the relationship between the minimum variance and minimax disparity rim quantifier problems recently liu and lou on the equivalence of some approaches to the owa operator and rim quantifier determination fuzzy sets and systems 159 2007 1673 1688 investigated the equivalence of solutions to the minimum variance and minimax disparity rim quantifier problems however their proofs are very sensitive to the assumption and some are mathematically incomplete in this regard this paper provides a counterexample of the minimax disparity rim quantifier problem for the case in which generating functions are continuous the paper also provides a correct proof of the minimax disparity rim quantifier problem for the case in which generating functions are absolutely continuous and a generalized result for the minimum variance rim quantifier problem for the case in which generating functions are lebesgue integrable based on the results the paper provides a correct relationship between the minimum variance and minimax disparity rim quantifier problems

group decision making model using fuzzy multiple attributes analysis for the evaluation of advanced manufacturing technology selection of advanced manufacturing technology is important for improving manufacturing system competitiveness this study builds a group decision making model using fuzzy multiple attributes analysis to evaluate the suitability of manufacturing technology since numerous attributes have been considered in evaluating the manufacturing technology suitability most information available in this stage is subjective and imprecise and fuzzy sets theory provides a mathematical framework for modeling imprecision and vagueness the proposed approach involved developing a fusion method of fuzzy information which was assessed using both linguistic and numerical scales in addition an interactive decision analysis is developed to make a consistent decision when evaluating the suitability of manufacturing technology it may be necessary to improve upon the technology and naturally advanced manufacturing technology is seen as the best direction for improvement the flexible manufacturing system adopted in the taiwanese bicycle industry is used in this study to illustrate the computational process of the proposed method the results of this study are more objective and unbiased owing to being generated by a group of decision makers

constrained ordered weighted averaging aggregation with multiple comonotone constraints abstract the constrained ordered weighted averaging owa aggregation problem arises when we aim to maximize or minimize a convex combination of order statistics under linear inequality constraints that act on the variables with respect to their original sources the standalone approach to optimizing the owa under constraints is to consider all permutations of the inputs which becomes quickly infeasible when there are more than a few variables however in certain cases we can take advantage of the relationships amongst the constraints and the corresponding solution structures for example we can consider a land use allocation satisfaction problem with an auxiliary aim of balancing land types whereby the response curves for each species are non decreasing with respect to the land types this results in comonotone constraints which allow us to drastically reduce the complexity of the problem in this paper we show that if we have an arbitrary number of constraints that are comonotone i e they share the same ordering permutation of the coefficients then the optimal solution occurs for decreasing components of the solution after investigating the form of the solution in some special cases and providing theoretical results that shed light on the form of the solution we detail practical approaches to solving and give real world examples

relativistic and newtonian κ space times the deformations of the galilei algebra and their associated noncommutative newtonian space times are investigated this is done by analyzing the possible nonrelativistic limits of an eleven generator pseudo extended poincare algebra p and their implications for the existence of a first order differential calculus the additional one form needed to achieve a consistent calculus on minkowski space is shown to be related to the additional central generator entering in the p hopf algebra in the process deformations of the extended galilei and galilei algebras are introduced which have respectively a cocycle and a bicrossproduct structure

projective representations of k galilei group the projective representations of the k galilei group are found by contracting the relevant representations of the poincare group the projective multiplier is found it is shown that it is not possible to replace the projective representations of by vector representations of some of its extensions

how well does the owa operator represent real preferences we present the results of an empirical study in which we analyze the ability of the ordered weighted average owa operator to model actual preferences in a multi attribute ranking task we compare the owa to a competing model simple additive weighting saw and we also study whether its characteristic feature the ability to represent different attitudes toward compensation among attributes is reflected in the preferences provided by subjects we find that in general the owa model fits slightly less well to empirical data subjects whose preferences are better explained by the saw model are also more consistent in their choice behavior our results furthermore indicate that preferences of most subjects are not fully compensatory thus the ability of the owa operator to represent different attitudes toward compensation can be a useful feature in modeling actual preferences the structure of the weights estimated for the owa operator also suggests that it might provide a good approximation to certain types of decision heuristics

the holder continuity of the solution map to the b family equation in weak topology we prove that the solution map of the b family equation is holder continuous as a map from a bounded set of h s mathbb r s frac 3 2 with h r mathbb r 0 le r 0 moreover we show that the obtained exponent of the holder continuity is optimal when s 1 r s

benchmarking in linguistic importance weighted aggregations in this work we concentrate on the issue of weighted aggregations and provide a possibilistic approach to the process of importance weighted transformation when both the importances interpreted as benchmarks and the ratings are given by symmetric triangular fuzzy numbers we will show that using the possibilistic approach i small changes in the membership function of the importances can cause only small variations in the weighted aggregate ii the weighted aggregate of fuzzy ratings remains stable under small changes in the nonfuzzy importances iii the weighted aggregate of crisp ratings still remains stable under small changes in the crisp importances whenever we use a continuous implication operator for the importance weighted transformation we illustrate the proposed method by some simple examples

