quantitative weights and aggregation based on the strong idempotency of aggregation operators quantitative weights are incorporated into the fusion process our general method is compared with some previous specific cases more details about weighted aggregation based on some penalty function is given further weighted integral based aggregation linked to quantifier based fuzzy measures is investigated especially weighted owa operators several examples are included

aggregation of asymmetric distances in computer science in this paper we provide a general description of how to combine a collection not necessarily finite of asymmetric distances in order to obtain a single one as output to this end we introduce the notion of asymmetric distance aggregation function that generalizes the well known one for distance spaces given by borsik and dobos j borsik j dobos on a product of metricspaces math slovaca 31 1981 193 205 among other results a characterization of such functions is obtained in terms of monotony and subadditivity finally we relate our results to computer science in particular we show that the mathematical formalism based on complexity distances which has been introduced by romaguera and schellekens s romaguera m schellekens quasi metric properties of complexity spaces topol appl 98 1999 311 322 for the complexity analysis of programs and algorithms can be obtained as a particular case of our new framework using appropriate asymmetric aggregation distance functions

associative monotonic operations in fuzzy set theory abstract the properties of binary operations in a real interval are considered and used in the discussion of generalized operations on fuzzy sets on fuzzy numbers and on fuzzy probabilistic sets

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

on sugeno integral as an aggregation function the sugeno integral for a given fuzzy measure is studied under the viewpoint of aggregation in particular we give some equivalent expressions of it we also give an axiomatic characterization of the class of all the sugeno integrals some particular subclasses such as the weighted maximum and minimum functions are investigated as well

statistical analysis of parametric t norms theoretical aspects of aggregation functions particularly t norms have been deeply investigated a further step in the study of these functions is to consider statistical behavior of outputs this research approach has been initiated by the authors in a recent paper mainly focused on the compensatory functions such as averages now parametric t norms are especially studied in order to provide simply easy rules to be used by practitioners when choosing one parameter value a pairwise parametric comparison of several t norm families is provided by means of charts

on the dispersion measure of owa operators we describe some basic features of the owa operator we turn to the problem of determining the weights associated with this operator and particularly the maximal dispersion entropy approach we consider the possibility of using minimization of dispersion after discussing concerns with both maximization and minimization of dispersion we investigate the possibility of finding an optimal solution intermediate to these extremes we next consider alternative measures of dispersion we introduce a fundamental requirement for a measure of dispersion called the preference for equal division a number of general classes of dispersion measures are provided notable among these are those based on t norm and t conorm operators

weighted ordinal means the concept of weighted ordinal arithmetic means and other related weighted ordinal means is studied based on the relevant results on the scale 0 1 new types of weighted ordinal means are proposed in some cases these ordinal means coincide with those proposed by godo and torra but not in the case when ordinal means introduced by them are not idempotent based on divisible ordinal t conorms and modifying the approach of godo and torra we show how the previously introduced weighted ordinal means can be obtained without exploiting the formal similarity of the structure of continuous t conorms on 0 1 and divisible ordinal t conorms

affine construction methodology of aggregation functions abstract aggregation functions have attracted much attention in recent times because of its potential use in many areas such us data fusion and decision making in practice most of the aggregation functions that scientists use in their studies are constructed from very simple usually affine or polynomial functions however these are distinct in nature in this paper we develop a systematic study of these two classes of functions from a common point of view to do this we introduce the class of affine aggregation functions which cover both the aforementioned families and most of examples of aggregation functions that are used in practice including by its great applicability the symmetric case our study allows us to characterize when a function constructed from affine or polynomial functions is in fact a new aggregation function we also study when sums or products of this kind of functions are again an aggregation function

k maxitive fuzzy measures a scalable approach to model interactions abstract fuzzy measures are powerful at modeling interactions between elements unfortunately they use a number of coefficients that exponentially grows with the number of elements beyond the computational complexity assigning a value to any coalition of a large set of elements does not make sense k order measures model interactions involving at most k elements the number of coefficients to identify is reduced and their modeling capacity is preserved in real problems where the number of interacting elements is limited in extreme situations of full redundancy or complementariness it is mathematically proven that the complete fuzzy measure is both k additive and k maxitive a learning algorithm to identify k maxitive measures from labeled data is designed on the basis of hlms heuristic least mean squares in a classification context the study of synthetic data with partial redundancy or complementariness supports the idea that the difference between full and partial interaction is a matter of degree not of kind dealing with two real world datasets a comparison of the complete fuzzy measure and a k maxitive one shows the number of interacting elements is limited and the k maxitive measures yield the same characterization of interactions and a comparable classification accuracy

