particle lattices and fuzzy particle lattices abstract this paper introduces several new concepts a particle in a lattice which is a generalization of an atom in a distributive lattice by weakening the minimality property of atom a particle lattice which is a generalization of distributive complete atomic lattices by replacing atoms by particles a fuzzy particle lattice a particle lattice with an order reversing involution a particulate boolean algebra a fuzzy particle lattice whose involution is a complementation operator and other related concepts points fuzzy points boundary points and boundary quasi points the paper establishes representation theorems for fomse of these concepts establishes connections between others and some well established lattice theoretic concepts and provides some elementary properties for some of the new concepts

distributionally robust optimization and its tractable approximations in this paper we focus on a linear optimization problem with uncertainties having expectations in the objective and in the set of constraints we present a modular framework to obtain an approximate solution to the problem that is distributionally robust and more flexible than the standard technique of using linear rules our framework begins by first affinely extending the set of primitive uncertainties to generate new linear decision rules of larger dimensions and is therefore more flexible next we develop new piecewise linear decision rules that allow a more flexible reformulation of the original problem the reformulated problem will generally contain terms with expectations on the positive parts of the recourse variables finally we convert the uncertain linear program into a deterministic convex program by constructing distributionally robust bounds on these expectations these bounds are constructed by first using different pieces of information on the distribution of the underlying uncertainties to develop separate bounds and next integrating them into a combined bound that is better than each of the individual bounds

t prefilter theory abstract in the first part of this paper the notion of t prefilter is introduced and studied as are the applications t and t their properties and relations between them we characterize the minimal prime t prefilters finer than a given t prefilter by using ultrafilters on x and we give equivalents conditions of the t maximality in the second part we define t convergence and we obtain a characterization of t compactness gantner steinlage by means of the maximal t prefilters finally some applications of these concepts related to the continuity separation axioms and fuzzy compactness are studied

operations on l fuzzy topological spaces abstract the aim of the paper is mainly to introduce and study operations on l fuzzy topological spaces the algebraic properties of some of these operations are discussed most of the concepts of compactness continuity lindelof spaces and separation axioms are considered

distributionally robust stochastic knapsack problem this paper considers a distributionally robust version of a quadratic knapsack problem in this model a subsets of items is selected to maximizes the total profit while requiring that a set of knapsack constraints be satisfied with high probability in contrast to the stochastic programming version of this problem we assume that only part of the information on random data is known i e the first and second moment of the random variables their joint support and possibly an independence assumption as for the binary constraints special interest is given to the corresponding semidefinite programming sdp relaxation while in the case that the model only has a single knapsack constraint we present an sdp reformulation for this relaxation the case of multiple knapsack constraints is more challenging instead two tractable methods are presented for providing upper and lower bounds with its associated conservative solution on the sdp relaxation an extensive computational study is given to illustrate

distributionally robust convex optimization distributionally robust optimization is a paradigm for decision making under uncertainty where the uncertain problem data are governed by a probability distribution that is itself subject to uncertainty the distribution is then assumed to belong to an ambiguity set comprising all distributions that are compatible with the decision maker s prior information in this paper we propose a unifying framework for modeling and solving distributionally robust optimization problems we introduce standardized ambiguity sets that contain all distributions with prescribed conic representable confidence sets and with mean values residing on an affine manifold these ambiguity sets are highly expressive and encompass many ambiguity sets from the recent literature as special cases they also allow us to characterize distributional families in terms of several classical and or robust statistical indicators that have not yet been studied in the context of robust optimization we determine conditions under which distributionally robust optimization problems based on our standardized ambiguity sets are computationally tractable we also provide tractable conservative approximations for problems that violate these conditions

fuzzy nets and their application fuzzy net theory is enriched by the introduction of the fuzzy net of fuzzy sets the limsup liminf and limit of a fuzzy net of fuzzy sets are defined and their various properties are discussed alternative characterizations based on the notion of a fuzzy net are provided for several fuzzy topological concepts including open and closed fuzzy sets fuzzy continuity maps with closed fuzzy graph open fuzzy mapping etc thus the net theoretic approach is shown to be a promising tool in fuzzy topology

distributionally robust optimization under moment uncertainty with application to data driven problems stochastic programming can effectively describe many decision making problems in uncertain environments unfortunately such programs are often computationally demanding to solve in addition their solution can be misleading when there is ambiguity in the choice of a distribution for the random parameters in this paper we propose a model that describes uncertainty in both the distribution form discrete gaussian exponential etc and moments mean and covariance matrix we demonstrate that for a wide range of cost functions the associated distributionally robust or min max stochastic program can be solved efficiently furthermore by deriving a new confidence region for the mean and the covariance matrix of a random vector we provide probabilistic arguments for using our model in problems that rely heavily on historical data these arguments are confirmed in a practical example of portfolio selection where our framework leads to better performing policies on the true distribution underlying the daily returns of financial assets

fµ strongly semiopen sets fµ strong semicontinuity and fµ strongly semiretracts throughout the literature if x d is an f ts and y x the induced f topological subspace y d y is defined so that d y n g y n d macho stadler and de prada vicente fuzzy sets and systems 58 1993 365 introduced a new concept of f topological subspaces which coincides with the usual definition in the case that m g y also they introduced the concepts of f m open sets and f m continuity in this paper using the previous concepts we introduce weaker forms of f m open sets and f m continuity the notion of an f retract was introduced by rodabough j math anal appl 79 1981 273 here we introduce the notion of a f m retract and weaker forms of it the basic properties of these notions are given many results are obtained

some results on fuzzy supratopological spaces abstract in this note we study some results on the concepts of supracompactness and supracompactness in a fuzzy supratopological space we introduce the notions of hausdorffnessand lindelofness in a fuzzy supratopological space and characterize their properties interms of supracompactness we also introduce and study the concept of fuzzy supra regular space

a distributionally robust perspective on uncertainty quantification and chance constrained programming the objective of uncertainty quantification is to certify that a given physical engineering or economic system satisfies multiple safety conditions with high probability a more ambitious goal is to actively influence the system so as to guarantee and maintain its safety a scenario which can be modeled through a chance constrained program in this paper we assume that the parameters of the system are governed by an ambiguous distribution that is only known to belong to an ambiguity set characterized through generalized moment bounds and structural properties such as symmetry unimodality or independence patterns we delineate the watershed between tractability and intractability in ambiguity averse uncertainty quantification and chance constrained programming using tools from distributionally robust optimization we derive explicit conic reformulations for tractable problem classes and suggest efficiently computable conservative approximations for intractable ones

some strong separation in fuzzy topological spaces abstract recently macho stadler et al fuzzy sets and systems 43 1991 95 116 introduced the notion of fuzzy separation using the family of its level topologies lt t t i1 the present work deals with introducing and studying the operations on ri fuzzy topological spaces i 0 1 moreover the notion of fuzzy separation which is well defined as a fuzzy topological concept is described a comparison between the above notions with the analogous fuzzy ones are discussed an acceptable clue which indicates that these notions are equivalent is offered

multistage distributionally robust mixed integer programming with decision dependent moment based ambiguity sets we study multistage distributionally robust mixed integer programs under endogenous uncertainty where the probability distribution of stage wise uncertainty depends on the decisions made in previous stages we first consider two ambiguity sets defined by decision dependent bounds on the first and second moments of uncertain parameters and by mean and covariance matrix that exactly match decision dependent empirical ones respectively for both sets we show that the subproblem in each stage can be recast as a mixed integer linear program milp moreover we extend the general moment based ambiguity set in delage and ye oper res 58 3 595 612 2010 to the multistage decision dependent setting and derive mixed integer semidefinite programming misdp reformulations of stage wise subproblems we develop methods for attaining lower and upper bounds of the optimal objective value of the multistage misdps and approximate them using a series of milps we deploy the stochastic dual dynamic integer programming sddip method for solving the problem under the three ambiguity sets with risk neutral or risk averse objective functions and conduct numerical studies on multistage facility location instances having diverse sizes under different parameter and uncertainty settings our results show that the sddip quickly finds optimal solutions for moderate sized instances under the first two ambiguity sets and also finds good approximate bounds for the multistage misdps derived under the third ambiguity set we also demonstrate the efficacy of incorporating decision dependent distributional ambiguity in multistage decision making processes

the scenario approach to robust control design this paper proposes a new probabilistic solution framework for robust control analysis and synthesis problems that can be expressed in the form of minimization of a linear objective subject to convex constraints parameterized by uncertainty terms this includes the wide class of np hard control problems representable by means of parameter dependent linear matrix inequalities lmis it is shown in this paper that by appropriate sampling of the constraints one obtains a standard convex optimization problem the scenario problem whose solution is approximately feasible for the original usually infinite set of constraints i e the measure of the set of original constraints that are violated by the scenario solution rapidly decreases to zero as the number of samples is increased we provide an explicit and efficient bound on the number of samples required to attain a priori specified levels of probabilistic guarantee of robustness a rich family of control problems which are in general hard to solve in a deterministically robust sense is therefore amenable to polynomial time solution if robustness is intended in the proposed risk adjusted sense

ambiguous joint chance constraints under mean and dispersion information we study joint chance constraints where the distribution of the uncertain parameters is only known to belong to an ambiguity set characterized by the mean and support of the uncertainties and by an upper bound on their dispersion this setting gives rise to pessimistic optimistic ambiguous chance constraints which require the corresponding classical chance constraints to be satisfied for every for at least one distribution in the ambiguity set we demonstrate that the pessimistic joint chance constraints are conic representable if i the constraint coefficients of the decisions are deterministic ii the support set of the uncertain parameters is a cone and iii the dispersion function is of first order that is it is positively homogeneous we also show that pessimistic joint chance constrained programs become intractable as soon as any of the conditions i ii or iii is relaxed in the mildest possible way we further prove that the optimistic joint chance constraints are conic representab

on fuzzy t1 topological spaces on etudie diverses relations entre les differentes definitions des espaces topologiques t 1 flous

the information divergence hypothesis of informational masking in recent years there has been growing interest in masking that cannot be attributed to interactions in the cochlea so called informational masking im similarity in the acoustic properties of target and masker and uncertainty regarding the masker are the two major factors identified with im these factors involve quite different manipulations of signals and are believed to entail fundamentally different processes resulting in im here however evidence is presented that these factors affect im through their mutual influence on a single factor the information divergence of target and masker given by simpson fitter s da lutfi et al 2012 j acoust soc am 132 el109 113 four experiments are described involving multitone pattern discrimination multi talker word recognition sound source identification and sound localization in each case standard manipulations of masker uncertainty and target masker similarity including the covariation of target masker frequencies are found to have the same effect on performance provided they produce the same change in da the function relating d performance to da moreover appears to be linear with constant slope across listeners the overriding dependence of im on da is taken to reflect a general principle of perception that exploits differences in the statistical structure of signals to separate figure from ground

data driven chance constrained stochastic program in this paper we study data driven chance constrained stochastic programs or more specifically stochastic programs with distributionally robust chance constraints dccs in a data driven setting to provide robust solutions for the classical chance constrained stochastic program facing ambiguous probability distributions of random parameters we consider a family of density based confidence sets based on a general phi divergence measure and formulate dcc from the perspective of robust feasibility by allowing the ambiguous distribution to run adversely within its confidence set we derive an equivalent reformulation for dcc and show that it is equivalent to a classical chance constraint with a perturbed risk level we also show how to evaluate the perturbed risk level by using a bisection line search algorithm for general phi divergence measures in several special cases our results can be strengthened such that we can derive closed form expressions for the perturbed risk levels in addition we show that the conservatism of dcc vanishes as the size of historical data goes to infinity furthermore we analyze the relationship between the conservatism of dcc and the size of historical data which can help indicate the value of data finally we conduct extensive computational experiments to test the performance of the proposed dcc model and compare various phi divergence measures based on a capacitated lot sizing problem with a quality of service requirement