an analytic approach for obtaining maximal entropy owa operator weights one important issue in the theory of ordered weighted averaging owa operators is the determination of the associated weights one of the first approaches suggested by o hagan determines a special class of owa operators having maximal entropy of the owa weights for a given level of orness algorithmically it is based on the solution of a constrained optimization problem in this paper using the method of lagrange multipliers we shall solve this constrained optimization problem analytically and derive a polynomial equation which is then solved to determine the optimal weighting vector

hesitant analytic hierarchy process abstract in traditional analytic hierarch process ahp decision makers dms are required to provide crisp judgments over paired comparisons of objectives to construct comparison matrices to enhance the modeling ability of traditional ahp we propose hesitant ahp h ahp that can consider the hesitancy experienced by the dms in decision h ahp is characterized by hesitant judgments where each hesitant judgment can be represented by several possible values different probability distributions can be used to further describe hesitant judgments according to the dms preferences based on a hesitant comparison matrix hcm that consists of hesitant judgments we define two indices to measure the consistency degree and the consensus degree of the hcm respectively from a stochastic point of view a new prioritization method is developed to derive priorities from hcms where the results are with probability interpretations we provide a step by step procedure for h ahp and demonstrate this new method with a real life decision making problem

well posedness of the fornberg whitham equation on the circle abstract in this paper we show that the fornberg whitham equation is well posed in sobolev spaces h s for s 3 2 and in the periodic case we then show that the well posedness is sharp in the sense that the continuity of the data to solution map is not better than continuous by using the method of approximate solutions however we also show that the solution map is holder continuous in a weaker topology these results are based on the well posedness result as well as the solution size and lifespan estimates

wave breaking analysis for the fornberg whitham equation abstract in this paper the wave breaking of the fornberg whitham equation is studied we first investigate the local well posedness and show a blow up scenario by local in time a priori estimates next we present a sufficient condition on the initial data to ensure wave breaking moreover the estimates of life span and blow up rate are obtained

on solving linear programs with the ordered weighted averaging objective abstract the problem of aggregating multiple criteria to form overall objective functions is of considerable importance in many disciplines the most commonly used aggregation is based on the weighted sum the ordered weighted averaging owa aggregation introduced by yager uses the weights assigned to the ordered values i e to the worst value the second worst and so on rather than to the specific criteria this allows to model various aggregation preferences preserving simultaneously the impartiality neutrality with respect to the individual criteria in this paper we analyze solution procedures for linear programs with the owa objective functions two alternative linear programming formulations are introduced and their computational efficiency is analyzed

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

on proving the extended minimax disparity owa problem determining associated weights in the theory of ordered weighted averaging owa operators is an important issue wang and parkan information sciences 175 2005 20 29 proposed a minimax disparity approach for obtaining owa operator weights which is based on the solution of a linear program lp model for a given degree of orness recently amin and emrouznejad computers industrial engineering 50 2006 proposed an extended minimax disparity model and improved their proposed lp to obtain weights that would be as close as possible they also left an open problem related to the extended model for an even number of arguments there would be an interval for the degree of orness such that the optimal solution of the extended model could be obtained by a compact mathematical form in this paper we completely prove this open problem mathematically for all orness levels whatever the number of arguments

on the properties of owa operator weights functions with constant level of orness the result of aggregation performed by the ordered weighted averaging owa operator heavily depends upon the weighting vector used a number of methods have been presented for obtaining the associated weights in this paper we present analytic forms of owa operator weighting functions each of which has properties of rank based weights and a constant level of orness irrespective of the number of objectives considered these analytic forms provide significant advantages for generating the owa weights over previously reported methods first the owa weights can be efficiently generated by using proposed weighting functions without solving a complicated mathematical program moreover convex combinations of these specific owa operators can be used to generate the owa operators with any predefined values of orness once specific values of orness are a priori stated by the decision maker those weights have a property of constant level of orness as well finally the owa weights generated at a predefined value of orness make almost no numerical difference with maximum entropy owa weights in terms of dispersion

traveling wave solutions of the camassa holm equation all weak traveling wave solutions of the camassa holm equation are classified we show that in addition to smooth solutions there are a multitude of traveling waves with singularities peakons cuspons stumpons and composite waves

the induced representations of the κ poincare group the induced representations of the poincare group for the massive case and the massless case are described it is shown that it extends many of the features of the classical case