notes on aggregation of fuzzy truth values takac recently introduced the notion of aggregation operations on fuzzy truth values called ftv aggregation operations and investigated extended aggregation operations on the algebra of convex normal fuzzy truth values with their left and right parts in this paper it is pointed out that the left resp right part of an arbitrary convex normal fuzzy truth value is not necessarily its increasing resp decreasing part moreover an arbitrary convex normal fuzzy truth value is not equivalent to either intersection or union of its left and right parts the conclusions of extended aggregation operations are revalidated in our paper which were proven with uncorrect assertions about convex normal fuzzy truth values

selective majority additive ordered weighting averaging operator abstract usually in order to summarize various opinions about a particular situation mainly product or service valuation on internet a process called aggregation is used this process basically consists of determining the appropriate value to represent the majority s opinion and many strategies and operators can be used for this purpose simple arithmetic mean is widely used to resume several opinions in a single value but this value is generally not representative or it is affected by the extreme values an alternative to aggregate opinions are the ordered weighting averaging owa operators nevertheless they have distribution problems when applied to aggregates with cardinalities these problems may be solved by using majority additive owa ma owa operator a sort of arithmetic mean of arithmetic means ma owa operator works adequately but in some cases discards the minority s opinion specifically when it does not coincide with the largest cardinality value in order to generalize the usage of ma owa operator the rest of opinions are taken into account using a cardinality relevance factor this paper introduces a selective majority additive owa sma owa which manages the significance of all opinions varying the cardinality relevance factor mathematical extension of sma owa its properties and some illustrative examples are presented in this article

aggregation of infinite sequences infinitary aggregation functions acting on sequences and possessing some a priori given properties as additivity comonotone additivity symmetry etc are investigated on the other side we discuss infinitary aggregation functions related to given extended aggregation functions where special attention is given to triangular norms triangular conorms and weighted means

discrete bipolar pseudo integrals abstract in the authors paper strboja et al 2016 42 the notion of the bipolar pseudo integral has been introduced this paper extends investigations related to this new type of bipolar integrals defined with respect to decomposable bi capacities we consider the main properties of the discrete bipolar pseudo integral a characterization theorem for the discrete bipolar pseudo integral is proven monotone convergence theorems and the fatou type lemma for the discrete bipolar pseudo integral are considered in order to illustrate obtained results many interesting examples are provided

weighted aggregation operators based on minimization minimization based aggregation operators a g d are discussed special attention is paid to weighting function g based cases related to some fixed dissimilarity function d when d 2 x y x y 2 we recognize mixture operators and we recall some sufficient conditions for g ensuring the monotonicity of a g d for d 1 x y x y and non decreasing non increasing g a g d is shown to be the upper lower median whenever a g d is an aggregation operator

an invariance of geometric mean with respect to lagrangian means abstract the invariance of the geometric mean g with respect to the lagrangian mean type mapping l f l g i e the equation g l f l g g is considered we show that the functions f and g must be of high class regularity this fact allows to reduce the problem to a differential equation and determine the second derivatives of the generators f and g

two new characterizations of universal integrals on the scale 0 1 the concept of universal integral recently proposed and axiomatized encompasses several integrals including the choquet shilkret and sugeno integrals in this paper we present two new axiomatizations of universal integrals on the scale 0 1 in the first characterization we look at universal integrals on the scale 0 1 as families of aggregation functions f satisfying some desired properties the second characterization is given in the framing in which the original definition of universal integral was provided

zero linear copulas abstract we introduce a new method for constructing copulas c a special type of aggregation functions based on the idea that c u v 0 if u g v for any continuous and decreasing function g 0 1 0 1 such that g 1 0 and c is linear if u g v 1 we also study the relationship between these copulas and other known families of copulas we provide some salient properties and measure the dependence and asymmetry in this class of copulas

