considers the aggregation operator also as a fuzzy variable and uses a generalized means function to fuzzify the aggregation operator within a fuzzy weighted average in practice the proposed model not only considers both the relative important of the criteria and its achieved performance but also conveys the influence of the dm s decision maker s evaluation attitude thus the proposed model can flexibly reflect any dm s evaluation attitude such as open neutral or rigorous thereby the proposed model can make an objective evaluation that approaches a real decision making situation and thus has the potential to be a useful management tool for improved resolution of fuzzy hierarchical evaluation problems

ranking engineering design concepts using a fuzzy outranking preference model abstract the conceptual design evaluation is important since the poor selection of a design concept can rarely be compensated at later design stages due to subjective and incomplete design information collected at the early design stage it is difficult to select the best design concepts from a number of alternatives to tackle this problem an outranking preference model based on the possibility theory is developed in this paper the fuzzy outranking relation is developed to model the imprecise preference relation between each pair of design concepts a design concept outranked others if and only if there is sufficient evidence to support that the concept is superior or at least equal to the others according to the fuzzy outranking relation identified between each pair of design concepts three types of indices are developed to determine the non dominated design concepts for continuous improvement or further development at later design stages moreover the sensitivity analysis is used to examine the robustness of the result the fuzzy outranking preference model developed is more suitable to be used for concept selection in the imprecise and uncertain design environment

on equivalence classes of fuzzy connectives the case of fuzzy integrals an equivalence relation between connectives or operators in the framework of multiple criteria decision making is introduced two operators are said to be equivalent if they lead to the same ranking of alternatives some general results to find equivalence classes of operators are given through the concept of level surfaces in a second part these results are applied to the case of discrete fuzzy integrals which are considered here as n place operators first some general results on the situation of fuzzy integrals among fuzzy operators are given and then the equivalence classes of fuzzy integrals

a fuzzy extension of saaty s priority theory we present a fuzzy method for choosing among a number of alternatives under conflicting decision criteria a fuzzy version of saaty s pairwise comparison method 1980 extended by de graan 1980 and lootsma 1981 each ratio expressing the relative significance of a pair of factors is displayed in a matrix from which suitable weights can be extracted since these ratios are essentially fuzzy they express the opinion of a decision maker on the importance of a pair of factors we have adapted the above mentioned method in such a way that decision makers are asked to express their opinions in fuzzy numbers with triangular membership functions we apply the method at two distinct levels first to find fuzzy weights for the decision criteria and second to find fuzzy weights for the alternatives under each of the decision criteria by a suitable combination of these results we obtain fuzzy scores for the alternatives as well as their sensitivities using these fuzzy scores the decision makers should be able to make a choice for one of the alternatives

new classes of threshold aggregation functions based upon the tsallis q exponential with applications to perceptual computing we introduce two new classes of single parameter aggregation functions based upon the tsallis q exponential qe function of nonextensive statistical mechanics these aggregation functions denoted qe aggregation facilitate simple modeling of the common human reasoning trait of threshold inference where either 1 at least one input must exceed a threshold in order to achieve a nonzero aggregation output or 2 if any one of the inputs exceeds a different threshold the aggregation output takes its maximum value we illustrate the thresholding behavior of these functions on interval type 2 fuzzy inputs using an example known in the literature as the investment judgment advisor we believe that the new qe class of aggregation operators will prove useful in extending the range of options available for the design of perceptual computing systems

triangular norms position paper i basic analytical and algebraic properties we present the basic analytical and algebraic properties of triangular norms we discuss continuity as well as the important classes of archimedean strict and nilpotent t norms triangular conorms and de morgan triples are also mentioned finally a brief historical survey on triangular norms is given

lever aggregation operators we make use of the physical concept of lever to generalize well known operators based on weights all these operators can be understood as levers in equilibrium with weights masses located at the points in 0 1 that opinions represent