discontinuous traveling waves as weak solutions to the fornberg whitham equation abstract we analyze the weak solution concept for the fornberg whitham equation in case of traveling waves with a piecewise smooth profile function the existence of discontinuous weak traveling wave solutions is shown by means of analysis of a corresponding planar dynamical system and appropriate patching of disconnected orbits

classification of travelling waves in the fornberg whitham equation abstract in this paper the fornberg whitham fw equation is investigated by using the improved qualitative method which combines characteristics of several methods to solve equations we classify all travelling wave solutions of this equation in specified regions of the parametric space besides already known solutions such as peaked and kink like wave solutions this equation also admits looped and cusped wave solutions especially some composite waves including fractal like waves and stumpons what is more interesting is that we give the limit behavior of all periodic solutions as the parameters trend to some special values

on the issue of obtaining owa operator weights we first investigate the issue of obtaining the weights associated with the owa aggregation in the situation when we have observed data on the arguments and the aggregated value we next introduce a family of owa operators called exponential owa operators finally we look at a simple procedure for generating the weights given a required degree of orness

which deformations of the poincare group we analyse the present status of poincare group in considering it as a fundamental object independent of the minkowski space we examine the observables associated with it after having introduced the notion of kinematical observable we derive the class of deformed poincare groups which are compatible with physics

compatible weighting method with rank order centroid maximum entropy ordered weighted averaging approach in a situation where imprecise attribute weights such as a rank order are captured various approximate weighting methods have been proposed to aid multiattribute decision analysis among others it is well known that the rank order centroid roc weights result in the highest performance in terms of the identification of the best alternative under the ranked attribute weights in this paper we aim to reinterpret the meaning of the roc weights and to develop a compatible weighting method that is based on other well established academic disciplines the ordered weighted averaging owa method is a nonlinear aggregation method in that the weights are associated with the objects reordered according to their magnitudes in the aggregation process some interesting semantics can be attached to the approximate weights in view of the measure developed in the owa method furthermore the weights generated by the maximum entropy method show equally compatible performance with the roc weights under some condition which is demonstrated by theoretical and simulation analysis

ordered weighted average optimization in multiobjective spanning tree problem abstract multiobjective spanning tree problems are studied in this paper the ordered median objective function is used as an averaging operator to aggregate the vector of objective values of feasible solutions this leads to the ordered weighted average spanning tree problem a nonlinear combinatorial optimization problem different mixed integer linear programs are proposed based on the most relevant minimum cost spanning tree models in the literature these formulations are analyzed and several enhancements presented their empirical performance is tested over a set of randomly generated benchmark instances the results of the computational experiments show that the choice of an appropriate formulation allows to solve larger instances with more objectives than those previously solved in the literature

a note on constrained owa aggregation yager considered the problem of maximizing an owa aggregation of a group of variables that are interrelated and constrained by a collection of linear inequalities and he showed how this problem can be modelled as a mixed integer linear programming problem in this short communication we show a simple algorithm for exact computation of optimal solutions to a constrained owa aggregation problem with a single constraint on the sum of all decision variables

owa operators in regression problems we consider an application of fuzzy logic connectives to statistical regression we replace the standard least squares least absolute deviation and maximum likelihood criteria with an ordered weighted averaging owa function of the residuals depending on the choice of the weights we obtain the standard regression problems high breakdown robust methods least median least trimmed squares and trimmed likelihood methods as well as new formulations we present various approaches to numerical solution of such regression problems owa based regression is particularly useful in the presence of outliers and we illustrate the performance of the new methods on several instances of linear regression problems with multiple outliers

quantum poincare group related to the kappa poincare algebra the classical r matrix implied by the quantum kappa poincare algebra of lukierski nowicki and ruegg is used to generate a poisson structure on the poincare group a quantum deformation of the poincare group on the hopf algebra level is obtained by a trivial quantization

non uniform dependence on initial data of solutions to the euler equations of hydrodynamics we show that continuous dependence on initial data of solutions to the euler equations of incompressible hydrodynamics is optimal more precisely we prove that the data to solution map is not uniformly continuous in sobolev h s topology for any s in mathbb r if the domain is the flat torus mathbb t n mathbb r n 2 pi mathbb z n and for any s 0 if the domain is the whole space mathbb r n

applying logistic regression to relevance feedback in image retrieval systems this paper deals with the problem of image retrieval from large image databases a particularly interesting problem is the retrieval of all images which are similar to one in the user s mind taking into account his her feedback which is expressed as positive or negative preferences for the images that the system progressively shows during the search here we present a novel algorithm for the incorporation of user preferences in an image retrieval system based exclusively on the visual content of the image which is stored as a vector of low level features the algorithm considers the probability of an image belonging to the set of those sought by the user and models the logit of this probability as the output of a generalized linear model whose inputs are the low level image features the image database is ranked by the output of the model and shown to the user who selects a few positive and negative samples repeating the process in an iterative way until he she is satisfied the problem of the small sample size with respect to the number of features is solved by adjusting several partial generalized linear models and combining their relevance probabilities by means of an ordered averaged weighted operator experiments were made with 40 users and they exhibited good performance in finding a target image 4 iterations on average in a database of about 4700 images the mean number of positive and negative examples is of 4 and 6 per iteration a clustering of users into sets also shows consistent patterns of behavior

