truncation strategies in matching markets roth and rothblum roth a e u g rothblum 1999 truncation strategies in matching markets in search of advice for participants econometrica67 21 43 showed that for matching markets using the deferred acceptance algorithm a physician with symmetric incomplete information possibly gains only by truncating her true ranking we show that in symmetric information environments this result is identical for all priority mechanisms and all linear programming mechanisms introduced in british entry level medical markets and in public school choice in some american cities

conflict and coincidence of interest in job matching some new results and open questions the game theoretic solution to certain job assignment problems allows the interests of agents on the same side of the market e g firms or workers to be simultaneously maximized this is shown to follow from the lattice structure of the set of stable outcomes however it is shown that in a more general class of problems the optimality results persist but the lattice structures do not thus this paper raises as many questions as it answers

attractors and asymptotic stability for fuzzy dynamical systems abstract in this work we study the asymptotic properties of maps on fuzzy spaces which are extensions of maps on the main results are in section 4 see theorem 21 and we give an illustrative example in the last section

a strong consistency result for fuzzy relative frequencies interpreted as estimator for the fuzzy valued probability the unavoidable imprecision of measurements of continuous physical quantities can be modelled by using the concept of fuzzy numbers and fuzzy vectors concerning a quantitative usage of such data the classical concept of relative frequencies for real data has to be extended to so called fuzzy relative frequencies for fuzzy data whereby the fuzzy relative frequency of a set is a fuzzy number analogous to a dempster s interval valued probabilities induced by multi valued mappings fuzzy valued probabilities induced by fuzzy random vectors are considered and analyzed it is proved that fuzzy relative frequencies can be interpreted as strongly consistent estimator for the corresponding fuzzy valued probability

the s differentiability of a fuzzy valued mapping several approaches to define the differential of fuzzy valued mappings can be found in the literature in this paper we introduce a new concept of differential of a fuzzy valued mapping which is based on the notion of differential of the support function associated with such a mapping properties of the new concept as well as the relation between it and previous approaches are also analyzed in detail

hard variants of stable marriage the stable marriage problem and its many variants have been widely studied in the literature gusfield and irving the stable marriage problem structure and algorithms mit press cambridge ma 1989 roth and sotomayor two sided matching a study in game theoretic modeling and analysis econometric society monographs vol 18 cambridge university press cambridge 1990 knuth stable marriage and its relation to other combinatorial problems crm proceedings and lecture notes vol 10 american mathematical society providence ri 1997 partly because of the inherent appeal of the problem partly because of the elegance of the associated structures and algorithms and partly because of important practical applications such as the national resident matching program roth j political economy 92 6 1984 991 and similar large scale matching schemes here we present the first comprehensive study of variants of the problem in which the preference lists of the participants are not necessarily complete and not necessarily totally ordered we show that under surprisingly restrictive assumptions a number of these variants are hard and hard to approximate the key observation is that in contrast to the case where preference lists are complete or strictly ordered or both a given problem instance may admit stable matchings of different sizes in this setting examples of problems that are hard are finding a stable matching of maximum or minimum size determining whether a given pair is stableeven if the indifference takes the form of ties on one side only the ties are at the tails of lists there is at most one tie per list and each tie is of length 2 and finding or approximating both an egalitarian and a minimum regret stable matching however we give a 2 approximation algorithm for the problems of finding a stable matching of maximum or minimum size we also discuss the significant implications of our results for practical matching schemes

popular edges and dominant matchings given a bipartite graph g a cup b e with strict preference lists and given an edge e in e we ask if there exists a popular matching in g that contains e we call this the popular edge problem a matching m is popular if there is no matching m such that the vertices that prefer m to m outnumber those that prefer m to m it is known that every stable matching is popular however g may have no stable matching with the edge e in this paper we identify another natural subclass of popular matchings called dominant matchings and show that if there is a popular matching that contains the edge e then there is either a stable matching that contains e or a dominant matching that contains e this allows us to design a linear time algorithm for identifying the set of popular edges when preference lists are complete we show an o n 3 algorithm to find a popular matching containing a given set of edges or report that none exists where n a b