effects of membership function parameters on the performance of a fuzzy signal detector this paper describes a signal detection algorithm based on fuzzy logic the detector combines evidence provided by two waveform features and explicitly considers uncertainty in the detection decision the detector classifies waveforms including a signal not including a signal or being uncertain in which case no conclusion regarding presence or absence of a signal is drawn piecewise linear membership functions are used and a method to describe the membership functions in terms of two parameters is developed the performance of the detector is compared to a bayesian maximum likelihood detector using brainstem auditory evoked potential signals in simulated noise and the effects of the steepness slope and overlap of the membership functions on detector performance are evaluated by varying the membership function steepness and overlap the fuzzy detector can almost completely eliminate classification errors at the cost of a large number of uncertain classifications or it can be made to perform similarly to the bayesian detector

multilevel polarization shift keying optimum receiver structure and performance evaluation multilevel digital coherent optical modulation schemes based on the state of polarization of a fully polarized lightwave are proposed and analyzed based on the complete statistical characterization of the stokes parameters extracted through appropriate signal processing in the presence of shot and additive gaussian noise the optimum maximum likelihood receiver operating symbol by symbol is derived the exact performance in terms of the average symbol error probability is found optimum constellations for the case of equipower 4 8 16 and 32 signals are found on the basis of the minimization of the error probability for a given average power their performance turns out to be promising as compared to other standard modulation techniques the spectral analysis of polarization modulated signals is presented a new receiver structure which solves the problem of the excess penalties incurred in the presence of channel dichroism is proposed and analyzed

asa and its application to multi criteria decision making case study aggregation plays an important role in many applications related to the development of intelligent systems in a fuzzy environment the existing aggregation operators are generally the t norm t conorm mean operators yager s operator and operator however these aggregation operators do not properly reflect the situation in the aggregation process that is these types of aggregation operators are independent of the aggregation situation in order to solve these problems we propose a new aggregation method to reflect the situation in the aggregation process it is the aggregation based on situation assessment asa method it consists of the situation assessment model sam and the asa algorithm in this asa method the sam is utilized to reflect the situation in the aggregation process this model generates the parameter which is controlled by decision maker it indicates the current degree of aggregation situation therefore our method can be adapted to certain situations by using the parameter in this paper asa method is applied to the multi criteria decision making environment

pictorial representations of fuzzy connectives part i cases of t norms t conorms and averaging operators part i of this paper shows a number of examples of existing t norms and t conorms which are known as good models of fuzzy set theoretic intersection and union and then the pictorial representations of t norms and t conorms are made with the aid of a computer several new examples of t norms and t conorms are also given averaging operators between min and max are summarized and their pictorial representations are also made

an extended rule based inference for general decision making problems complex decision making problems are usually modeled in terms of a number of decisive variables that are related hierarchically pieces of evidence are aggregated in a bottom up way to determine the final decision goal for dealing with such problems ishizuka et al 5 6 developed a rule based inference procedure by using fuzzy sets to represent imprecise data and employed the dempster shafer theory to aggregate evidence for structural damage assessment this paper highlights the necessity of applying the rules with all possible consequent clauses in the procedure with the considerations of information quality and quantity when applying the procedure to more general decision making problems the use of such rules can provide high quality information which contains much less ignorance in the resultant information also it can afford more information due to the decrease in total ignorance a simple example with two cases is used to compare the results based on the two different presentations of rules in the inference procedure for illustrating the importance of considering the rules proposed in this paper

connectives and quantifiers in fuzzy sets abstract we discuss some of the issues involved in the selection of appropriate operators for implementing the union and intersection of fuzzy subsets we discuss the extension principles used in extending operators to fuzzy subsets we provide a structure for aggregating linguistic variables in the theory of approximate reasoning we look at mean operators on fuzzy subsets as well as the inclusion of importances in aggregation we discuss non monotone set operators we introduce the concept of linguistic quantifiers and look at some applications of these structures we are particularly concerned with their application to linguistic summarizers syllogistic reasoning and multi criteria decision making

fuzzy rule generation methods for high level computer vision abstract in many decision making systems involving multiple sources the decisions made may be considered as the result of a rule based system in which the decision rules are usually enumerated by experts or generated by a learning process in this paper we discuss the various issues involved in the generation of fuzzy rules automatically from training data for high level computer vision features are treated as linguistic variables that appear in the antecedent clauses of the rules we present methods to generate the corresponding linguistic labels values and their membership functions rules are generated by constructing a minimal approximate fuzzy aggregation network and then training the network using gradient descent methods several examples are given