choosing owa operator weights in the field of social choice one of the most important issues in the theory of owa operators is the determination of associated weights this matter is essential in order to use the best suited owa operator in each aggregation process given that some aggregation processes can be seen as extensions of majority rules to the field of gradual preferences it is possible to determine the owa operator weights by taking into account the class of majority rule that we want to obtain when individuals do not grade their pairwise preferences however a difficulty with this approach is that the same majority rule can be obtained through a wide variety of owa operators for this reason a model for selecting the best suited owa operators is proposed in this paper

on obtaining minimal variability owa operator weights one important issue in the theory of ordered weighted averaging owa operators is the determination of the associated weights one of the first approaches suggested by o hagan determines a special class of owa operators having maximal entropy of the owa weights for a given level of orness algorithmically it is based on the solution of a constrained optimization problem another consideration that may be of interest to a decision maker involves the variability associated with a weighting vector in particular a decision maker may desire low variability associated with a chosen weighting vector in this paper using the kuhn tucker second order sufficiency conditions for optimality we shall analytically derive the minimal variability weighting vector for any level of orness

bicrossproduct structure of the quantum weyl group abstract the quantum weyl group formula associated to a complex simple lie algebra g consists of the quantum group uq g with certain quantum simple reflections w i adjoined let kw be the group algebra of the standard covering w of the weyl group of g here k c we show that formula has the structure of a cocycle bicrossproduct formula kw uq g it consists as an algebra of a cocycle semidirect product by a cocycle action of kw on uq g defined with respect to a certain non abelian cocycle it consists as a coalgebra of an extension by a non abelian dual cocycle the dual of formula is also a bicrossproduct and consists as an algebra of an extension of the dual of uq g by the commutative algebra of functions on w via a cocycle

on equitable resource allocation problems a lexicographic minimax approach in this expository paper we review a variety of resource allocation problems in which it is desirable to allocate limited resources equitably among competing activities applications for such problems are found in diverse areas including distribution planning production planning and scheduling and emergency services location each activity is associated with a performance function representing for example the weighted shortfall of the selected activity level from a specified target a resource allocation solution is called equitable if no performance function value can be improved without either violating a constraint or degrading an already equal or worse off i e larger performance function value that is associated with a different activity a lexicographic minimax solution determines this equitable solution that is it determines the lexicographically smallest vector whose elements the performance function values are sorted in nonincreasing order the problems reviewed include large scale allocation problems with multiple knapsack resource constraints multiperiod allocation problems for storable resources and problems with substitutable resources the solution of large scale problems necessitates the design of efficient algorithms that take advantage of special mathematical structures indeed efficient algorithms for many models will be described we expect that this paper will help practitioners to formulate and solve diverse resource allocation problems and motivate researchers to explore new models and algorithmic approaches

on the constrained owa aggregation problem with single constraint abstract in this note we present a simple proof for the constrained owa aggregation problem with a single constraint but with variable coefficients

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

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

an orness measure for quasi arithmetic means in this paper an orness measure to reflect the or like degree of the quasi arithmetic mean operator is proposed with the generating function representation method some properties of a quasi arithmetic mean associated with its orness measure are analyzed then the paper focuses on two kinds of parameterized quasi arithmetic means with exponential function and power function generators respectively some properties of them are examined and compared as the aggregation value for any set always monotonically increases with the orness level the orness level can be used as a control parameter to represent the decision maker s preference a generic method to get the quasi arithmetic mean operator which makes the aggregation result consistent with its orness level is also examined finally the properties of the quasi arithmetic mean and that of the exponential and power function generators are extended to the weighted quasi arithmetic mean by considering the importance of the aggregated elements

aggregating preference rankings using owa operator weights one important issue of aggregating preference rankings is to determine the weights of different ranking places this paper proposes the use of ordered weighted averaging owa operator weights to aggregate preference rankings which allows the weights associated with different ranking places to be determined in terms of a decision maker dm s optimism level characterized by an orness degree by adjusting the dm s optimism level ties can be avoided and winner can be selected two numerical examples are examined using owa operator weights to show their applications simplicity and flexibility in aggregating preference rankings

constrained owa aggregation abstract the ordered weighted averaging operators are introduced and some of their properties described attention is then focused on the problem of maximizing an owa aggregation of a group of variables that are interrelated and constrained by a collection of linear inequalities it is shown how this problem can be modeled as an integer linear programming problem an evaluation procedure for linguistically quantified propositions using owa operators is described use is made of this procedure to provide a solution to fuzzy linear programming problems in which some linguistically proscribed number of the goals must be satisfied