smart or and smart and fuzzy average operators a generalized proposal abstract in this paper we introduce new average operators for merging any number of fuzzy numbers without any exogenous components the proposed n ary operators are based on a specific adaptation of marzullo s algorithm and depart from the usual fuzzy arithmetic mean according to the degree of agreement or disagreement among the memberships of input fuzzy numbers such merging operators are suitable to be applied in any model where the same quantity usually a parameter can be measured estimated through different fuzzy memberships stemming by different sources of information the special case of two fuzzy memberships was the focus of our previous contributions that were elicited in order to estimate the fuzzy volatility parameter in an hybrid fuzzy stochastic model for option pricing in this paper we generalize the setting to the case of n fuzzy inputs to be merged and also remove exogenous factors from the definition of the operators in order to have an application at hand we consider the same example treated in the quoted paper and we compare the outcomes obtained via the new operators named s m a r t with the fuzzy arithmetic mean as a canonical benchmark

indicators for the characterization of discrete choquet integrals ordered weighted averaging owa operators and their extensions are powerful tools used in numerous decision making problems this class of operator belongs to a more general family of aggregation operators where each operator of this family is understood as a discrete choquet integral aggregation operators are usually characterized by indicators in this article four indicators usually associated with the owa operator are extended to the discrete choquet integral namely the degree of balance the divergence the variance indicator and renyi entropies all of these indicators are considered from a local and a global perspective linearity of indicators for linear combinations of capacities is investigated and to illustrate the usefulness of results indicators of the probabilistic ordered weighted averaging powa operator are derived finally a numerical example is provided to discuss the results in a specific context

efficiently processing p e approximate join aggregation on massive data abstract join aggregation is an important operation in database systems to return aggregate information on the join of two or several tables compared with exact query it is a better choice in many cases to return approximate result satisfying a user specified confidence interval in a much faster response time it is found that none of previous works can efficiently process approximate join aggregation on massive data with arbitrary accuracy this paper proposes a novel algorithm p e aja p e approximate join aggregation to obtain approximate join aggregate result with arbitrary confidence interval efficiently two data structures of low space overhead jrs and jpipt are presented in this paper p e aja first makes use of jrs to return a quick response if the approximate result computed by jrs does not satisfy the given confidence interval jpipt is exploited to obtain enough random join tuples this paper presents a novel sampling algorithm to acquire random jpipt tuples of specified size and devises its correctness proof a tuple fetching method is proposed to retrieve join tuples by the sampled jpipt tuples in one pass sequential scan on joined tables the construction and maintenance algorithms of jpipt and jrs are provided also in this paper the experimental results show that p e aja obtains 3 times to 2 orders of magnitude speedup over the existing algorithms and runs 1 to 4 orders of magnitude faster than exact query

quantum thetas on noncommutative bb t 4 from embeddings into lattice in this paper we investigate the theta vector and quantum theta function over noncommutative from the embedding of manin has constructed the quantum theta functions from the lattice embedding into vector space finite group we extend manin s construction of the quantum theta function to the embedding of vector space lattice case we find that the holomorphic theta vector exists only over the vector space part of the embedding and over the lattice part we can only impose the condition for the schwartz function the quantum theta function built on this partial theta vector satisfies the requirement of the quantum theta function however two subsequent quantum translations from the embedding into the lattice part are nonadditive contrary to the additivity of those from the vector space part

equivalent representations of set functions this paper introduces four alternative representations of a set function the ma bius transformation the co ma bius transformation and the interactions between elements of any subset of a given set as extensions of shapley and banzhaf values the links between the five equivalent representations of a set function are emphasized in this presentation

subjective and objective information in linguistic multi criteria group decision making abstract linguistic decision making systems represent situations that cannot be assessed with numerical information but it is possible to use linguistic variables this paper introduces new linguistic aggregation operators in order to develop more efficient decision making systems the linguistic probabilistic weighted average lpwa is presented its main advantage is that it considers subjective and objective information in the same formulation and considering the degree of importance that each concept has in the aggregation a key feature of the lpwa operator is that it considers a wide range of linguistic aggregation operators including the linguistic weighted average the linguistic probabilistic aggregation and the linguistic average further generalizations are presented by using quasi arithmetic means and moving averages an application in linguistic multi criteria group decision making under subjective and objective risk is also presented in the context of the european union law

some properties of weak uninorms a weak uninorm is not only a generalization of a uninorm but also of a nullnorm in this paper we will show that if a weak uninorm is archimedean then it is an archimedean nullnorm and if a weak uninorm is e archimedean then it is an archimedean uninorm moreover the de morgan triples of the weak uninorms will be characterized too