the mixing efficiency of open flows abstract mixing in open incompressible flows is studied in a model problem with inhomogeneous passive scalar injection on an inlet boundary as a measure of the efficiency of stirring the bulk scalar concentration variance is bounded and the bound is shown to be sharp at low peclet number although no specific flow saturating the bound at high peclet number is produced here the estimate is conjectured to be approached for flows possessing sufficiently sustained chaotic regions

on a family of t norms abstract this paper deals with the study of a certain type of dependence between the values of a t norm and those of its diagonal a family of t norms based on the ukasiewicz t norm is obtained

soft learning vector quantization and clustering algorithms based on ordered weighted aggregation operators this paper presents the development and investigates the properties of ordered weighted learning vector quantization lvq and clustering algorithms these algorithms are developed by using gradient descent to minimize reformulation functions based on aggregation operators an axiomatic approach provides conditions for selecting aggregation operators that lead to admissible reformulation functions minimization of admissible reformulation functions based on ordered weighted aggregation operators produces a family of soft lvq and clustering algorithms which includes fuzzy lvq and clustering algorithms as special cases the proposed lvq and clustering algorithms are used to perform segmentation of magnetic resonance mr images of the brain the diagnostic value of the segmented mr images provides the basis for evaluating a variety of ordered weighted lvq and clustering algorithms

optimal encoding of graph homomorphism energy using fuzzy information aggregation operators abstract the attributed relational graph matching arg strategy is a well known approach to object pattern recognition in the past for the parallel solution of arg matching problem an overall objective function was constructed using linearly weighted information aggregation function and one set of parameter values was chosen for all models by trial and error for the parameters in the function in this paper the compatibility between every pair of model and scene attributes is interpreted as a fuzzy value and subsequently the nonlinear fuzzy information aggregation operators are used to fuse the information captured in the chosen attributes to learn the parameters in the fuzzy information aggregation operators the learning from samples strategy is used the learning of weight parameters is formulated as an optimisation problem and solved using the gradient projection algorithm based learning procedure the learning procedure implicitly evaluates ambiguity robustness and discriminatory power of the relational attributes chosen for graph matching and assigns weights appropriately to the chosen attributes the learning procedure also enables us to compute a distinct set of optimal parameters for every model to reflect the characteristics of the model so that the homomorphic arg matching problem can be optimally encoded in the energy function for the model experimental results are presented to illustrate effectiveness and necessity of the parameter estimation and learning procedures

basic concepts for a theory of evaluation hierarchical aggregation via autodistributive connectives in fuzzy set theory abstract the aggregative operator introduced by combi 1982 in his analysis of basic concepts for a theory of evaluation in this journal is based on the axioms of associativity continuity and monotonicity in this paper an alternative approach is given where associativity is replaced by another axiom viz autodistributivity implying a kind of hierarchical aggregation instead of the former horizontal one the new set of properties yields a general class of operators for connecting fuzzy sets which are formally similar to the aggregative operators but are purely compensative in a strong sense moreover this modified approach generalizes a recent approach based on generalized means as compensative connectives it appears to be similar to expected utility approaches in decision making under uncertainty and seems to be a very promising tool to handle representation problems as they grow from other fields of human decision making e g of multicriteria analysis and of welfare theory

the self dual core and the anti self dual remainder of an aggregation operator in most decisional models based on pairwise comparison between alternatives the reciprocity of the individual preference representations expresses a natural assumption of rationality in those models self dual aggregation operators play a central role in so far as they preserve the reciprocity of the preference representations in the aggregation mechanism from individual to collective preferences in this paper we propose a simple method by which one can associate a self dual aggregation operator to any aggregation operator on the unit interval the resulting aggregation operator is said to be the self dual core of the original one and inherits most of its properties our method constitutes thus a new characterization of self duality with some technical advantages relatively to the traditional symmetric sums method due to silvert in our framework moreover every aggregation operator can be written as a sum of a self dual core and an anti self dual remainder which in some cases seems to give some indication on the dispersion of the variables in order to illustrate the method proposed we apply it to two important classes of continuous aggregation operators with the properties of idempotency symmetry and stability for translations the owa operators and the exponential quasiarithmetic means

multiscale mixing efficiencies for steady sources multiscale mixing efficiencies for passive scalar advection are defined in terms of the suppression of variance weighted at various length scales we consider scalars maintained by temporally steady but spatially inhomogeneous sources stirred by statistically homogeneous and isotropic incompressible flows including fully developed turbulence the mixing efficiencies are rigorously bounded in terms of the p eclet number and specific quantitative features of the source scaling exponents for the bounds at high p eclet number depend on the spectrum of length scales in the source indicating that molecular diffusion plays a more important quantitative role than that implied by classical eddy diffusion theories