improved minimax disparity model for obtaining owa operator weights the determination of weights vector is one of the key issues in the theory of ordered weighted averaging owa operators for this reason many weight generating models have been proposed in the literature the main purpose of this note is to point out that the improved minimax disparity model which is suggested by emrouznejad and amin 2010 has infinite solutions as a consequence this model is not reliable

holder continuity of the solution map for the novikov equation the novikov equation ne has been discovered recently as a new integrable equation with cubic nonlinearities that is similar to the camassa holm and degasperis procesi equations which have quadratic nonlinearities ne is well posed in sobolev spaces hs on both the line and the circle for s 3 2 in the sense of hadamard and its data to solution map is continuous but not uniformly continuous this work studies the continuity properties of ne further for initial data in hs s 3 2 it is shown that the solution map for ne is holder continuous in hr topology for all 0 r s with exponent depending on s and r

models to determine parameterized ordered weighted averaging operators using optimization criteria this paper proposes a general optimization model for determining ordered weighted averaging owa operators and three specific models for generating monotonic and symmetric owa operators as well as those with any function shape in these models entropy and variance concepts are generalized as general dispersion indices for use in the objective functions while the ordinary orness level constraints are used in the constraint equations as a special case we define an orness function for monotonic owa operators which measures the closeness of the aggregation value to the maximum value and a medianness function for symmetric owa operators which measures the closeness of the aggregation value to the median value we also extend the commonly used models for determining owa operators under given orness values to determine monotonic owa operators with given orness function values and symmetric owa operators with given medianness function values analytical solutions and properties of these models are discussed we also provide analytical solutions of the maximum entropy and minimum variance problems with given linear medianness values by setting different forms of the objective function and constraints the parameterized owa operator family elements can achieve various distributions in any desired shape two examples are given to show the owa operator elements distributed in quadratic and gaussian distribution function shapes

owa operators with maximal renyi entropy this paper lays bare a parametric class of ordered weighted averaging owa operators with maximal renyi entropy owa weights for any level of orness in particular we shall formulate an extended approach to decision making with owa operators by introducing considerations of maximizing information content in the aggregation according to a general parametric class of dispersion measures

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

lexicographic optimality in the multiple objective linear programming the nucleolar solution abstract in this paper we study the problem of multiple objective linear programming molp we introduce a new solution concept which is related to that of the nucleolus of n person cooperative game theory we prove that a general molp problem always has a solution in the new sense the points in the nucleolus are efficient in the classic way we prove existence and at the same time we introduce a constructing algorithm for computing it

well posedness and blow up solutions for an integrable nonlinearly dispersive model wave equation abstract we establish local well posedness in the sobolev space hs with any s 3 2 for an integrable nonlinearly dispersive wave equation arising as a model for shallow water waves known as the camassa holm equation however unlike the more familiar korteweg devries model we demonstrate conditions on the initial data that lead to finite time blow up of certain solutions

well posedness global existence and blowup phenomena for a periodic quasi linear hyperbolic equation we establish the local well posedness of a recently derived model for small amplitude shallow water waves for a large class of initial data we prove global existence of the corresponding solution criteria guaranteeing the development of singularities in finite time for strong solutions with smooth initial data are obtained and an existence and uniqueness result for a class of global weak solutions is also given c 1998 john wiley sons inc

a priori identification of preferred alternatives of owa operators by relational analysis of arguments we present a reverse decision aiding method that is distinct from previously reported ordered weighted averaging owa aggregation methods the proposed method is implemented in two phases in the first phase potentially best alternative defined as one having any weighting vector that enables it to be at least as good as the others is identified in the second phase the maximum and the minimum attitudinal characters for such an alternative are computed as the highest and the lowest values which it can attain under the weights set identified in the first phase these two phases are governed only by the relational analysis of input arguments without soliciting the decision maker to supply a specific attitudinal character the proposed method can be applied to cases when it is difficult to obtain a precise attitudinal character and when even if a precise one is obtained the owa operator weights are different depending on the weights generating methods adopted further if uncertain attitudinal character in the form of the interval number is available its projection into the results of the proposed method yields less alternatives of consideration in some cases a single best alternative the proposed method also allows for a priori identification of alternatives prone to change at a particular range of attitudinal character

a preemptive goal programming method for aggregating owa operator weights in group decision making this paper reveals that owa operator weights cannot be aggregated by the weighted arithmetic or geometric average method in group decision making a preemptive goal programming method pgpm is proposed for aggregating owa operator weights which is an extension of the minimax disparity approach developed earlier by the same authors the effectiveness of pgpm is illustrated with a numerical example