strong and ultra separation axioms of fuzzy bitopological spaces given a fuzzy bitopological space x 1 2 we introduce a new notion of fuzzy pairwise separation axioms by using the family of its level bitopologies 1 2 0 1 we prove that these concepts are good extension and we compare them with its corresponding fpt kandil and ei shafee 1991 and fpt1 abu safiya et al 1994 i 0 1 2 3 4 respectively we show that these notions are not equivalent and we give a number of examples which illustrate this fact

on deterministic reformulations of distributionally robust joint chance constrained optimization problems a joint chance constrained optimization problem involves multiple uncertain constraints i e constraints with stochastic parameters that are jointly required to be satisfied with probability exc

multi stage stochastic optimization applied to energy planning this paper presents a methodology for the solution of multistage stochastic optimization problems based on the approximation of the expected cost to go functions of stochastic dynamic programming by piecewise linear functions no state discretization is necessary and the combinatorial explosion with the number of states the well known curse of dimensionality of dynamic programming is avoided the piecewise functions are obtained from the dual solutions of the optimization problem at each stage and correspond to benders cuts in a stochastic multistage decomposition framework a case study of optimal stochastic scheduling for a 39 reservoir system is presented and discussed

optimized bonferroni approximations of distributionally robust joint chance constraints a distributionally robust joint chance constraint involves a set of uncertain linear inequalities which can be violated up to a given probability threshold epsilon over a given family of probability distributions of the uncertain parameters a conservative approximation of a joint chance constraint often referred to as a bonferroni approximation uses the union bound to approximate the joint chance constraint by a system of single chance constraints one for each original uncertain constraint for a fixed choice of violation probabilities of the single chance constraints such that their sum does not exceed epsilon it has been shown that under various settings a distributionally robust single chance constraint admits a deterministic convex reformulation thus the bonferroni approximation approach can be used to build convex approximations of distributionally robust joint chance constraints in this paper we consider an optimized version of bonferroni approximation where the violation probabilities of the individual single chance constraints are design variables rather than fixed a priori we show that such an optimized bonferroni approximation of a distributionally robust joint chance constraint is exact when the uncertainties are separable across the individual inequalities i e each uncertain constraint involves a different set of uncertain parameters and corresponding distribution families unfortunately the optimized bonferroni approximation leads to np hard optimization problems even in settings where the usual bonferroni approximation is tractable when the distribution family is specified by moments or by marginal distributions we derive various sufficient conditions under which the optimized bonferroni approximation is convex and tractable we also show that for moment based distribution families and binary decision variables the optimized bonferroni approximation can be reformulated as a mixed integer second order conic set finally we demonstrate how our results can be used to derive a convex reformulation of a distributionally robust joint chance constraint with a specific non separable distribution family

a class of stochastic programs with decision dependent uncertainty we address a class of problems where decisions have to be optimized over a time horizon given that the future is uncertain and that the optimization decisions influence the time of information discovery for a subset of the uncertain parameters the standard approach to formulate stochastic programs is based on the assumption that the stochastic process is independent of the optimization decisions which is not true for the class of problems under consideration we present a hybrid mixed integer disjunctive programming formulation for the stochastic program corresponding to this class of problems and hence extend the stochastic programming framework a set of theoretical properties that lead to reduction in the size of the model is identified a lagrangean duality based branch and bound algorithm is also presented