on houseswapping the strict core segmentation and linear programming we consider then player houseswapping game of shapley and scarf 1974 with indifferences in preferences allowed it is well known that the strict core of such a game may be empty single valued or multi valued we define a condition on such games called segmentability which means that the set of players can be partitioned into a top trading segmentation it generalizes gale s well known idea of the partition of players into top trading cycles which is used to find the unique strict core allocation in the model with no indifference we prove that a game has a nonempty strict core if and only if it is segmentable we then use this result to devise ano n3 algorithm which takes as input any houseswapping game and returns either a strict core allocation or a report that the strict core is empty finally we are also able to construct a linear inequality system whose feasible region s extreme points precisely correspond to the allocations of the strict core this last result parallels the results of vande vate 1989 and rothblum 1992 for the marriage game of gale and shapley 1962

polyhedral aspects of stable marriage in the setting of the stable matching sm problem it has been observed that some of the man woman pairs cannot be removed although they participate in no stable matching since such a removal would alter the set of solutions these pairs are yet to be identified likewise and despite the sizeable literature some of the fundamental characteristics of the sm polytope e g its dimension its facets etc have not been established in the current work we show that these two seemingly distant open issues are closely related more specifically we identify the pairs with the above mentioned property and present a polynomial algorithm for producing a set of minimal preference lists we utilize this result in the context of two different representations of the sm structure rotation poset graph and algebraic formulation and derive the dimension of the sm polytope to obtain all alternative minimal linear descriptions

estimation of a fuzzy regression model using fuzzy distances regression analysis is a powerful statistical tool that has many applications in different areas the problem of regression analysis under a fuzzy environment has been treated in the literature from different points of view and considering a variety of input output data crisp or fuzzy however we realize that in general most research papers have a conflict between the solution of the fuzzy regression problem using crisp distances minimizing a real error function and the interpretation of fuzzy data as possibility distributions the main aim of this paper is to develop a methodology to solve this problem introducing a fuzzy partial order and a family of fuzzy distance measures on the whole set of fuzzy numbers the new approach allows us to obtain linear and nonlinear models that reach the lowest fuzzy error the estimation process in general can be considered easier to apply in practice and it is not limited to triangular fuzzy numbers numerical examples are provided to illustrate the usefulness and applicability of these results and comparisons with existing methodologies show that the performance of the proposed solution is very satisfactory

many to one stable matching geometry and fairness baiou and balinski characterized the stable admissions polytope using a system of linear inequalities the structure of feasible solutions to this system of inequalities fractional stable matchings is the focus of this paper the main result associates a geometric structure with each fractional stable matching this insight appears to be interesting in its own right and can be viewed as a generalization of the lattice structure for integral stable matchings to fractional stable matchings in addition to obtaining simple proofs of many known results the geometric structure is used to prove the following two results first it is shown that assigning each agent their median choice among all stable partners results in a stable matching which can be viewed as a fair compromise second sufficient conditions are identified under which stable matchings exist in a problem with externalities in particular in the stable matching problem with couples

approximability results for stable marriage problems with ties we consider instances of the classical stable marriage problem in which persons may include ties in their preference lists we show that in such a setting strong lower bounds hold for the approximability of each of the problems of finding an egalitarian minimum regret and sex equal stable matching we also consider stable marriage instances in which persons may express unacceptable partners in addition to ties in this setting we prove that there are constants such that each of the problems of approximating a maximum and minimum cardinality stable matching within factors of respectively is np hard under strong restrictions we also give an approximation algorithm for both problems that has a performance guarantee expressible in terms of the number of lists with ties this significantly improves on the best known previous performance guarantee for the case that the ties are sparse our results have applications to large scale centralized matching schemes

stable matchings optimal assignments and linear programming vande vate 1989 described the polytope whose extreme points are the stable core matchings in the marriage problem rothblum 1989 simplified and extended this result this paper explores a corresponding linear program its dual and consequences of the fact that the dual solutions have an unusually direct relation to the primal solutions this close relationship allows us to provide simple proofs both of vande vate and rothblum s results and of other important results about the core of marriage markets these proofs help explain the structure shared by the marriage problem without sidepayments and the assignment game with sidepayments the paper further explores fractional matchings which may be interpreted as lotteries over possible matches or as time sharing arrangements we show that those fractional matchings in the stable marriage polytope form a lattice with respect to a partial ordering that involves stochastic dominance thus all expected utility functions corresponding to the same ordinal preferences will agree on the relevant comparisons finally we provide linear programming proofs of slightly stronger versions of known incentive compatibility results