median value and median interval of a fuzzy number median value and median interval of a fuzzy number are investigated effects of concentration and dilation of a trapezoidal fuzzy number on the location of the median value and the median interval are studied relationship between the median interval and the mean interval is explored central value and central interval of a fuzzy number are proposed

parameterized defuzzification with continuous weighted quasi arithmetic means an extension parameterized aggregation becomes an attractive idea in many applications by applying the quasi arithmetic mean based defuzzification method and its orness measure we extend the properties of discrete quasi arithmetic mean with an orness measure to the case of continuous weighted quasi arithmetic means and apply them to the parameterized estimation of fuzzy or random variables when facing the uncertainty of these variables the decision maker can obtain the crisp value estimation which is always consistent with his her preference information two families of continuous weighted quasi arithmetic means with exponential and power function generators are discussed combining these conclusions with that of the discrete case we can understand better the properties of quasi arithmetic means and extend their possible applications

well posedness and continuity properties of the fornberg whitham equation in besov spaces abstract in this paper we prove well posedness of the fornberg whitham equation in besov spaces b 2 r s in both the periodic and non periodic cases this will imply the existence and uniqueness of solutions in the aforementioned spaces along with the continuity of the data to solution map provided that the initial data belongs to b 2 r s we also establish sharpness of continuity on the data to solution map by showing that it is not uniformly continuous from any bounded subset of b 2 r s to c t t b 2 r s furthermore we prove a cauchy kowalevski type theorem for this equation that establishes the existence and uniqueness of real analytic solutions and also provide blow up criterion for solutions

a minimax disparity approach for obtaining owa operator weights one of the key issues in the theory of ordered weighted averaging owa operators is the determination of owa operator weights in this paper a minimax disparity approach for obtaining owa operator weights is proposed this involves the formulation and solution of a linear programming lp model for a given degree of orness the proposed approach generates the owa operator weights by minimizing the maximum difference between any two adjacent weights a numerical example is provided to illustrate the application of the proposed approach in generating viable owa operator weights in a simple and effective way

global conservative solutions of the camassa holm equation this paper develops a new approach in the analysis of the camassa holm equation by introducing a new set of independent and dependent variables the equation is transformed into a semilinear system whose solutions are obtained as fixed points of a contractive transformation these new variables resolve all singularities due to possible wave breaking returning to the original variables we obtain a semigroup of global solutions depending continuously on the initial data our solutions are conservative in the sense that the total energy equals a constant for almost every time

an efficient pruning method for decision alternatives of owa operators in this paper we present an efficient method for pruning decision alternatives in the case of using ordered weighted averaging owa operators for decision making the proposed method helps to identify inferior alternatives that are less likely to be selected out of competing alternatives as the owa aggregation proceeds it thus enables us to diminish the number of alternatives before applying the owa operators the reordering process unique to the owa aggregation plays an important role in identifying inferior alternatives the efficacy of the proposed method is demonstrated by simulation analysis in which artificial decision problems of diverse sizes are generated and then examined with four scenarios pruning alternatives pruning alternatives with rank order owa weights pruning alternatives with a normalized decision problem and pruning alternatives with both a normalized decision problem and rank order owa weights the proposed method is easy to use and the simulation results show that the number of alternatives can be reduced drastically by applying this method

an analytic approach to obtain the least square deviation owa operator weights an important issue in the theory of ordered weighted averaging owa operators is the determination of the associated weights one important approach suggested by wang luo and liu in 2007 determines a special class of owa operators with the least square deviation lsd of owa weights for a given orness level in this paper using the method of lagrange multipliers we solve this constrained optimization problem analytically and derive a polynomial equation to determine the optimal weighting vector numerical examples illustrate our proposed approach

a new approach to solve the constrained owa aggregation problem constrained ordered weighted averaging owa aggregation attempts to optimize the owa aggregation problem with multiple constraints it is inherently nonlinear and yager presented a novel method to transform the nonlinear problem to a mixed integer linear problem later a simple algorithm for exact computation of optimal solutions to a single constrained owa aggregation problem was presented in this paper we deal with the same problem but in completely different ways in a sense that it is linearized by utilizing the reordering property of the owa operators we attempt to solve the linear programming problem via the extreme points in lieu of using a linear programming package for the purpose of deriving an explicit formula for the optimal solution furthermore we consider its dual problem that leads to an equivalent optimal solution finally the proposed method is extended to the owa optimization problem with multiple constraints including the attitudinal character as well as a range of incomplete arguments

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

the quantum isl 2 c group the classical r matrix implied by the quantum kappa poincare algebra of lukierski nowicki and ruegg is used to generate a poisson structure on the isl 2 c group a quantum deformation of the isl 2 c group on the hopf algebra level is obtained by a trivial quantization

inequality measures and equitable approaches to location problems abstract location problems can be considered as multiple criteria models where for each client spatial unit there is defined an individual objective function which measures the effect of a location pattern with respect to the client satisfaction e g it expresses the distance or travel time between the client and the assigned facility this results in a multiple criteria model taking into account the entire distribution of individual effects distances moreover the model enables us to introduce the concept of equitable efficiency which links location problems with theories of inequality measurement in this paper special attention is paid to solution concepts based on the bicriteria optimization of the mean distance and the absolute inequality measures the restrictions for the trade offs are identified which guarantee that the bicriteria approaches comply with the concept of equitable efficiency these results are further generalized to bicriteria approaches not using directly the trade off technique

continuity properties of the data to solution map for the generalized camassa holm equation abstract this work studies a generalized camassa holm equation with higher order nonlinearities g kbch the camassa holm the degasperis procesi and the novikov equations are integrable members of this family of equations g kbch is well posed in sobolev spaces h s s 3 2 on both the line and the circle and its solution map is continuous but not uniformly continuous in this work it is shown that the solution map is holder continuous in h s equipped with the h r topology for 0 r s and the holder exponent is expressed in terms of s and r

on the analytic representation of the leximin ordering and its application to flexible constraint propagation we discuss the basic formulation of constraint propagation problems and extend it to the flexible constraint propagation environment where constraints are represented as fuzzy subsets some methods for ordering alternative solutions with respect to a collection of flexible constraints are discussed along with their drawbacks among the methods introduced is the leximin method where we note its lack of an analytic formulation with the aid of the ordered weighted averaging owa operator we suggest an analytic formulation for the leximin method some properties of this formulation are provided we then describe the application of this new formulation for the leximin method to situations in which the constraints are describable in a linear fashion we show how we can use mixed integer programming techniques to find an optimal solution

distribution systems design with role dependent objectives in this paper we introduce flexible models for capacitated discrete location problems we describe three different points of view of a location problem in a logistics system different mathematical programming formulations are presented illustrated by examples and compared using a battery of test problems extensive computational tests are done showing the potentials and limits of this kind of resolution approach

generalized ordered weighted utility proportional averaging hyperbolic absolute risk aversion operators and their applications to group decision making under the general utility we provide a new operator called gowupa operator under hara utility we present a new operator called the gowupa hara operator we put forward an orness measure of the gowupa hara operator we construct a new model for determining the weight of the gowupa hara operator we develop a new approach for multiple attributes group decision making this paper develops a new class of aggregation operator based on utility function which introduces the risk attitude of decision makers dms in the aggregation process first under the general framework of utility function we provide a new operator called the generalized ordered weighted utility proportional averaging gowupa operator and study its properties which are suitable for any utility function then under the hyperbolic absolute risk aversion hara utility function we propose another new operator named as the generalized ordered weighted utility proportional averaging hyperbolic absolute risk aversion gowupa hara operator and further investigate its families including a wide range of aggregation operators to determine the gowupa hara operator weights we put forward an orness measure of the gowupa hara operator and analyze its properties considering that different dms may have different opinions towards decision making and their opinions can be characterized by different orness measures we construct a new nonlinear optimization model to determine the optimal weights which can aggregate all the individual sets of weights into an overall set of weights furthermore based on the gowupa hara operator a method for multiple attribute group decision making magdm is developed finally an example is given to illustrate the application of the gowupa hara operator to the magdm

multiobjective linguistic optimization generalizing our earlier results on optimization with linguistic variables we introduce a novel statement of fuzzy multiobjective mathematical programming problems and provide a method for finding a fair solution to these problems suppose we are given a multiobjective mathematical programming problem in which the functional relationship between the decision variables and the objective functions is not completely known our knowledge base consists of a block of fuzzy if then rules where the antecedent part of the rules contains some linguistic values of the decision variables and the consequence part consists of a linguistic value of the objective functions we suggest the use of tsukamoto s fuzzy reasoning method to determine the crisp functional relationship between the decision variables and objective functions we model the anding of the objective functions by a t norm and solve the resulting usually nonlinear programming problem to find a fair optimal solution to the original fuzzy multiobjective problem

programming based owa operator weights with quadratic objective function yager s ordered weighted averaging owa operators are extensively employed to perform mean type aggregations their success heavily depends on proper determination of the associated weights that characterize the operators several methods have been established to determine the weights and thereby to support successful owa aggregation in this study the least square method which is one of the nonlinear programs with a quadratic objective function is reformulated by using the extreme points that correspond to its constraints and then solved by a few steps of matrix operations finally we present a new weighting method called the minimizing distances from the extreme points mdp wherein the owa operator weights that minimize the expected quadratic distance with respect to the set of extreme points are chosen a different attitudinal character leads to different extreme points and thus the mdp seeks to find the owa operator weights that are dynamically adjusted to be at the center of attitude dependent polytope