ambiguous risk constraints with moment and unimodality information optimization problems face random constraint violations when uncertainty arises in constraint parameters effective ways of controlling such violations include risk constraints e g chance constraints and conditional value at risk constraints this paper studies these two types of risk constraints when the probability distribution of the uncertain parameters is ambiguous in particular we assume that the distributional information consists of the first two moments of the uncertainty and a generalized notion of unimodality we find that the ambiguous risk constraints in this setting can be recast as a set of second order cone soc constraints in order to facilitate the algorithmic implementation we also derive efficient ways of finding violated soc constraints finally we demonstrate the theoretical results via computational case studies on power system operations

on inductive dimensions for fuzzy topological spaces an approach to the dimension theory for fuzzy topological spaces is being developed the appropriate context for this theory is not the category cft of chang fuzzy topological spaces or some of its modifications but the category hut introduced in the paper this category is a slight extension of the category h of hutton fuzzy topological spaces hutton 1980 the frames of this category allow us to make exposition simple and uniform and on the other hand to make it applicable in quite a general setting

discrimination of stimulus variance in real world settings auditory signals such as speech are highly variable and differ across occurrences and sources the question addressed is our sensitivity to such differences in global stimulus variability in a variance discrimination task the stimuli were sequences of five 100 ms tone pulses separated by 30 ms the frequency of each tone was sampled independently from a probability distribution that was gaussian on logarithmic frequency in the non signal interval of the 2ifc task the sampled distribution had a mean frequency mf and variance vf in the signal interval the variance of the sequence was vf vf the task was to choose the interval with the larger variance feedback was provided to restrict the use of decision strategies mf was randomly chosen for each presentation m f 2 khz psychometric functions p c vs vf were obtained for various values of vf and overall performance was poorer than that of an ideal observer however like the ideal weber s law behavior was observed

ambiguous chance constrained binary programs under mean covariance information we consider chance constrained binary programs where each row of the inequalities that involve uncertainty needs to be satisfied probabilistically only the information of the mean and covariance

fuzzy preopen sets and fuzzy preseparation axioms abstract in this paper the concept of preopen sets due to a s mashhour m e abd el monsef and s n el debb 7 has been generalised to the fuzzy setting further fuzzy separation axioms have been introduced and investigated with the help of fuzzy preopen sets

from cvar to uncertainty set implications in joint chance constrained optimization we review and develop different tractable approximations to individual chance constrained problems in robust optimization on a variety of uncertainty sets and show their interesting connections with bounds on the conditional value at risk cvar measure we extend the idea to joint chance constrained problems and provide a new formulation that improves upon the standard approach our approach builds on a classical worst case bound for order statistics problems and is applicable even if the constraints are correlated we provide an application of the model on a network resource allocation problem with uncertain demand

on the convergence of decomposition methods for multistage stochastic convex programs we prove the almost sure convergence of a class of sampling based nested decomposition algorithms for multistage stochastic convex programs in which the stage costs are general convex functions of the decisions and uncertainty is modelled by a scenario tree as special cases our results imply the almost sure convergence of stochastic dual dynamic programming cutting plane and partial sampling cupps algorithm and dynamic outer approximation sampling algorithms when applied to problems with general convex cost functions

distributionally robust joint chance constraints with second order moment information we develop tractable semidefinite programming based approximations for distributionally robust individual and joint chance constraints assuming that only the first and second order moments as well as the support of the uncertain parameters are given it is known that robust chance constraints can be conservatively approximated by worst case conditional value at risk cvar constraints we first prove that this approximation is exact for robust individual chance constraints with concave or not necessarily concave quadratic constraint functions and we demonstrate that the worst case cvar can be computed efficiently for these classes of constraint functions next we study the worst case cvar approximation for joint chance constraints this approximation affords intuitive dual interpretations and is provably tighter than two popular benchmark approximations the tightness depends on a set of scaling parameters which can be tuned via a sequential convex optimization algorithm we show that the approximation becomes essentially exact when the scaling parameters are chosen optimally and that the worst case cvar can be evaluated efficiently if the scaling parameters are kept constant we evaluate our joint chance constraint approximation in the context of a dynamic water reservoir control problem and numerically demonstrate its superiority over the two benchmark approximations