uncertain alternating renewal process and its application uncertain process is a sequence of uncertain variables indexed by time and space first this paper presents a kind of uncertain process known as the uncertain alternating renewal process whose alternating interarrival times are uncertain variables then it proves an uncertain alternating renewal theorem on the limit value of average working rate finally an application of the alternating renewal theorem is discussed

identities on fractional integrals and various integral transforms in this work we will introduce theorems relating the riemann liouville fractional integral and the weyl fractional integral to some well known integral transforms including laplace transforms stieltjes transforms generalized stieltes transforms hankel transforms and k transforms as applications of the theorems and their results a number of infinite integrals of elementary functions and special functions are evaluated and some illustrative examples are presented

matching with indifferences a comparison of algorithms in the context of course allocation abstract we evaluate six one and eight two sided matching mechanisms with preferences based on a collection of 28 field data sets although important properties of matching mechanisms such as strategy proofness or pareto efficiency can be shown by formal proofs the size the average rank and the popularity of matchings ask for an empirical evaluation we introduce different metrics to compare the results the study shows trade offs between various design desiderata which are relevant in the field the results provide guidelines for the selection of matching mechanisms

some parseval goldstein type identities involving the fs 2 transform the fc 2 transform and the p4 transform and their applications abstract in the present paper the authors consider several new integral transforms including the f s 2 transform the f c 2 transform and the p 4 transform as generalizations of the classical fourier sine transform the classical fourier cosine transform and the classical stieltjes transform respectively many identities involving these transforms are given by making use of these identities a number of new parseval goldstein type identities are obtained for these and many other well known integral transforms the identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions some examples are also given as illustrations of the results presented here

existence and uniqueness for solutions to fuzzy stochastic differential equations driven by local martingales under the non lipschitzian condition abstract this paper makes a research into a class of fuzzy stochastic differential equations fsdes driven by a continuous local martingale under the non lipschitzian condition such equations can be useful in modelling of hybrid systems where the phenomena are subjected to two kinds of uncertainties randomness and fuzziness simultaneously the solutions of fsdes are the fuzzy stochastic processes and their uniqueness is considered to be in a strong sense thus the existence and uniqueness of solutions to fsdes under the non lipschitzian condition is first proven and the continuity of solutions to fsdes with respect to the initial data or the coefficients of the equations is investigated

a theorem on widder s potential transform and its applications abstract in the present paper the authors prove a parseval goldstein type theorem involving the classical laplace transform the fourier sine transform and widder s potential transform the theorem is then shown to yield a simple algorithm for evaluating infinite integrals some illustrative examples are also given

the l average value and the fuzzy expectation of a fuzzy random variable abstract the concepts of fuzzy random variable and the associated fuzzy expected value have been introduced by puri and ralescu as an extension of measurable set valued functions random sets and of the aumann integral of these functions respectively on the other hand the average function has been suggested by campos and gonzalez as an appropriate function to rank fuzzy numbers in this paper we are going to analyze some useful properties concerning the average value of the expectation of a fuzzy random variable and some practical implications of these properties are also commented on

expected value of fuzzy variable and fuzzy expected value models this paper will present a novel concept of expected values of fuzzy variables which is essentially a type of choquet integral and coincides with that of random variables in order to calculate the expected value of general fuzzy variable a fuzzy simulation technique is also designed finally we construct a spectrum of fuzzy expected value models and integrate fuzzy simulation neural network and genetic algorithms to produce a hybrid intelligent algorithm for solving general fuzzy expected value models

a matroid approach to stable matchings with lower quotas in 2010 huang introduced the laminar classified stable matching problem lcsm for short that is motivated by academic hiring this problem is an extension of the well known hospitals residents problem in which a hospital has laminar classes of residents and it sets lower and upper bounds on the number of residents that it can hire in each class against the intuition that variations of the stable matching problem with lower quotas are difficult in general huang proved that lcsm can be solved in polynomial time in this paper we present a matroid based approach to lcsm and we obtain the following results i we solve a generalization of lcsm in which both sides have quotas ii huang raised a question about a polyhedral description of the set of stable assignments in lcsm we give a positive answer for this question by exhibiting a polyhedral description of the set of stable assignments in a generalization of lcsm iii we prove that the set of stable assignments in a generalization of lcsm has a la