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

algebraic representations of the weighted mean abstract we introduce a general framework for the algebraic representation of the weighted mean in the case in which priorities and values refer to a common aggregation domain for instance in hierarchical multicriteria decision models of the ahp type the general framework proposed is based on the semifield structure of open interval domains and provides a natural algebraic description of weighted mean aggregation including the essential mechanism of normalization which transforms priorities into weights such description necessarily involves two operations addition abelian semigroup and multiplication abelian group which generalize the role of addition and multiplication in p 0 in this sense the semifield framework extends recent work by cavallo d apuzzo and squillante on the multiplicative group structure on the basis of the representation of pairwise comparison matrices and their associated priority vectors we consider open interval domains s r whose semifield structures are generated by bijections s r p continuous thus strictly monotonic bijections play a central role in such case continuous strict triangular conorms norms and uninorms emerge naturally in the representation of the semifield structure and in their weighted version they also provide the representation of the weighted mean in both the arithmetic and geometric forms

the distribution of the probability mass of biconic copulas we study the probability mass distribution of biconic copulas provide a counterexample to a result given in jwaid et al 2012 29 concerning a characterization of singular biconic copulas and provide a new one

note on monotonicity of generalized weighted mean values in the note using the cauchy schwarz buniakowski inequality the authors prove that the generalized weighted mean values mp f r s x y are increasing with respect to the two parameters r and s for any given non negative weight p and positive function f

parametric conditions for a monotone tsk fuzzy inference system to be an n ary aggregation function despite the popularity and practical importance of the fuzzy inference system fis the use of an fis model as an n ary aggregation function which is characterized by both the monotonicity and boundary properties is yet to be established this is because research on ensuring that fis models satisfy the monotonicity property i e monotone fis is relatively new not to mention the additional requirement of satisfying the boundary property the aim of this paper therefore is to establish the parametric conditions for the takagi sugeno kang tsk fis model to operate as an n ary aggregation function hereafter denoted as n tsk fis via the specifications of fuzzy membership functions fmfs and fuzzy rules an absorption property with fuzzy rules interpretation is outlined and the use of n tsk fis as a uni norm is explained exploiting the established parametric conditions a framework for which an n tsk fis model can be constructed from data samples is formulated and analyzed along with a number of remarks synthetic data sets and a benchmark example on education assessment are presented and discussed to be best of the authors knowledge this study serves as the first use of the tsk fis model as an n ary aggregation function

on the associativity functional equation abstract let a b be any bounded closed real interval the class of all continuous nondecreasing associative functions m a b 2 a b fulfilling the boundary conditions m a a a and m b b b is described

average utility maximization a preference foundation this paper provides necessary and sufficient preference conditions for average utility maximization over sequences of variable length we obtain full generality by using a new algebraic technique that exploits the richness structure naturally provided by the variable length of the sequences thus we generalize many preceding results in the literature for example continuity in outcomes a condition needed in other approaches now is an option rather than a requirement applications to expected utility decisions under ambiguity welfare evaluations for variable population size discounted utility and quasilinear means in functional analysis are presented