probabilistically constrained linear programs and risk adjusted controller design the focal point of this paper is the probabilistically constrained linear program pclp and how it can be applied to control system design under risk constraints the pclp is the counterpart of the classical linear program where it is assumed that there is random uncertainty in the constraints and therefore the deterministic constraints are replaced by probabilistic ones it is shown that for a wide class of probability density functions called log concave symmetric densities the pclp is a convex program an equivalent formulation of the pclp is also presented which provides insight into numerical implementation this concept is applied to control system design it is shown how the results in this paper can be applied to the design of controllers for discrete time systems to obtain a closed loop system with a well defined risk of violating the so called property of superstability furthermore we address the problem of risk adjusted pole placement

convergence analysis of sampling based decomposition methods for risk averse multistage stochastic convex programs we consider a class of sampling based decomposition methods to solve risk averse multistage stochastic convex programs we prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions this formula can be used to obtain an efficient implementation of stochastic dual dynamic programming applied to convex nonlinear problems we prove the almost sure convergence of these decomposition methods when the relatively complete recourse assumption holds we also prove the almost sure convergence of these algorithms when applied to risk averse multistage stochastic linear programs that do not satisfy the relatively complete recourse assumption the analysis is first done assuming the underlying stochastic process is interstage independent and discrete with a finite set of possible realizations at each stage we then indicate two ways of extending the methods and convergence analysis to the case when the process is interstage dependent

strong separation and strong countability in fuzzy topological spaces given a fuzzy topological space x we introduce new notions of fuzzy separation and fuzzy countability using the family of its level topologies t t 0 1 we check that these are well defined fuzzy topological concepts and we compare them with the analogous fuzzy ones introduced in the literature we verify that these notions are not equivalent and we give a large number of examples which illustrate this fact

an integer programming approach for linear programs with probabilistic constraints linear programs with joint probabilistic constraints pclp are difficult to solve because the feasible region is not convex we consider a special case of pclp in which only the right hand side is random and this random vector has a finite distribution we give a mixed integer programming formulation for this special case and study the relaxation corresponding to a single row of the probabilistic constraint we obtain two strengthened formulations as a byproduct of this analysis we obtain new results for the previously studied mixing set subject to an additional knapsack inequality we present computational results which indicate that by using our strengthened formulations instances that are considerably larger than have been considered before can be solved to optimality

on fuzzy topological spaces abstract in this paper a few separation properties and some aspects of subspace fuzzy topology have been studied where both the crisp and the fuzzy elements have been taken into consideration since the conventional definition of compactness is not quite meaningful in hausdorff fuzzy spaces as introduced by us a new more natural definition of proper compactness is given and a few properties resulting from this are established

a comparison of some hausdorff notions in fuzzy topological spaces abstract several different notions of the hausdorff separation property for fuzzy topological spaces have appeared in the literature this paper is a study of the relationships between 12 of these concepts

convex approximations of chance constrained programs we consider a chance constrained problem where one seeks to minimize a convex objective over solutions satisfying with a given close to one probability a system of randomly perturbed convex constraints this problem may happen to be computationally intractable our goal is to build its computationally tractable approximation i e an efficiently solvable deterministic optimization program with the feasible set contained in the chance constrained problem we construct a general class of such convex conservative approximations of the corresponding chance constrained problem moreover under the assumptions that the constraints are affine in the perturbations and the entries in the perturbation vector are independent of each other random variables we build a large deviation type approximation referred to as bernstein approximation of the chance constrained problem this approximation is convex and efficiently solvable we propose a simulation based scheme for bounding the optimal value in the chance constrained problem and report numerical experiments aimed at comparing the bernstein and well known scenario approximation approaches finally we extend our construction to the case of ambiguous chance constrained problems where the random perturbations are independent with the collection of distributions known to belong to a given convex compact set rather than to be known exactly while the chance constraint should be satisfied for every distribution given by this set