set valued choquet integrals revisited this paper performs a further investigation on the set valued choquet integral given by jang and kwon fuzzy sets and systems 112 2000 233 some incorrect properties are revised it is pointed out that the definition for convergence of sequence of sets or set valued functions is unreasonable by using the usual kuratowski s convergence some new convergence theorems for the set valued choquet integral are shown meanwhile some other properties are obtained

characterization of stable matchings as extreme points of a polytope the purpose of this paper is to extend a modified version of a recent result of vande vate 1989 which characterizes stable matchings as the extreme points of a certain polytope our proofs are simpler and more transparent than those of vande vate

on a cutting plane heuristic for the stable roommates problem and its applications abstract we propose a new cutting plane heuristic for the classical stable roommates problem our approach utilises a new linear programming formulation for the problem and the underlying geometric properties of the fractional solution to construct the violated inequality we test the approach on moderate size problems with encouraging computational performance to further illustrate the versatility of this approach we also show how it can be suitably extended to handle variants of the basic stable roommates model

random paths to stability in two sided matching empirical studies of two sided matching have so far concentrated on markets in which certain kinds of market failures were addressed by resorting to centralized deterministic matching procedures loosely speaking the results of these studies are that those centralized procedures which achieved stable outcomes resolved the market failures while those markets organized through procedures that yielded unstable outcomes continued to fail 2 so the market failures seem to be associated with instability of the outcomes but many entry level labor markets and other two sided matching situations don t employ centralized matching procedures and yet aren t observed to experience such failures so we can conjecture that at least some of these markets may reach stable outcomes by means of decentralized decision making and decentralized decision making in complex environments presumably introduces some randomness into what matchings are achieved however as far as we are aware no nondeterministic models leading to stable outcomes have yet been studied the present paper demonstrates that starting from an arbitrary matching the process of allowing randomly chosen blocking pairs to match will converge to a stable matching with probability one this resolves an open question raised by knuth 1976 who showed that such a process may cycle furthermore every stable matching can arise

blockers and antiblockers of stable matchings an implicit linear description of the stable matching polytope is provided in terms of the blocker and antiblocker sets of constraints of the matroid kernel polytope the explicit identification of both these sets is based on a partition of the stable pairs in which each agent participates here we expose the relation of such a partition to rotations we provide a time optimal algorithm for obtaining such a partition and establish some new related results most importantly that this partition is unique

almost periodic solutions of fuzzy systems we prove the existence of almost periodic solutions and asymptotically almost periodic solutions for the fuzzy functional differential equations moreover we consider uniform stable and uniformly asymptotically stable of almost periodic solutions for the fuzzy system

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

of stable marriages and graphs and strategy and polytopes this expository paper develops the principal known results and some new ones on the stable matchings of marriage games in the language of directed graphs this both unifies and simplifies the presentation and renders it more symmetric in addition it yields a new algorithm and a new proof for the existence of stable matchings new proofs for many known facts and some new results notably concerning players strategies and the properties of the stable matching polytope

the college admissions problem with lower and common quotas we study two generalised stable matching problems motivated by the current matching scheme used in the higher education sector in hungary the first problem is an extension of the college admissions problem in which the colleges have lower quotas as well as the normal upper quotas here we show that a stable matching may not exist and we prove that the problem of determining whether one does is np complete in general the second problem is a different extension in which as usual individual colleges have upper quotas but in addition certain bounded subsets of colleges have common quotas smaller than the sum of their individual quotas again we show that a stable matching may not exist and the related decision problem is np complete on the other hand we prove that when the bounded sets form a nested set system a stable matching can be found by generalising in non trivial ways both the applicant oriented and college oriented versions of the classical gale shapley algorithm finally we present an alternative view of this nested case using the concept of choice functions and with the aid of a matroid model we establish some interesting structural results for this case

strong law of large numbers for t normed arithmetics we prove a strong law of large numbers for sequences of pairwise i i d fuzzy random variables addition is given by the extension principle associated with a general continuous triangular norm our result includes the slln for levelwise sums obtained when the chosen triangular norm is the minimum

identities for the e2 1 transform and their applications in the present paper the authors introduce the e 2 1 transform with kernel the exponential integral function it is shown that the third iterate of the l 2 transform is the exponential integral transform and some identities involving the new transform the l 2 transform and the widder potential transform are given using the identities parseval goldstein type results involving these transforms are proved some illustrative examples are also given

a polyhedral description of kernels let g be a digraph and let g be the linear system consisting of nonnegativity stability and domination inequalities we call g kernel ideal if h defines an integral polytope for each induced subgraph h of g and we call g kernel mengerian if h is totally dual integral tdi for each induced subgraph h of g in this paper we show that a digraph is kernel ideal iff it is kernel mengerian iff it contains none of three forbidden structures our characterization yields a polynomial time algorithm for the minimum weighted kernel problem on kernel ideal digraphs we also prove that it is np hard to find a kernel of minimum size even in a planar bipartite digraph with maximum degree at most three

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

stable matchings and linear programming abstract this paper continues the work of abeledo and rothblum who study nonbipartite stable matching problems from a polyhedral perspective we establish here additional properties of fractional stable matchings and use linear programming to obtain an alternative polynomial algorithm for solving stable matching problems

stable fractional matchings abstract we study a generalization of the classical stable matching problem that allows for cardinal preferences as opposed to ordinal and fractional matchings as opposed to integral in this cardinal setting stable fractional matchings can have much larger social welfare than stable integral ones our goal is to understand the computational complexity of finding an optimal i e welfare maximizing stable fractional matching we consider both exact and approximate stability notions and provide simple approximation algorithms with weak welfare guarantees our main result is that somewhat surprisingly achieving better approximations is computationally hard to the best of our knowledge these are the first computational complexity results for stable fractional matchings in the cardinal model en route to these results we provide a number of structural observations that could be of independent interest

risk assessment of serious crime with fuzzy random theory this paper presents a novel approach for assessing the potential risk of serious crime events e g terrorist attack the modelling and assessment of such risk is carried out under uncertain circumstances because of both the randomness and fuzziness inherent in crime data the approach is based on fuzzy random theory that complements probability theory with an additional dimension of imprecision this allows for potential loss caused by a crime to be expressed as a fuzzy random variable crime risk is therefore estimated as the mean chance of a fuzzy random event where the resulting loss reaches a given confidence level the concept of the average loss per unit of time is also introduced in order to calculate the rate at which the loss may increase due to possible crime events the work is compared with typical existing approaches and supported with examples throughout that illustrate its utility

identities and parseval type relations for the l2 transform abstract in the present paper the authors introduce identities for the l 2 transform which yield a parseval type relationship for the l 2 transform the parseval type relationship proven in this paper give rise to useful corollaries for evaluating indefinite integrals of special functions some examples are also given as illustrations of the results presented here

the intersection operation in light of joint observables and bell inequalities in operational probability theory operational probability theory appears as a smooth extension of classical probability theory that fulfills quantum physics needs in this paper we first explain the need to extend the concept of the intersection operation in the light of the concept of joint observables then we tried to determine the basic features that characterize any possible definition of the intersection operation furthermore we tried to know if there is a relation between the definitions of the intersection operation of both fuzzy and operational probability theories these relations are used first to find a suitable suggestion to define the intersection operation second they are used besides the studies made on bell inequalities in fuzzy probability theory to find the conditions that should be satisfied by the intersection operation to ensure the possibility of the violation of bell inequalities in operational probability theory

identities for the hankel transform and their applications abstract in the present paper the authors show that iterations of the hankel transform with k transform is a constant multiple of the widder transform using these iteration identities several parseval goldstein type theorems for these transforms are given by making use of these results a number of new goldstein type exchange identities are obtained for these and the laplace transform the identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions some examples are also given as illustration of the results presented here

risk model with fuzzy random individual claim amount in this paper we consider a risk model in which individual claim amount is assumed to be a fuzzy random variable and the claim number process is characterized as a poisson process the mean chance of the ultimate ruin is researched particularly the expressions of the mean chance of the ultimate ruin are obtained for zero initial surplus and arbitrary initial surplus if individual claim amount is an exponentially distributed fuzzy random variable the results obtained in this paper coincide with those in stochastic case when the fuzzy random variables degenerate to random variables finally two numerical examples are presented

the revealed preference theory of stable and extremal stable matchings we investigate the testable implications of the theory of stable matchings we provide a characterization of the matchings that are rationalizable as stable matchings when agents preferences are unobserved the characterization is a simple nonparametric test for stability in the tradition of revealed preference tests we also characterize the observed stable matchings when monetary transfers are allowed and the stable matchings that are best for one side of the market extremal stable matchings we find that the theory of extremal stable matchings is observationally equivalent to requiring that there be a unique stable matching or that the matching be consistent with unrestricted monetary transfers

an efficient algorithm for the optimal stable marriage in an instance of size n of the stable marriage problem each of n men and n women ranks the members of the opposite sex in order of preference a stable matching is a complete matching of men and women such that no man and woman who are not partners both prefer each other to their actual partners under the matching it is well known 2 that at least one stable matching exists for every stable marriage instance however the classical gale shapley algorithm produces a marriage that greatly favors the men at the expense of the women or vice versa the problem arises of finding a stable matching that is optimal under some more equitable or egalitarian criterion of optimality this problem was posed by knuth 6 and has remained unsolved for some time here the objective of maximizing the average or equivalently the total satisfaction of all people is used this objective is achieved when a person s satisfaction is measured by the position of his her partner in his her preference list by exploiting the structure of the set of all stable matchings and using graph theoretic methods an o n 4 algorithm for this problem is derived

b fuzzy probabilities abstract we treat b fuzzy probabilities in nonstandard frameworks by the methods based on boolean valued models and especially boolean powers these formal methods apart from the difficulties associated with the formal model itself give a simple and powerful theory for fuzzy probability spaces and fuzzy random variables essentially everything is reduced to a transfer principle however one can also work using classical methods of proofs we first give the necessary background on nonstandard frameworks within these frameworks we develop boolean fuzzy probabilities and fuzzy random variables

fuzziness and randomness in an optimization framework abstract a semi infinite approach for linear programming in the presence of fuzzy random variable coefficients is described as a byproduct a way for dealing with optimization problems including both fuzzy and random data is obtained numerical examples are provided for the sake of illustration

linear programming with fuzzy random variable coefficients abstract linear programming with fuzzy random variable coefficients is introduced by discussing a practical engineering problem in order to study the solution of the linear programming with fuzzy random variable coefficients we discuss the simplex algorithm for linear programming with random variable coefficients furthermore the solution and distribution problem of this new fuzzy random programming are studied

compatibility between fuzzy set operations and level set operations applications to fuzzy difference abstract three types of binary operation between any two fuzzy sets are proposed in this paper the concept of 0 level set of fuzzy set plays an important role for defining the binary operations between two fuzzy sets according to the decomposition theorem of fuzzy sets the consistency between the membership functions and level sets should be rigorously verified when the binary operation between two fuzzy sets is defined by using their level sets the consistency is investigated thoroughly in this paper for the purpose of guaranteeing the existence of such binary operations moreover we also propose the so called hausdorff difference between any two fuzzy sets to define the difference of any two fuzzy numbers

jensen and chebyshev inequalities for pseudo integrals of set valued functions set valued functions are an important mathematical notion and play a crucial role in several practical areas at the same time pseudo analysis as a background allows extension of some classical mathematical notions to the forms that are highly applicable in some nonstandard situations this paper focuses on pseudo integration of set valued functions which is generalization of aumann s research and corresponding extensions of the jensen and chebyshev integral inequalities to the set valued case since the integral inequalities in question are widely used in various aspects of mathematics the main motivation for the presented research lies in the possibility of expanding the applicability of these inequalities by combining the properties of set valued functions with pseudo analysis

convergence of set valued sub and supermartingales in the kuratowski mosco sense the purpose of this paper is to prove some convergence theorems of closed and convex set valued sub and supermartingales in the kuratowski mosco sense to get submartingale convergence theorems we give sufficient conditions for the kudo aumann integral and hiai umegaki conditional expectation to be closed both for compact convex set valued random variables and for closed convex set valued random variables we also give an example of a bounded closed convex set valued random variable whose kudo aumann integral is not closed

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

a theorem on the generalized stieltjes transform and its applications abstract this paper presents a proof of parseval goldstein type theorem involving the generalized stieltjes transform and the classical laplace transform the theorem is then shown to yield a number of results about the widder potential transform and the laguerre transform some illustrative examples are also given

the stable admissions polytope the stable admissions polytope the convex hull of the stable assignments of the university admissions problem is described by a set of linear inequalities it depends on a new characterization of stability and arguments that exploit and extend a graphical approach that has been fruitful in the analysis of the stable marriage problem

the geometry of fractional stable matchings and its applications we study the classical stable marriage and stable roommates problems using a polyhedral approach we propose a new lp formulation for the stable roommates problem which has a feasible solution if and only if the underlying roommates problem has a stable matching furthermore for certain special weight functions on the edges we construct a 2 approximation algorithm for the optimal stable roommates problem our technique exploits features of the geometry of fractional solutions of this formulation for the stable marriage problem we show that a related geometry allows us to express any fractional solution in the stable marriage polytope as a convex combination of stable marriage solutions this also leads to a genuinely simple proof of the integrality of the stable marriage polytope

strategy proofness makes the difference deferred acceptance with responsive priorities in college admissions and student placements at public schools the admission decision can be thought of as assigning indivisible objects with capacity constraints to a set of students such that each student receives at most one object and monetary compensations are not allowed in these important market design problems the agent proposing deferred acceptance da mechanism with responsive strict priorities performs well and economists have successfully implemented da mechanisms or slight variants thereof we show that almost all real life mechanisms used in such environments including the large classes of priority mechanisms and linear programming mechanisms satisfy a set of simple and intuitive properties once we add strategy proofness to these properties da mechanisms are the only ones surviving in market design problems that are based on weak priorities like school choice generally multiple tie breaking mtb procedures are used and then a mechanism is implemented with the obtained strict priorities by adding stability with respect to the weak priorities we establish the rst normative foundation

efficient algorithms for generalized stable marriage and roommates problems we consider a generalization of the stable roommates problem sr in which preference lists may be partially ordered and forbidden pairs may be present denoted by srpf this includes as a special case a corresponding generalization of the classical stable marriage problem sm denoted by smpf by extending previous work of feder we give a two step reduction from srpf to 2 sat this has many consequences including fast algorithms for a range of problems associated with finding optimal stable matchings and listing all solutions given variants of sr and sm for example given an smpf instance i we show that there exists an o m succinct certificate for the unsolvability of i an o m algorithm for finding all the super stable pairs in i an o m kn algorithm for listing all the super stable matchings in i an o m 1 5 algorithm for finding an egalitarian super stable matching in i and an o m algorithm for finding a minimum regret super stable matching in i where n is the number of men m is the total length of the preference lists and k is the number of super stable matchings in i analogous results apply in the case of srpf

hukuhara derivative of the fuzzy expected value in this paper we establish sufficient conditions to guarantee the exchange of the fuzzy expected value for a fuzzy random variable depending on certain parameter and its hukuhara derivative with respect to the parameter main results are obtained for two different sets of general conditions one of them requiring measurability conditions with respect to the product space the fuzzy random variable is defined from and the second one just requiring conditions over the projections of the fuzzy random variables

stable matching with incomplete information we formulate a notion of stable outcomes in matching problems with one sided asymmetric information the key conceptual problem is to formulate a notion of a blocking pair that takes account of the inferences that the uninformed agent might make from the hypothesis that the current allocation is stable we show that the set of stable outcomes is nonempty in incomplete information environments and is a superset of the set of complete information stable outcomes we then provide sucient conditions for incomplete information stable matchings to be ecient lastly we dene a notion of price sustainable allocations and show that the set of incomplete information stable matchings is a subset of the set of such allocations

the economics of matching stability and incentives this paper considers some game theoretic aspects of matching problems and procedures of the sort which involve matching the members of one group of agents with one or more members of a second disjoint group of agents ail of whom have preferences over the possible resulting matches the main focus of this paper is on determining the extent to which matching procedures can be designed which give agents the incentive to honestly reveal their preferences and which produce stable matches two principal results are demonstrated the first is that no matching procedure exists which always yields a stable outcome and gives players the incentive to reveal their true preferences even though procedures exist which accomplish either of these goals separately the second result is that matching procedures do exist however which always yield a stable outcome and which always give all the agents in one of the two disjoint sets of agents the incentive to reveal their true preferences

a fixed point approach to stable matchings and some applications we describe a fixed point based approach to the theory of bipartite stable matchings by this we provide a common framework that links together seemingly distant results like the stable marriage theorem of gale and shapley the mendelsohn dulmage theorem the kundu lawler theorem tarski s fixed point theorem the cantor bernstein theorem pym s linking theorem or the monochromatic path theorem of sands et al in this framework we formulate a matroid generalization of the stable marriage theorem and study the lattice structure of generalized stable matchings based on the theory of lattice polyhedra and blocking polyhedra we extend results of vande vate and rothblum on the bipartite stable matching polytope

numerical solutions of fuzzy differential and integral equations using the embedding method numerical procedures for solving fuzzy differential equations fdes and fuzzy integral equations fies with arbitrary kernels have been investigated sufficient conditions for convergence of the proposed algorithms are given and their applicability is illustrated with examples this work and its conclusions may narrow the gap between the theoretical research on fdes and fies and the practical applications already existing in the design of various fuzzy dynamical systems

three fast algorithms for four problems in stable marriage the stable marriage problem is a well known problem of matching n men to n women to achieve a certain type of stability the o n 2 time gale shapley gs algorithm for finding two particular but extreme stable marriages out of a possibly exponential number of stable marriages is also well known in this paper we consider four problems concerned with finding information about the set of all stable marriages and with finding stable marriages other than those obtained by the gale shapley algorithm in particular we give an o n 2 time algorithm which for any problem instance of n men and n women finds every man woman pair that is contained in at least one stable marriage we show that the same algorithm finds all the rotations for the problem instance in o n 2 time we give an o n 2 n s time and o n 2 space bounded algorithm which is time and space optimal to enumerate all stable marriages where s is the set of them and we give an o n 2 time algorithm to find the mini

new identities involving the laplace and the ℒ 2 transforms and their applications in the present paper parseval goldstein type theorems involving the 2 transforms and the laplace transform are proved the theorems are then shown to yield a number of new identities involving several well known integral transforms and special functions using the theorem and its corollaries a number of interesting infinite integrals of elementary and special functions are presented some illustrative examples are also given

fuzzy rr dfcsp and planning constraint satisfaction is a fundamental artificial intelligence technique for knowledge representation and inference however the formulation of a static constraint satisfaction problem csp with hard imperative constraints is insufficient to model many real problems fuzzy constraint satisfaction provides a more graded viewpoint priorities and preferences are placed on individual constraints and aggregated via fuzzy conjunction to obtain a satisfaction degree for a solution to the problem this paper examines methods for solving an important instance of dynamic flexible constraint satisfaction dfcsp combining fuzzy csp and restriction relaxation based dynamic csp fuzzy rrdfcsp this allows the modelling of complex situations where both the set of constraints may change over time and there is flexibility inherent in the definition of the problem this paper also presents a means by which classical planning can be extended via fuzzy sets to enable flexible goals and preferences to be placed on the use of planning operators a range of plans can be produced trading compromises made versus the length of the plan the flexible planning operators are close in definition to fuzzy constraints hence through a hierarchical decomposition of the planning graph the work shows how flexible planning reduces to the solution of a set of fuzzy rrdfcsps

total dual integrality of rothblum s description of the stable marriage polyhedron rothblum showed that the convex hull of the stable matchings of a bipartite preference system can be described by an elegant system of linear inequalities in this paper we prove that the description given by rothblum is totally dual integral we give a constructive proof based on the results of gusfield and irving on rotations which gives rise to a strongly polynomial algorithm for finding an integer optimal dual solution

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

a unified approach to asymptotic behaviors for the autoregressive model with fuzzy data we propose a unified estimator for the autoregressive model with fuzzy input output variables based on the least squares method the least squares estimation is investigated in presence of a unified r distance defined on the space of fuzzy numbers we investigate asymptotic properties of the unified estimator under some simple conditions as well as a generalization which reduces to the asymptotic properties under those distances when the distances are the special cases of r distance some simulation studies are included to compare the asymptotic properties of estimators formed under several distances being the special cases of r distance

courtship and linear programming this paper demonstrates that the celebrated gale shapley algorithm for obtaining stable matchings in stable marriage problems is essentially an application of the dual simplex method