generalizations of the camassa holm equation we classify generalized camassa holm type equations which possess infinite hierarchies of higher symmetries we show that the obtained equations can be treated as negative flows of integrable quasi linear scalar evolution equations of orders 2 3 and 5 we present the corresponding lax representations or linearization transformations for these equations some of the obtained equations seem to be new

symplectic structures their backlund transformations and hereditary symmetries abstract it is shown that compatible symplectic structures lead in a natural way to hereditary symmetries we recall that a hereditary symmetry is an operator valued function which immediately yields a hierarchy of evolution equations each having infinitely many commuting symmetries all generated by this hereditary symmetry furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations this result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations in addition we show how symplectic structures transform under backlund transformations this leads to a method for generating a whole class of symplectic structures from a given one several examples and applications are given illustrating the above results also the connection of our results with those of gelfand and dikii and of magri is briefly pointed out

heisenberg xxz model and quantum galilei group the 1d heisenberg spin model with an anisotropy of the xxz type is analysed in terms of the symmetry given by the quantum galilei group gamma q 1 for a chain with an infinite number of sites the authors show that the magnon excitations and the s 1 2 n magnon bound states are determined by the algebra in this case the gamma q 1 symmetry provides a description naturally compatible with the bethe ansatz the recurrence relations determined by gamma q 1 permit one to express the energy of the n magnon bound states in a closed form in terms of tchebischeff polynomials

leximin optimality and fuzzy set theoretic operations abstract the leximin ranking of vectors of values taken from a totally ordered set is sometimes encountered in fields like operational research social choice or numerical analysis but has seldom been studied in connexion with fuzzy optimization in this paper we prove that a leximin optimal solution to a vector ranking problem on the unit hypercube can be obtained as the limit of optimal solutions to a problem of fuzzy multiple criteria optimization where fuzzy sets are aggregated either using a triangular norm or a generalized mean or an ordered weighted average owa operation

on the equivalence of some approaches to the owa operator and rim quantifier determination the ordered weighted averaging owa operator is a widely used aggregation method and its determination is usually a prerequisite step in many related applications the regular increasing monotone rim quantifier can be seen as the continuous case of the owa operator with the quantifier aggregation method some approaches with optimization criteria for the determination of owa operator and rim quantifier were proposed although these problems look different at the first sight a deeper investigation can reveal the equivalence of solutions between them inspired by the solution equivalence of minimum variance problems and minimax disparity problem for owa operator we propose the minimax disparity rim quantifier problem and two minimax ratio problems for owa operator and rim quantifier respectively we investigate the equivalence of solutions for the maximum entropy and minimax ratio problems and solutions for the minimum variance and minimax disparity problems of owa operator and rim quantifier respectively by a theoretical point of view

induced representations of quantum 1 1 galilei algebras we develop a systematic method to construct induced representations of quantum algebras the procedure makes use of two hopf algebras with a nondegenerate pairing and a pair of dual bases for them we apply the method on three different quantum deformations of the galilei algebra in 1 1 dimensions we obtain several families of induced representations including some results already known

the relationship between the maximum entropy and minimax ratio rim quantifier problems liu and lou fuzzy sets and systems 159 2007 1673 1688 investigated the equivalence of solutions to the maximum entropy and minimax ratio rim quantifier problems the paper improves liu and lou s theorems from a mathematical perspective because their theorems are not suitable for absolutely continuous generating functions the paper provides a correct proof of the minimax ratio rim quantifier problem for the case in which generating functions are absolutely continuous and a generalized solution to the maximum entropy rim quantifier problem for the case in which generating functions are lebesgue integrable based on the results the paper provides a correct relationship between the maximum entropy and minimax ratio rim quantifier problems

generalized ordered weighted utility averaging hyperbolic absolute risk aversion operators and their applications to group decision making abstract this paper develops a new class of aggregation operator based on utility function which introduces the risk attitude of decision makers dms in the aggregation process first under the general framework of utility function we provide a new operator called the generalized ordered weighted utility averaging gowua operator and study its properties which are suitable for any utility function then under the hyperbolic absolute risk aversion hara utility function we propose another new operator named as the generalized ordered weighted utility averaging hyperbolic absolute risk aversion gowua hara operator and further investigate its families including a wide range of aggregation operators to determine the gowua hara operator weights we put forward an orness measure of the gowua hara operator and analyze its properties considering that different dms may have different opinions toward decision making and their opinions can be characterized by different orness measures we construct a new optimization model to determine the optimal weights which can aggregate all the individual sets of weights into an overall set of weights furthermore based on the gowua hara operator a method for the multiple attribute group decision making magdm is developed finally an example is given to illustrate the application of the gowua hara operator to the magdm