a sample approximation approach for optimization with probabilistic constraints we study approximations of optimization problems with probabilistic constraints in which the original distribution of the underlying random vector is replaced with an empirical distribution obtained from a random sample we show that such a sample approximation problem with a risk level larger than the required risk level will yield a lower bound to the true optimal value with probability approaching one exponentially fast this leads to an a priori estimate of the sample size required to have high confidence that the sample approximation will yield a lower bound we then provide conditions under which solving a sample approximation problem with a risk level smaller than the required risk level will yield feasible solutions to the original problem with high probability once again we obtain a priori estimates on the sample size required to obtain high confidence that the sample approximation problem will yield a feasible solution to the original problem finally we present numerical illustrations of how these results can be used to obtain feasible solutions and optimality bounds for optimization problems with probabilistic constraints

nonanticipative duality relaxations and formulations for chance constrained stochastic programs we propose two new lagrangian dual problems for chance constrained stochastic programs based on relaxing nonanticipativity constraints we compare the strength of the proposed dual bounds and demonstrate that they are superior to the bound obtained from the continuous relaxation of a standard mixed integer programming mip formulation for a given dual solution the associated lagrangian relaxation bounds can be calculated by solving a set of single scenario subproblems and then solving a single knapsack problem we also derive two new primal mip formulations and demonstrate that for chance constrained linear programs the continuous relaxations of these formulations yield bounds equal to the proposed dual bounds we propose a new heuristic method and two new exact algorithms based on these duals and formulations the first exact algorithm applies to chance constrained binary programs and uses either of the proposed dual bounds in concert with cuts that eliminate solutions found by the subproblems the second exact method is a branch and cut algorithm for solving either of the primal formulations our computational results indicate that the proposed dual bounds and heuristic solutions can be obtained efficiently and the gaps between the best dual bounds and the heuristic solutions are small

discrimination of frequency variance for tonal sequences real world auditory stimuli are highly variable across occurrences and sources the present study examined the sensitivity of human listeners to differences in global stimulus variability in a two interval forced choice task variance discrimination was measured using sequences of five 100 ms tone pulses the frequency of each pulse was sampled randomly from a distribution that was gaussian in logarithmic frequency in the non signal interval the sampled distribution had a variance of stan2 while in the signal interval the variance of the sequence was sig2 with sig2 stan2 the listener s task was to choose the interval with the larger variance to constrain possible decision strategies the mean frequency of the sampling distribution of each interval was randomly chosen for each presentation psychometric functions were measured for various values of stan2 although the performance was remarkably similar across listeners overall performance was poorer than that of an ideal observer io which perfectly compares interval variances however like the io weber s law behavior was observed with a constant ratio of sig2 stan2 to stan2 yielding similar performance a model which degraded the io with a frequency resolution noise and a computational noise provided a reasonable fit to the real data

quantifying distributional model risk via optimal transport this paper deals with the problem of quantifying the impact of model misspecification when computing general expected values of interest the methodology that we propose is applicable in great gene

functions and as closedness in fuzzy topological spaces abstract in this paper we discuss s closedness in fuzzy topological spaces and we give some characterizations of s closedness also we investigate the image and the inverse image of s closed spaces under some types of functions and we improve and generalize some results on s closed spaces in fuzzy setting

on the goodness of some types of fuzzy paracompactness abstract we introduce in fuzzy topological spaces definitions of paracompactness almost paracompactness and nearly paracompactness all of which turn out to be good extensions of their classical topological counterparts fuzzy semi paracompact para s closed weakly compact and rs paracompact spaces are treated to a similar approach