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

a sensitivity analysis approach to introducing weight factors into decision functions in fuzzy multicriteria decision making in fuzzy multicriteria decision making the evaluations for criteria are aggregated using a suitable decision function many of the aggregation operators from fuzzy set theory that can be used as decision functions assume that the criteria have equal importance this paper considers the extension of these functions when the criteria are not equally weighted the criteria weights are interpreted as factors influencing the sensitivity of the decision function to the corresponding criteria a set of conditions is specified which a weighted decision function should satisfy this leads to a systematic way of introducing the weight factors into the decision functions the proposed analysis is applied to a class of operators in which the parameter may be interpreted as the decision maker s characteristic optimism index in this context it is shown that the well known method of multiplication of weight factors with membership values is suitable for optimistic decision makers while yager s power raising method is suitable for pessimistic decision makers only a geometric interpretation of the decision making process is also given

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

bounds on the mixing enhancement for a stirred binary fluid abstract the cahn hilliard equation describes phase separation in binary liquids here we study this equation with spatially varying sources and stirring or advection we specialize to symmetric mixtures and time independent sources and discuss stirring strategies that homogenize the binary fluid by measuring fluctuations of the composition away from its mean value we quantify the amount of homogenization achievable we find upper and lower bounds on our measure of homogenization using only the cahn hilliard equation and the incompressibility of the advecting flow we compare these theoretical bounds with numerical simulations for two model flows the constant flow and the random phase sine flow using the sine flow as an example we show how our bounds on composition fluctuations provide a measure of the effectiveness of a given stirring protocol in homogenizing a phase separating binary fluid

rough set analysis of a general type of fuzzy data using transitive aggregations of fuzzy similarity relations abstract in this paper we initially present and compile the tools and theories that are necessary for a rough set analysis of a general type of fuzzy data from this study we have developed two original contributions that can enhance the application of fuzzy rough sets techniques to data that may be affected by several sources of uncertainty in its measurement process for this type of analysis we have first considered the construction of homogeneous granules in which reflexivity symmetry and a certain transitivity property are satisfied this has encouraged us to study the application of t similarity relations in this framework and to examine the available theorems that permit us to aggregate this type of relations as a part of this study we have also developed a new theorem that allows us to use the dual of the generalized means as an aggregation operator in the fuzzy rough sets context another theoretical development that tries to respond to a practical problem is the concept of precision aggregation we use this new notion to export ziarko s variable precision rough set model to the analysis of fuzzy data a generalization that becomes a necessity for the fuzzy rough sets analysis of large databases the utility of this approach is demonstrated with an application example in the vehicle database donated by the turing institute

a fuzzy clustering based rapid prototyping for fuzzy rule based modeling this paper presents different approaches to the problem of fuzzy rules extraction by using fuzzy clustering as the main tool within these approaches we describe six methods that represent different alternatives in the fuzzy modeling process and how they can be integrated with a genetic algorithms these approaches attempt to obtain a first approximation to the fuzzy rules without any assumption about the structure of the data because the main objective is to obtain an approximation the methods we propose must be as simple as possible but also they must have a great approximative capacity and in that way we work directly with fuzzy sets induced in the variables input space the methods are applied to four examples and the errors obtained are specified in the different cases

multilevel differential polarization shift keying we analyze the performance of coherent optical communication systems which employ polarization shift keying polsk modulation introducing for the first time the requirements for multilevel differential polsk for m ary signal constellations with m 2 the three dimensional 3 d nature of the signal constellations within stokes space requires the use of double differential modulation and detection m ddpolsk coding constraints on the signals place an additional restriction on such systems we present detailed analysis and simulations for a 6 ddpolsk modulation scheme in which the signal points are located at the vertices of an octahedron in stokes space

