operational asymptotic stochastic dominance abstract levy 2016 proposes asymptotic first degree stochastic dominance as a distribution ranking criterion for all non satiable decision makers with infinite investment horizons given levy s setting this paper defines and offers the equivalent distributional conditions for asymptotic second degree stochastic dominance as well as operational asymptotic first and second degree stochastic dominance interestingly the operational asymptotic stochastic dominance provides a full rank over assets with lognormal returns and different means empirical applications show that our conditions can be readily implemented in practice

robust comparative statics of risk changes the standard method for establishing the comparative statics of risk changes in optimization problems has been confined to comparing unique interior solutions relying on strong assumptions about payoff functions and decision variables we propose a simple and intuitive approach that hinges on considerably weaker assumptions merging insights from the monotone comparative statics literature with insights from the risk apportionment literature we show that the ranking of simple lottery pairs is all that is needed for establishing the comparative statics of risk changes we use this approach to analyze the comparative statics of nth degree stochastic dominance shifts in a general setting with one and with multiple decision variables and we show how these results can be applied to generalize the classical theories of precautionary saving self protection and others this paper was accepted by james smith decision analysis

representation of uncertain multichannel digital signal spaces and study of pattern recognition based on metrics and difference values on fuzzy n cell number spaces in this paper we discuss the problem of characterization for uncertain multichannel digital signal spaces propose using fuzzy n cell number space to represent uncertain n channel digital signal space and put forward a method of constructing such fuzzy n cell numbers we introduce two new metrics and concepts of certain types of difference values on fuzzy n cell number space and study their properties further based on the metrics or difference values appropriately defined we put forward an algorithmic version of pattern recognition in an imprecise or uncertain environment and we also give practical examples to show the application and rationality of the proposed techniques

fuzzy n cell numbers and the differential of fuzzy n cell number value mappings in this paper we give the definition of a special kind of n dimension fuzzy numbers fuzzy n cell numbers discuss their operations and representation theorems define a complete metric on the fuzzy n cell number space and prove that the metric is equivalent to the supremum metric derived by the hausdorff metric between the level sets of the n dimension fuzzy numbers and obtain an embedding theorem of the fuzzy n cell number space isometrically embeds it into a concrete banach space we also consider the differential of the fuzzy mappings from an interval into the fuzzy n cell number space by using the embedding theorem

closed geodesics on a riemann surface with application to the markov spectrum this paper determines those riemann surfaces on which each nonsimple closed geodesic has a parabolic intersection that is an intersection in the form of a loop enclosing a puncture or a deleted disk an application is made characterizing the simple closed geodesic on hlr 3 in terms of the markov spectrum the thrust of the situation is this if we call loops about punctures or deleted disks boundary curves then if the surface has little topology each nonsimple closed geodesic must contain a boundary curve but if there is enough topology there are nonsimple closed geodesics not containing boundary curves 1 let r be a riemann surface of genus g with k punctures and d disks removed k d o k d o in this paper we consider the closed geodesics on r the method used is to represent r as a quotient r hlrx where h z x iy y 0 and r is a fuchsian group acting on h let 1r h h r be the projection map we assume h 1r is an unramified covering so r has no elliptic elements for most of this paper we shall assume k 0 and d 0 the remaining cases are considered in 5 each hyperbolic axis projects to a closed geodesic in r each closed geodesic a in r lifts to a conjugacy class os in r and under known conditions al is hyperbolic let ty e r be hyperbolic with axis a from now on we assume py primitive i e ty generates the stabilizer of a it is easily seen that 1r a is simple iff az n bar 0 for all e r we write a a ba to mean that a n ba z for some z in h thus 1 1 x a is nonsimple self intersecting iff a a pa for some e r since ogar a 1 conjugate elements are both simple or both nonsimple we use the phrase a hyperbolic ty is simple nonsimple to mean 1r a is simple nonsimple it is readily checked that if ty is nonsimple we can choose b in 1 1 to be hyperbolic indeed we may replace d by 13 n for large n however it is not always possible to choose 3 to be parabolic and in this connection we prove the following result received by the editors jaunary 8 1985 1980 mathematics subject caassification 1985 revision primary 30f35 secondary llj06 lthird author partially supported by nsf and psc cuny grants 1986 american mathematical society 0002 9947 86 1 00 25 per page

