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

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

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

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

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

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

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

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

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

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

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

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

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

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

high frequency asymptotics of edge waves on a beach of nonconstant slope the paper is devoted to the construction of asymptotic expansions for frequencies of water waves trapped by a beach of nonconstant slope as the longshore wave number tends to infinity the existence of such trapping modes in this asymptotic regime was proved recently in a s bonnet ben dhia and p joly siam j appl math 53 1993 pp 1507 1550 for a beach of constant slope the formulas obtained reduce to the classical result of ursell some generalizations to other geometries waves trapped by afloating semisubmerged cylinder and by shores of a channel of finite width are indicated the main analytical tool used for the construction of the asymptotics is an explicit solution of a mixed boundary value problem for the helmholtz equation in an angle with nonhomogeneous boundary conditions

undirected single source shortest paths with positive integer weights in linear time the single source shortest paths problem sssp is one of the classic problems in algorithmic graph theory given a positively weighted graph g with a source vertex s find the shortest path from s to all other vertices in the graph since 1959 all theoretical developments in sssp for general directed and undirected graphs have been based on dijkstra s algorithm visiting the vertices in order of increasing distance from s thus any implementation of dijkstra s algorithm sorts the vertices according to their distances from s however we do not know how to sort in linear time here a deterministic linear time and linear space algorithm is presented for the undirected single source shortest paths problem with positive integer weights the algorithm avoids the sorting bottleneck by building a hierarchical bucketing structure identifying vertex pairs that may be visited in any order