on decomposition of proper compactness in fuzzy topological spaces on introduit les notions de 2 compacite et de metacompacite floue pour des espaces topologiques flous et on demontre le theoreme suivant un espace topologique flou x est proprement compact si et seulement si il est 2 compact et metacompact flou

a short note on fuzzy neighbourhood spaces abstract lowen introduced the concept of fuzzy neighbourhood spaces fns s and proved that the family of level topologies of a fns is an antichain wuyts characterized fns s as being those fully stratified fuzzy topological spaces fts s whose level topologies form antichains and whose fuzzy topologies are the finest possible for thier level topologies mashhour et al introduced the axiom of structure a on fts s and derived for it several characterizations and fuzzy topological consequences we use those characterizations of structure a and wuyts characterization of fns s to prove that a fts is a fns iff it is of structure a and fully stratified

a cutting surface algorithm for semi infinite convex programming with an application to moment robust optimization we present and analyze a central cutting surface algorithm for general semi infinite convex optimization problems and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments moments of arbitrary order as well as nonpolynomial moments can be included in the formulation we show that this gives rise to a hierarchy of optimization problems with decreasing levels of risk aversion with classic robust optimization at one end of the spectrum and stochastic programming at the other although our primary motivation is to solve distributionally robust optimization problems with moment uncertainty the cutting surface method for general semi infinite convex programs is also of independent interest the proposed method is applicable to problems with nondifferentiable semi infinite constraints indexed by an infinite dimensional index set examples comparing the cutting surface algorit

stochastic dual dynamic integer programming multistage stochastic integer programming msip combines the difficulty of uncertainty dynamics and non convexity and constitutes a class of extremely challenging problems a common formulation for these problems is a dynamic programming formulation involving nested cost to go functions in the linear setting the cost to go functions are convex polyhedral and decomposition algorithms such as nested benders decomposition and its stochastic variant stochastic dual dynamic programming sddp which proceed by iteratively approximating these functions by cuts or linear inequalities have been established as effective approaches however it is difficult to directly adapt these algorithms to msip due to the nonconvexity of integer programming value functions in this paper we propose an extension to sddp called stochastic dual dynamic integer programming sddip for solving msip problems with binary state variables the crucial component of the algorithm is a new reformulation of the subproblems in each stage and a new class of cuts termed lagrangian cuts derived from a lagrangian relaxation of a specific reformulation of the subproblems in each stage where local copies of state variables are introduced we show that the lagrangian cuts satisfy a tightness condition and provide a rigorous proof of the finite convergence of sddip with probability one we show that under fairly reasonable assumptions an msip problem with general state variables can be approximated by one with binary state variables to desired precision with only a modest increase in problem size thus our proposed sddip approach is applicable to very general classes of msip problems extensive computational experiments on three classes of real world problems namely electric generation expansion financial portfolio management and network revenue management show that the proposed methodology is very effective in solving large scale multistage stochastic integer optimization problems

on a topological model for the category of fuzzy topological spaces i we study global properties of fuzzy topological spaces which depend only on open sets fuzzy continuous functions and the relations we obtain many known theorems as purely topological theorems

data driven distributionally robust optimization using the wasserstein metric performance guarantees and tractable reformulations we consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset using the wasserstein metric we construct a ball in the space of multivariate and non discrete probability distributions centered at the uniform distribution on the training samples and we seek decisions that perform best in view of the worst case distribution within this wasserstein ball the state of the art methods for solving the resulting distributionally robust optimization problems rely on global optimization techniques which quickly become computationally excruciating in this paper we demonstrate that under mild assumptions the distributionally robust optimization problems over wasserstein balls can in fact be reformulated as finite convex programs in many interesting cases even as tractable linear programs leveraging recent measure concentration results we also show that their solutions enjoy powerful finite sample performance guarantees our theoretical results are exemplified in mean risk portfolio optimization as well as uncertainty quantification