revisiting almost second degree stochastic dominance leshno and levy leshno m levy h 2002 preferred by all and preferred by most decision makers almost stochastic dominance management sci 48 8 1074 1085 established almost stochastic dominance to reveal preferences for most rather than all decision makers with an increasing and concave utility function in this paper we first provide a counterexample to the main theorem of leshno and levy related to almost second degree stochastic dominance we then redefine this dominance condition and show that the newly defined almost second degree stochastic dominance is the necessary and sufficient condition to rank distributions for all decision makers excluding the pathological concave preferences we further extend our results to almost higher degree stochastic dominance this paper was accepted by peter wakker decision analysis

diophantine approximation on hyperbolic riemann surfaces following the leads of h cohn and a schmidt we shall investigate geometric structures on hyperbolic riemann surfaces for which markoff like theorems hold the idea which is similar to the approach taken by d sullivan in 21 is to look at the affinity of a geodesic for the noncompact end of a surface more precisely we consider the maximal depth a geodesic travels into a noncompact end the spectrum of depths has the same structure as markoff s spectrum with the correspondence given in terms of the geodesics length and topology the upper discrete part of the spectrum is occupied by the simple closed geodesics and the lower limit value of the discrete spectrum is occupied by the geodesics that are limits of simple closed ones the reason for this interaction between the geometry and the number theory becomes apparent when we transfer our attention to a fuchsian group representing the hyperbolic surface for example consider the classical modular group m6bz the orbit of infinity under the action of m6bz is exactly the set of rational numbers it is also the set of limit points which are fixed by parabolic transformations in the group each parabolic fixed point corresponds in a sense to the noncompact end on the quotient surface as we shall see the degree to which a number x is approximated by a rational number is directly related to the depth a geodesic with the endpoint x travels

extending the fuzzy database with fuzzy numbers abstract the fuzzy relational database model originated by the authors permits fuzzy domain values from a discrete finite universe the model is extended here by demonstrating that fuzzy numbers may be employed as domain values without loss of consistency with respect to representation or the relational algebra where equivalence is required in an ordinary relational database similarity is employed in a fuzzy relational database for discrete finite universes similarity between atomic elements is described via a fuzzy similarity relation with max min transitivity two or more fuzzy numbers are defined to be similar if their union forms a continuous level set over the real line this convention effects the partitioning of fuzzy number domains that is necessary to assure the well definedness of the fuzzy relational algebra

some problems on the definition of fuzzy preference relations in this paper we deal with decision making problems over an unfuzzy set of alternatives on one hand we propose the problem of finding a max min transitive relation as near as possible to a given initial preference relation under the least squares criterion and such that it does not introduce deep qualitative changes on the other hand we define a linear extension of the initial preference relation between alternatives to a preference relation between lotteries

preference relations on a set of fuzzy utilities as a basis for decision making abstract in fuzzy decision problems we often encounter situations of choosing among alternatives which are assigned fuzzy utilities these problems have been approached using fuzzy implications or direct comparisons among fuzzy utilities in the literature however there are few attempts to investigate the issues addressing reasonable choice or reasonable ordering using fuzzy sets theory this paper first introduces some fundamental properties of fuzzy binary relations and certain conditions of reasonable orderings of fuzzy utilities then a method for constructing a fuzzy preference relation on a given set of fuzzy utilities is proposed for the sake of rational decision making this procedure employs the concepts of the extended minimum and the hamming distance between the greatest upper sets or the greatest lower sets of fuzzy utilities finally it is shown that the proposed fuzzy preference relations have reasonable properties as fuzzy orderings for decision making

on fuzzy n cell numbers and n dimension fuzzy vectors fuzzy n cell numbers are a kind of special n dimension fuzzy numbers whose sets of cuts are all hyperrectangles n dimension fuzzy vectors are the cartesian products of n one dimension fuzzy numbers in this paper we show that the fuzzy n cell number space and the n dimension fuzzy vector space are identical and obtain the relations of the joint membership function and the edge membership functions of a fuzzy n cell number i e a n dimension fuzzy vector using fuzzy vector form representations of fuzzy n cell numbers we study the metric of two fuzzy n cell numbers the supremum of a set of fuzzy n cell numbers and operational rules of addition scalar multiplication and multiplication of fuzzy n cell numbers and get the fuzzy vector form characterizations of the differentiability measurability and integrability of fuzzy n cell number valued fuzzy mappings