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

aggregation functions construction methods conjunctive disjunctive and mixed classes in this second part of our state of the art overview on aggregation theory based again on our recent monograph on aggregation functions we focus on several construction methods for aggregation functions and on special classes of aggregation functions covering the well known conjunctive disjunctive and mixed aggregation functions some fields of applications are included

quasi conjunction quasi disjunction t norms and t conorms probabilistic aspects we make a probabilistic analysis related to some inference rules which play an important role in nonmonotonic reasoning in a coherence based setting we study the extensions of a probability assessment defined on n conditional events to their quasi conjunction and by exploiting duality to their quasi disjunction the lower and upper bounds coincide with some well known t norms and t conorms minimum product lukasiewicz and hamacher t norms and their dual t conorms on this basis we obtain quasi and and quasi or rules these are rules for which any finite family of conditional events p entails the associated quasi conjunction and quasi disjunction we examine some cases of logical dependencies and we study the relations among coherence inclusion for conditional events and p entailment we also consider the or rule where quasi conjunction and quasi disjunction of premises coincide with the conclusion we analyze further aspects of quasi conjunction and quasi disjunction by computing probabilistic bounds on premises from bounds on conclusions finally we consider biconditional events and we introduce the notion of an n conditional event then we give a probabilistic interpretation for a generalized loop rule in an appendix we provide explicit expressions for the hamacher t norm and t conorm in the unitary hypercube

the binomial decomposition of generalized gini welfare functions the s gini and lorenzen cases abstract we consider the binomial decomposition of generalized gini welfare functions in terms of the binomial welfare functions and the associated binomial inequality indices we examine in detail the weights of the binomial welfare functions and the coefficients of the associated binomial inequality indices which progressively focus on the poorest sector of the population and we illustrate the numerical behavior of the binomial welfare functions and inequality indices in relation with a new parametric family of income distributions the main contribution of the paper is to investigate the analogy between the binomial welfare functions and the s gini and lorenzen parametric families of generalized gini welfare functions particularly in the context of the binomial decomposition finally we examine the orness of the parametric s gini and lorenzen families of generalized gini welfare functions

on the relationship between modular functions and copulas copulas are nothing else but supermodular functions with absorbing element 0 and neutral element 1 although a copula c cannot be modular on the unit square itself it is effectively so on every rectangle with zero c volume in this paper we show that an appropriate modular function on the unit square can be transformed into a copula by performing a simple truncation operation either from below or above to ensure the compatibility with the frechet hoeffding bounds modular functions on the unit square admit an additive representation in terms of two univariate functions we specifically focus on cases where these univariate functions are sections horizontal vertical diagonal of a given copula ample illustrations are provided

biconic aggregation functions we introduce a new method to construct aggregation functions these aggregation functions are called biconic aggregation functions with a given diagonal resp opposite diagonal section and their construction is based on linear interpolation on segments connecting the diagonal resp opposite diagonal of the unit square to the points 0 1 and 1 0 resp 0 0 and 1 1 subclasses of biconic aggregation functions such as biconic semi copulas biconic quasi copulas and biconic copulas are studied in detail

characterization and comparison of sugeno and choquet integrals abstract starting from the concept of equiordered functions we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure sugeno and choquet integrals the characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals pointing out their formal similarities and their conceptual differences

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

a characterization of the ordered weighted averaging functions based on the ordered bisymmetry property this paper deals with the characterization of a class of aggregation operators this class concerns operators that are symmetric increasing stable for the same positive linear transformations and present a property close to the bisymmetry property the ordered bisymmetry property it is proved that the class investigated contains exactly the ordered weighted averaging operators introduced by yager 1988

improving minimax disparity model to determine the owa operator weights determining the ordered weighted averaging owa operator weights is important in decision making applications several approaches have been proposed in the literature to obtain the associated weights this paper provides an alternative disparity model to identify the owa operator weights the proposed mathematical model extends the existing disparity approaches by minimizing the sum of the deviation between two distinct owa weights the proposed disparity model can be used for a preference ranking aggregation a numerical example in preference ranking and an application in search engines prove the usefulness of the generated owa weights

distance metrics for high dimensional nearest neighborhood recovery compression and normalization previous work has shown that the minkowski p distance metrics are unsuitable for clustering very high dimensional document data we extend this work we frame statistical theory on the relationships between the euclidean cosine and correlation distance metrics in terms of item neighborhoods we discuss the differences between the cosine and correlation distance metrics and illustrate our discussion with an example from collaborative filtering we introduce a family of normalized minkowski metrics and test their use on both document data and synthetic data generated from the uniform distribution we describe a range of criteria for testing neighborhood homogeneity relative to underlying latent classes we discuss how these criteria are explicitly and implicitly linked to classification performance by testing both normalized and non normalized minkowski p metrics for multiple values of p we separate out distance compression effects from normalization effects for multi class classification problems we believe that distance compression on high dimensional data aids classification and data analysis for document data we find that the cosine and normalized euclidean correlation and proportioned city block metrics give strong neighborhood recovery the proportioned city block metric gives particularly good results for nearest neighbors recovery and should be used when utilizing document data analysis techniques for which nearest neighborhood recovery is important for data generated from the uniform distribution neighborhood recovery improves as the value of p increases

on representations of 2 increasing binary aggregation functions in this paper we provide two different representations of 2 increasing binary aggregation functions by means of their lower and upper margins and a suitable copula

aggregation functions means this two part state of the art overview on aggregation theory summarizes the essential information concerning aggregation issues an overview of aggregation properties is given including the basic classification on aggregation functions in this first part the stress is put on means i e averaging aggregation functions both with fixed arity n ary means and with multiple arities extended means

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

generators of copulas and aggregation the most applied class of copulas for fitting purposes is undoubtedly the class of archimedean copulas due to their representation by means of single functions of one variable i e by means of additive generators or the corresponding pseudo inverses in this paper we characterize aggregation functions preserving additive generators pseudo inverses of additive generators of archimedean copulas as a by product we obtain an efficient method to construct new additive generators from some given ones

a tool for aggregation with words the need of computing with words has become an important topic in many areas dealing with vague information the aim of this paper is to present different tools which support computing with words especially we are concerned with the weighted aggregation of linguistic term sets whose results are just the words themselves without using the fuzzy numbers that represent the semantics of their linguistic terms we propose a new aggregation operator referred to as the symbolic weighted median that computes the most representative element from an ordered collection of weighted linguistic terms this operator aggregates the linguistic labels such that its result is expressed in terms of the initial linguistic term set though is modified by using dedicated tools called the generalized symbolic modifiers one advantage of this proposal is that the expression domain does not change we increase or decrease the granularity only where it becomes necessary additionally this new operator exhibits several interesting mathematical properties

jensen type inequality for the bipolar pseudo integrals abstract the main purpose of this paper is to establish conditions under which the jensen type inequality for the discrete bipolar pseudo integral is valid besides we extend investigations of the properties of the bipolar pseudo integral the observations concern the discrete bipolar pseudo integrals based on the following three canonical cases of two binary symmetric operations in the first case they are generated by an odd strictly increasing and continuous function in the remaining two cases a symmetric addition is the symmetric maximum while in the second case the corresponding pseudo multiplication is a non idempotent operation and in the third case it is the symmetric minimum

characterization of uninorms on bounded lattices in this paper we propose a characterization of uninorms on a general bounded lattice l by means of a sextuple of a triangular norm a triangular conorm and four aggregation functions on l observe that in the case when l is a chain it is enough to consider a triple consisting of a t norm a t conorm and an averaging aggregation function an example of a proper uninorm which has an absorbing element differing from both 0 and 1 is also shown note that this cannot happen if we consider uninorms acting on a chain two general constructions of uninorms on l are added letting a t norm a t conorm linked to a fixed neutral element e of the constructed uninorm to be free and fixing the remaining functions

generalized aggregation of fuzzy truth values we study generalized extended aggregation operations we further discuss the equivalent expressions of partial orders and the generalized extended aggregation operation is proven to be an ftv aggregation op eration this paper deals with generalized extended aggregation operations in accordance with generalized extension principle and provides a theoretical basis for generalized extended aggregation operations generalized extended aggregation operations are studied on the algebra of convex resp normal fuzzy truth values when an aggregation operation is continuous the generalized extended aggregation operation is proven to be an aggregation operation on fuzzy truth values ftv aggregation operation for short for arbitrary t norm on the algebra of convex normal fuzzy truth values

spread measures and their relation to aggregation functions abstract the theory of aggregation most often deals with measures of central tendency however sometimes a very different kind of a numeric vector s synthesis into a single number is required in this paper we introduce a class of mathematical functions which aim to measure spread or scatter of one dimensional quantitative data the proposed definition serves as a common abstract framework for measures of absolute spread known from statistics exploratory data analysis and data mining e g the sample variance standard deviation range interquartile range iqr median absolute deviation mad etc additionally we develop new measures of experts opinions diversity or consensus in group decision making problems we investigate some properties of spread measures show how are they related to aggregation functions and indicate their new potentially fruitful application areas

characterization of some aggregation functions stable for positive linear transformations abstract this paper deals with the characterization of some classes of aggregation functions often used in multicriteria decision making problems the common properties involved in these characterizations are increasing monotonicity and stability for positive linear transformations additional algebraic properties related to associativity allow to completely specify the functions

aggregation with generalized mixture operators using weighting functions this paper regards weighted aggregation operators in multiple attribute decision making and its main goal is to investigate ways in which weights can depend on the satisfaction degrees of the various attributes criteria we propose and discuss two types of weighting functions that penalize poorly satisfied attributes and reward well satisfied attributes we discuss in detail the characteristics and properties of both functions moreover we present an illustrative example to clarify the use and behaviour of such weighting functions comparing the results with those of standard weighted averaging operators

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

1 lipschitz power stable aggregation functions in this paper we study the structure of the class of all binary 1 lipschitz power stable aggregation functions a special attention is devoted to the characterization of power stable quasi copulas moreover the relations between copulas and quasi copulas as 1 lipschitz aggregation functions with neutral element e 1 sup and inf closures of copulas and track defined functions based on copulas in the framework of binary power stable aggregation functions are characterized

on a certain class of aggregative operators abstract here our starting point is a study of connection with dombi aggregative operators uninorms strict t norms and t conorms we present a new representation theorem of strong negations that explicitly contains the neutral value then the relationships for aggregative operators and strong negations are verified as well as those for the t norm and t conorm using the pan operator concept we introduce the multiplicative pliant concept and give the necessary and sufficient conditions for it we study a certain class of weighted aggregative operators representable uninorms which build a self demorgan class with infinitely many negations we provide the necessary and sufficient conditions for these operators

mean variance portfolio selection with the ordered weighted average portfolio selection is the theory that studies the process of selecting the optimal proportion of different assets the first approach was introduced by harry markowitz and was based on a mean variance framework this paper introduces the ordered weighted average owa in the mean variance model the main idea is to replace the classical mean and variance by the owa operator by doing so the new model is able to study different degrees of optimism and pessimism in the analysis being able to develop an approach that considers the decision makers attitude in the selection process this paper also suggests a new framework for dealing with the attitudinal character of the decision maker based on the numerical values of the available arguments the main advantage of this method is the ability to adapt to many situations offering a more complete representation of the available data from the most pessimistic situation to the most optimistic one an illustrative with fictitious data and a real example are studied

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

aggregation operators preserving quasiconvexity quasiconvexity of a fuzzy set is the necessary and sufficient condition for its cuts to be convex we study the class of those two variable aggregation operators that preserve quasiconvexity on a bounded lattice i e a m n is quasiconvex for quasiconvex lattice valued fuzzy sets m n the class of all such aggregation operators is characterized by a lattice identity that they have to fulfill in case of a unit interval we show the construction of aggregation operators preserving quasiconvexity from a pair of real valued functions on the unit interval as a consequence we get that the intersection of quasiconvex fuzzy sets is quasiconvex if and only if the intersection is based on the minimum triangular norm

set characterization selection towards classification based on interaction index in many real world datasets both the individual and coordinated action of features may be relevant for class identification in this paper a computational strategy for relevant feature selection based on the characterization of redundant or complementary features is proposed the characterization is achieved using fuzzy measures and an interaction index computed from fuzzy measure coefficients fuzzy measure identification requires raw data to be turned into confidence degrees this key step is carried out considering the distributions of feature values across all the classes fuzzy measure coefficients are then estimated with an improved version of the heuristic least mean squares algorithm that includes an efficient management of untouched coefficients then a generalization of the shapley index for an arbitrary number of features is used simulations experiments on synthetic datasets are performed to study the behavior of this generalized interaction index for extreme datasets containing either redundant or complementary features as well as noise the index value is defined by mathematical formula this result is used to motivate feature selection guidelines that take into account feature interactions experimental results on benchmark datasets show that the proposal allows for the design of compact interpretable and competitive classification models