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

basic concepts for a theory of evaluation the aggregative operator abstract starting with an explication of the aggregative concept and deducing a general structure which satisfies a number of minimal requirements properties of clustering the main features of a new mathematical theory called theory of evaluation are developed the theory sheds new light on such well known concepts as membership conjunction and disjunction and seems to be a very promising tool to handle representation problems as they grow from the fields of theory of fuzzy set and its many applications of human decision making and of multicriteria analysis

compensatory operators in fuzzy linear programming with multiple objectives previously h j zimmermann 11 presented a fuzzy approach to solve the linear vectormaximum problem in the mentioned approach the author uses the minimum or the product operators to translate the semantic meaning of the and the aim of this paper is to reconsider this approach by using operators which allow some degree of compensation between aggregated membership functions firstly the c operator already defined in 12 is used to combine our fuzzy objectives it is shown that solutions obtained by this way are always efficient unfortunately the substitute problem is not generally computationally feasible we suggest then the min bounded sum operator which is a compensatory one has some desired properties and is supported by empirical arguments it allows a considerable decrease of the computational burden in the substitute problem and leads to a solution which is attractive from the stand point of efficiency

a differential coding method for the symmetrically differential polarization shift keying system this paper presents a novel differential coding method for the symmetrically differential polarization shift keying system the proposed differential coding method which can overcome the slow polarization variation in the fiber constructs the reference frame by setting the sum the difference and the cross product of previous two symbols as the first second and the last axes of the signal space obviously each axis is determined by the previous two symbols together thus at the receiver the new scheme constructs a noisy reference frame more accurately than other schemes and yields better performance the optimal constellation for the system is symmetric and easy to find the analytical integral form for the bit error rate ber of the proposed system is derived and the saddle point method is applied to obtain the analytical results it is found that the performance in terms of ber is much better than that of other differential polarization shift keying systems the analytical results agree with the simulation very well

empiric considerations on the fuzzy metric truth approach the fuzzy metric truth approach has as its objective computing with words in the full sense of this expression in order to achieve this aim a logico methodological user interface based on the semantic differential technique theory of truthlikeness and fuzzy systems has been constructed in the previous articles this article considers empiric aspects of the fuzzy metric truth approach by simulating and testing three typical data sets the system outputs of the user interface are compared with the desired outputs in the light of two main criteria the root mean square and the correlation coefficient the user interface is also compared with the algorithms which are used within non linear regression analysis the mamdani method and sugeno takagi method the results show that particularly in the case of the first two data sets the interface seems satisfactory and justifiable

stirring up trouble multi scale mixing measures for steady scalar sources abstract the mixing efficiency of a flow advecting a passive scalar sustained by steady sources and sinks is naturally defined in terms of the suppression of bulk scalar variance in the presence of stirring relative to the variance in the absence of stirring these variances can be weighted at various spatial scales leading to a family of multi scale mixing measures and efficiencies we derive a priori estimates on these efficiencies from the advection diffusion partial differential equation focusing on a broad class of statistically homogeneous and isotropic incompressible flows the analysis produces bounds on the mixing efficiencies in terms of the peclet number a measure of the strength of the stirring relative to molecular diffusion we show by example that the estimates are sharp for particular source sink and flow combinations in general the high peclet number behavior of the bounds scaling exponents as well as prefactors depends on the structure and smoothness properties of and length scales in the scalar source and sink distribution the fundamental model of the stirring of a monochromatic source sink combination by the random sine flow is investigated in detail via direct numerical simulation and analysis the large scale mixing efficiency follows the upper bound scaling within a logarithm at high peclet number but the intermediate and small scale efficiencies are qualitatively less than optimal the peclet number scaling exponents of the efficiencies observed in the simulations are deduced theoretically from the asymptotic solution of an internal layer problem arising in a quasi static model

bounding biomass in the fisher equation the fisher kolmogorov petrovskii piskunov equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents if the average growth rate is negative then the model has a survival extinction transition the location of this transition in the parameter space is constrained using variational arguments and delimited by simulations the statistical steady state reached when the system is in the survival region of parameter space is characterized by integral constraints and upper and lower bounds on the biomass and productivity that follow from variational arguments and direct inequalities in the limit of zero decorrelation time the velocity field is shown to act as fickian diffusion with an eddy diffusivity much larger than the molecular diffusivity this allows a one dimensional model to predict the biomass productivity and extinction transitions all results are illustrated with a simple growth and stirring model

decisions and evaluations by hierarchical aggregation of information usually in preparing a decision a hierarchy of criteria for evaluating alternatives can he agreed upon by the decision makers the problem addressed in this paper is the appropriate modelling of such evaluations and their aggregation in order to arrive at a proper overall evaluation function by which the decision alternatives can be ordered easily representing the criteria subjective categories by fuzzy sets it is possible to use aggregation operators as models for the amalgamation of those criteria in the framework of an empirical research project a hierarchy of criteria was developed for the evaluation of credit worthiness of customers 50 credit applications were evaluated by a number of credit managers of banks and their judgement could be appropriately modelled by a four level hierarchy of criteria

universal long time properties of lagrangian statistics in the batchelor regime and their application to the passive scalar problem we consider the transport of dynamically passive quantities in the batchelor regime of a smooth in space velocity field for the case of arbitrary temporal correlations of the velocity we formulate the statistics of relevant characteristics of lagrangian motion this allows us to generalize many results obtained previously for strain ensuremath delta correlated in time thus answering a question about the universality of these results

optimizing the source distribution in fluid mixing abstract a passive scalar is advected by a velocity field with a nonuniform spatial source that maintains concentration inhomogeneities for example the scalar could be temperature with a source consisting of hot and cold spots such that the mean temperature is constant which source distributions are best mixed by this velocity field this question has a straightforward yet rich answer that is relevant to real mixing problems we use a multiscale measure of steady state enhancement to mixing and optimize it by a variational approach we then solve the resulting euler lagrange equation for a perturbed uniform flow and for simple cellular flows the optimal source distributions have many broad features that are as expected they avoid stagnation points favour regions of fast flow and their contours are aligned such that the flow blows hot spots onto cold and vice versa however the detailed structure varies widely with diffusivity and other problem parameters though these are model problems the optimization procedure is simple enough to be adapted to more complex situations

on the order of triangular norms comments on a triangular norm hierarchy by e cretu in cretu fuzzy sets and systems 120 2001 371 the members of the families of frank dubois prade yager and hamacher t norms respectively are compared in a pointwise way with the minimum the product and the lukasiewicz t norm all these results are well known and trivial moreover these families of t norms cannot only be compared with the three basic t norms above but all these families are monotone with respect to their index a fact which is also well known and straightforward to prove with the exception of the family of frank t norms whose monotonicity has been first proven in butnariu and klement triangular norm based measures and games with fuzzy coalitions kluwer dordrecht 1993

fuzzy connective based hierarchical aggregation networks for decision making abstract decision making is usually based on the aggregation of several criteria although the aggregation can be performed at one level in simple cases in more complex situations it becomes necessary that it be performed in a hierarchical manner in a multilevel framework this is particularly true in many engineering applications in this paper we investigate the use of fuzzy connectives in multilayer networks to arrive at appropriate overall aggregation functions the characteristics of suitable fuzzy connectives are studied and an iterative algorithm to determine the type of aggregation function and its parameters at each node in the network is proposed we believe that our aggregation scheme is powerful and flexible since we use several types of aggregation connectives and since the parameters of the network can be determined using a simple algorithm the behavior of the network can also be modified depending on the desired attitude conditions for unique convergence of the algorithm in simple cases are discussed and examples of applications of the method are also presented

complex structured decision making model a hierarchical frame work for complex structured data we introduce a hierarchical framework we call complex structured decision making model for complexly structured knowledge representation in intelligent decision making we show that our model extends non hierarchical flat decision making models to hierarchical decision making models that are similar to comprehensible human decision making processes further we make an argument that hierarchial representation of knowledge in a complex structured decision making model simplifies the approximation of aggregation functions to easily adapt to the underline relation of the system additionally using a real world complex structured data set we show that hierarchically organized fuzzy integrals e g choquet integral and sugeno integral and fuzzy signatures outperform these non hierarchical fuzzy integrals