on the number of markoff numbers below a given bound according to a famous theorem of markoff the indefinite quadratic forms with exceptionally large minima greater than f of the square root of the discriminant are in 1 1 correspondence with the solutions of the diophantine equation p2 q2 r1 ipqr by relating markoffs algorithm for finding solutions of this equation to a problem of count ing lattice points in triangles it is shown that the number of solutions less than x equals clog2 3x 0 log x log log2 x with an explicitly computable constant c 0 18071704711507 numerical data up to 101300 is presented which suggests that the true error term is considerably smaller

tractable almost stochastic dominance abstract ll almost stochastic dominance ll asd is a relaxation of the stochastic dominance sd concept proposed by leshno and levy that explains more of realistic preferences observed in practice than sd alone does unfortunately numerical applications of this concept such as identifying if a given portfolio is efficient or determining a marketed portfolio that dominates a given benchmark are computationally prohibitive due to the structure of ll asd we propose a new almost stochastic dominance asd concept that is computationally tractable for instance a marketed dominating portfolio can be identified by solving a simple linear programming problem moreover the new concept performs well on all the intuitive examples from the literature and in some cases leads to more realistic predictions than the earlier concept we develop some properties of asd formulate efficient optimization models and apply the concept to analyzing investors preferences between bonds and stocks for the long run

canonical fuzzy numbers of dimension two and fuzzy utility difference for understanding preferential judgments abstract a notion of canonical fuzzy numbers of dimension two is introduced to represent flexible joint distributions of two fuzzy numbers whose membership functions are of a common functional type the relationships between fuzzy numbers are given by normalized scalar called relational factors in the joint distributions then the canonical fuzzy numbers are adopted to operate fuzzy utility differences and their aggregations for understanding human uncertain preferential judgments among multiattribute alternatives

estimating the critical parameter in almost stochastic dominance from insurance deductibles knowing how small a violation of stochastic dominance rules would be accepted by most individuals is a prerequisite to applying almost stochastic dominance criteria unlike previous laboratory expe

second order stochastic dominance constrained portfolio optimization theory and computational tests abstract due to the definition of second order stochastic dominance ssd in terms of utility theory portfolio optimization with ssd constraints is of major practical interest we contribute to the field in two ways first we present a self contained theory with some new results and new proofs of known results second we perform a set of tests for computational efficiency we provide new and simple arguments for the formulation of ssd constraints in a mathematical programming framework for many individuals an ssd constraint may seem too severe wherefore various relaxations assd have been proposed we introduce yet another relaxation directional ssd where a candidate portfolio is admissible if a step from the benchmark in the direction of the candidate yields a dominating portfolio optimal step size depends on individual preferences reflected by the objective function we compare computational efficiency of seven approaches for sd constrained portfolio problems including ssd and assd constrained cases

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

some comments on fuzzy variables abstract nahmias introduced the concept of a fuzzy variable as a possible axiomatic framework from which a rigorous theory of fuzziness may be constructed in this paper we attempt to shed more light on fuzzy variables in analogy with random variables in particular we study the problem if x1 x2 xn are mutually unrelated fuzzy variables with common membership function and 1 2 n are real numbers satisfying i o for every i and i 1n i 1 when does does z i 1n ixi have the same membership function

computing self intersections of closed geodesics on finite sheeted covers of the modular surface an algorithm is given for deciding whether a closed geodesic on a finite sheeted cover of the modular surface has self intersections if it does the algorithm gives them in the order they occur in traversing the geodesic the following general result on geodesics is proved any closed geodesic on a riemann surface r can be lifted to a simple closed geodesic on some finite sheeted cover of r in the last two sections the connection with the stabilizer under the modular group of a markov quadratic irrationality is discussed

the use of fuzzy variables in pert abstract in this paper we present a method called fpert for estimating a project completion time in the situation when activity duration times in the project network model are given in the form of fuzzy variables fuzzy sets on time space theoretical foundations of the method as well as results of calculations derived from a simple example are included

generalized almost stochastic dominance almost stochastic dominance allows small violations of stochastic dominance rules to avoid situations where most decision makers prefer one alternative to another but stochastic dominance cannot rank them while the idea behind almost stochastic dominance is quite promising it has not caught on in practice implementation issues and inconsistencies between integral conditions and their associated utility classes contribute to this situation we develop generalized almost second degree stochastic dominance and almost second degree risk in terms of the appropriate utility classes and their corresponding integral conditions and extend these concepts to higher degrees we address implementation issues and show that generalized almost stochastic dominance inherits the appealing properties of stochastic dominance finally we define convex generalized almost stochastic dominance to deal with risk prone preferences generalized almost stochastic dominance could be useful in decision analysis empirical researc

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities