existence of a global smooth solution for a degenerate goursat problem of gas dynamics the goursat problem of a mixed type equation p 0 is considered at the ends of its supports we have p 0 which means it is degenerate hyperbolic we prove the global existence of a smooth solution to the degenerate goursat problem up to a boundary where p 0 this problem comes from the expansion of a wedge of gas with constant velocity into vacuum in two dimensional pressure gradient equations in gas dynamics where p is the pressure and p 0 means vacuum

a complete axiomatization of fuzzy functional dependencies using fuzzy function the notion of functional dependency in classical relational databases corresponds to a partial function therefore it appears natural that the notion of fuzzy functional dependency should correspond to the notion of partial fuzzy function following this approach we introduce the notion of fuzzy functional dependency in fuzzy relational databases and show that the classical inference rules for functional dependencies form a sound and complete formal system in our case

an equivalence classes model of fuzzy relational databases abstract the technique of employing sets of values for tuple components to express imprecision in relational databases was proposed by buckles and petry in their classic works on fuzzy relational databases in addition to providing an intuitively appealing scheme for representing fuzzy information the model of buckles and petry possesses several key properties of the classical relational model by employing finite scalar domains with similarity relations and special fuzzy number domains buckles and petry have demonstrated that the classical properties of uniqueness of tuple interpretations and well definedness of the relational algebra can be retained in the fuzzy relational database model the key to the preservation of these properties is the fact that scalar domains with similarity relations and the fuzzy number domains can be partitioned into equivalence classes however since equivalence classes can be constructed without assuming the existence of similarity relations or special fuzzy number domains it is desirable to generalize the fuzzy relational database model to one based only on equivalence classes in this work we show that the important properties of classical relational databases and of fuzzy relational databases are preserved in a generalized model built on equivalence relations on finite database domains further we generalize the notion of a functional dependency to the fuzzy relational model

on a regularity result for the transonic pressure gradient system in gas dynamics abstract this paper is concerned with the regularity of transonic flows originated from the two dimensional riemann problem to the pressure gradient system in gas dynamics it is verified that if the transonic solution of the pressure gradient system is c 3 in a neighborhood of a sonic point and is c in the subsonic sonic region then the solution is also c in the sonic supersonic region near the sonic point

a computational approach to approximate and plausible reasoning with applications to expert systems the intended purpose of this paper is twofold proposing a common basis for the modeling of uncertainty and imprecision and discussing various kinds of approximate and plausible reasoning schemes in this framework together with probability different kinds of uncertainty measures credibility and plausibility functions in the sense of shafer possibility measures in the sense of zadeh and the dual measures of necessity sugeno s g fuzzy measures are introduced in a unified way the modeling of imprecision in terms of possibility distribution is then presented and related questions such as the measure of the uncertainty of fuzzy events the probability and possibility qualification of statements the concept of a degree of truth and the truth qualification of propositions are discussed at length deductive inference from premises weighted by different kinds of measures by uncertainty or by truth values in the framework of various multivalued logics is fully investigated then deductive inferences from imprecise or fuzzy premises are dealt with patterns of reasoning where both uncertainty and imprecision are present are also addressed the last section is devoted to the combination of uncertain or imprecise pieces of information given by different sources on the whole this paper is a tentative survey of quantitative approaches in the modeling of uncertainty and imprecision including recent theoretical proposals as well as more empirical techniques such as the ones developed in expert systems such as mycin or prospector the management of uncertainty and imprecision in reasoning patterns being a key issue in artificial intelligence

semi hyperbolic patches of solutions to the two dimensional euler equations we construct semi hyperbolic patches of solutions in which one family out of two nonlinear families of characteristics starts on sonic curves and ends on transonic shock waves to the two dimensional euler equations this type of solution appears in the transonic flow over an airfoil and guderley reflection and is common in the numerical solutions of riemann problems

data mining by attribute generalization with fuzzy hierarchies in fuzzy databases in this paper we examine the soft computing issues involving data generalization on fuzzy information the attribute induction process is formalized for these three cases crisp hierarchy fuzzy data fuzzy hierarchy crisp data fuzzy hierarchy fuzzy data each case is exemplified by applications of the algorithm to a prototype database

interaction of rarefaction waves of the two dimensional self similar euler equations we construct classical self similar solutions to the interaction of two arbitrary planar rarefaction waves for the polytropic euler equations in two space dimensions the binary interaction represents a major type of interaction in the two dimensional riemann problems and includes in particular the classical problem of the expansion of a wedge of gas into vacuum based on the hodograph transformation the method employed here involves the phase space analysis of a second order equation and the inversion back to or development onto the physical space

a constrained maximum likelihood approach to estimating switching regressions abstract it is widely known that the likelihood function for the switching regression model is unbounded if the error variances are unconstrained this paper shows that a constrained maximum likelihood formulation makes the likelihood function bounded relatively mild constraints are imposed on the parameters and if the true parameters satisfy the constraints there is a global maximizer of the likelihood function on the constrained parameter space which is consistent asymptotically normal and efficient a well known em algorithm is modified in order to compute constrained maximizers of the likelihood function

simple waves and a characteristic decomposition of the two dimensional compressible euler equations we present a characteristic decomposition of the potential flow equation in the self similar plane the decomposition allows for a proof that any wave adjacent to a constant state is a simple wave for the adiabatic euler system this result is a generalization of the well known result on 2 d steady potential flow and a recent similar result on the pressure gradient system

possibilistic functional dependencies and their relationship to possibility theory this paper introduces possibilistic functional dependencies these dependencies are associated with a particular possibility distribution over possible worlds of a classical database the possibility distribution reflects a layered view of the database the highest layer of the classical database consists of those tuples that certainly belong to it while the other layers add tuples that only possibly belong to the database with different levels of possibility the relation between the confidence levels associated with the tuples and the possibility distribution over possible database worlds is discussed in detail in the setting of possibility theory a possibilistic functional dependency is a classical functional dependency associated with a certainty level that reflects the highest confidence level where the functional dependency no longer holds in the layered database moreover the relationship between possibilistic functional dependencies and possibilistic logic formulas is established related work is reviewed and the intended use of possibilistic functional dependencies is discussed in the conclusion

probability inequalities for empirical processes and a law of the iterated logarithm given a class f of functions on x we can view vn as a stochastic process indexed by f and consider limit theorems for this process to prove such theorems it is often helpful to have bounds on the tail of the r v sup w i n f i see for example dudley 1978 kuelbs and dudley 1980 dudley and phillip 1983 or gine and zinn 1983 our main question of interest is for what classes f can best possible bounds be obtained so first we must ask what are these best possible bounds of course

interpreting and extracting fuzzy decision rules from fuzzy information systems and their inference information systems which contain only crisp data precise and unique attribute values for all objects have been widely investigated due to the fact that in realworld applications imprecise data are abundant uncertainty is inherent in real information systems in this paper information systems are called fuzzy information systems and formalized by objects attributes f in which f is a fuzzy set and expresses some uncertainty between an object and its attribute values to interpret and extract fuzzy decision rules from fuzzy information systems the meta theory based on modal logic proposed by resconi et al is modified the modified meta theory not only expresses uncertainty between objects and their attributes but also uncertainty in the process of recognizing fuzzy information systems in addition according to perception computing proposed by zadeh granules of fuzzy information systems can be represented by fuzzy decision rules so that fuzzy inference methods can be used to obtain the decision attribute of a new object finally a novel way of combining evidences based on the modified meta theory is introduced which extends the concept of combining evidences based on dempster shafer theory

axiomatisation of functional dependencies in incomplete relations abstract incomplete relations are relations which contain null values whose meaning is value is at present unknown such relations give rise to two types of functional dependency fd the first type called the strong fd sfd is satisfied in an incomplete relation if for all possible worlds of this relation the fd is satisfied in the standard way the second type called the weak fd wfd is satisfied in an incomplete relation if there exists a possible world of this relation in which the fd is satisfied in the standard way we exhibit a sound and complete axiom system for both strong and weak fds which takes into account the interaction between sfds and wfds an interesting feature of the combined axiom system is that it is not k ary for any natural number k 0 we show that the combined implication problem for sfds and wfds can be solved in time polynomial in the size of the input set of fds finally we show that armstrong relations exist for sfds and wfds

existence and stability of multidimensional transonic flows through an infinite nozzle of arbitrary cross sections we establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross sections including a slowly varying de laval nozzle the transonic flow is governed by the inviscid potential flow equation with supersonic upstream flow at the entrance uniform subsonic downstream flow at the exit at infinity and the slip boundary condition on the nozzle boundary our results indicate that if the supersonic upstream flow at the entrance is sufficiently close to a uniform flow there exists a solution that consists of a c1 subsonic flow in the unbounded downstream region converging to a uniform velocity state at infinity and a c1 multidimensional transonic shock separating the subsonic flow from the supersonic upstream flow the uniform velocity state at the exit at infinity in the downstream direction is uniquely determined by the supersonic upstream flow and the shock is orthogonal to the nozzle boundary at every point of their intersection in order to construct such a transonic flow we reformulate the multidimensional transonic nozzle problem into a free boundary problem for the subsonic phase in which the equation is elliptic and the free boundary is a transonic shock the free boundary conditions are determined by the rankine hugoniot conditions along the shock we further develop a nonlinear iteration approach and employ its advantages to deal with such a free boundary problem in the unbounded domain we also prove that the transonic flow with a transonic shock is unique and stable with respect to the nozzle boundary and the smooth supersonic upstream flow at the entrance

functional dependencies with null values fuzzy values and crisp values based on the concepts of the semantic proximity we present a definition of the fuzzy functional dependency we show that the inference rules for fuzzy functional dependencies which are the same as armstrong s axioms for the crisp case are correct and complete we also show that dependent constraints with dull values constitute a lattice functional dependencies in classical relational databases and null functional dependencies can be viewed as a special case of fuzzy functional dependencies by applying the unified functional dependencies to the relational database design we can represent the data with fuzzy values null values and crisp values under relational database management systems by using fuzzy functional dependencies we can compress the range of a fuzzy value and make this fuzzy value clearer

extending the akaike information criterion to mixture regression models we examine the problem of jointly selecting the number of components and variables in finite mixture regression models we find that the akaike information criterion is unsatisfactory for this purpose because it overestimates the number of components which in turn results in incorrect variables being retained in the model therefore we derive a new information criterion the mixture regression criterion mrc that yields marked improvement in model selection due to what we call the clustering penalty function moreover we prove the asymptotic efficiency of the mrc we show that it performs well in monte carlo studies for the same or different covariates across components with equal or unequal sample sizes we also present an empirical example on sales territory management to illustrate the application and efficacy of the mrc finally we generalize the mrc to mixture quasi likelihood and mixture autoregressive models thus extending its applicability to non gaussian models discrete responses and d

a constrained formulation of maximum likelihood estimation for normal mixture distributions in this context the normal densities are sometimes referred to as component densities the log likelihood function l zy corresponding to a random sample xl xnj is defined by l ty ek 1 10g pm xk y the first problem associated with maximum likelihood estimation arises from the unboundedness of l qy on r day 1969 a global maximum likelihood estimate always fails to exist in addition the unboundedness of l y causes failures of optimization algorithms of both the em redner and walker 1984 and quasi newton fowlkes 1979 types in spite of the unboundedness of l 4y statistical theory kiefer 1978 guarantees that a particular local maximizer of l y is strongly consistent and asymptotically efficient several local maximizers can exist for a given sample and the other major maximum likelihood difficulty is in determining when the correct one has been found day 1969 noted that spurious maximizers corresponding to parameter points having some component standard deviations very small relative to others are generated by any small number of sample points grouped sufficiently close together the spurious maximizers like the unboundedness of l zy can create difflculties when using the em or quasi newton algorithms the constrained maximum likelihood formulation presented in the next section avoids the unconstrained problems of singularities and spurious maximizers of the type noted by day section 3 contains the statement and proof of a consistency result for the corresponding constrained estimator

data summarization in relational databases through fuzzy dependencies in this paper we deal with the problem of treating with dependencies in relational databases which do not hold in an exact manner as classical functional dependencies but in a weaker sense i e we face with relations which satisfy dependencies such that people with similar age and height have similar weight we model this relationship through the concept of fuzzy dependency we see that these dependencies imply some kind of fuzzy redundancy and in order to avoid it we propose to use a projection operator which leads us to partition a relation r into two projections say r1 and r2 with a less amount of information then we proceed to replace the original relation by these projections in this process we must guarantee that we can recover the data we had in the original relation this will be possible by using a special join operator applied to r1 and r2 we must also guarantee that we can test the fuzzy dependency for new entries to the database in the same way either if we consider the original relation r or if we work with the projections r1 and r2 we also show that this definition of dependency maintains the good properties of completeness of the classical case 1999 elsevier science inc all rights reserved

the dependency preserving decomposition and a testing algorithm in a fuzzy relational data model abstract this paper focuses on one of the fundamental design issues in fuzzy database modeling namely the dependency preserving decomposition in a fuzzy relational data model where imprecision is reflected by possibility distributions for attribute values as well as by closeness relations for domain elements a poor model design can be remedied in many cases by decomposing relation schemes in order to eliminate reduce data redundancy and update anomalies on the other hand the decomposition should guarantee that the semantic knowledge and integrity constraints expressed by fuzzy functional dependency ffd are satisfactorily preserved by the resultant relation schemes based on the concept of ffd transitive closure an algorithm has been developed to test whether a given decomposition is dependency preserving with respect to a given set of ffds finally two special ffd sets one composed of a x 1 to x 1 ffd loop and the other composed of a x 1 x m ffd and a x 1 to x m ffd chain are investigated

a uniform framework for deductive processing of fuzzy information abstract fuzzy logic proposed by zadeh is a mathematical model expressing the degree of uncertainty in terms of possibility distribution in this paper we introduce fuzzy implicit predicate f ip for reconstructing the fuzzy relational database in the logical point of view we demonstrate that this new logic paradigm 1 provides a unified framework integrating various techniques related to fuzzy relational database and 2 provides a way exploiting powerful inference mechanisms to fuzzy data manipulation deductive database and fuzzy prolog can be examples of the inference mechanisms

transonic shock in a nozzle i 2d case in this paper we establish the existence and uniqueness of a transonic shock for the steady flow through a general two dimensional nozzle with variable sections the flow is governed by the inviscid potential equation and is supersonic upstream has no flow boundary conditions on the nozzle walls and an appropriate boundary condition at the exit of the exhaust section the transonic shock is a free boundary dividing two regions of c 1 1 0 flow in the nozzle the potential equation is hyperbolic upstream where the flow is supersonic and elliptic in the downstream subsonic region in particular our results show that there exists a solution to the corresponding free boundary problem such that the equation is always subsonic in the downstream region of the nozzle when the pressure in the exit of the exhaustion section is appropriately larger than that in the entry this problem is motivated by the conjecture of courant and friedrichs on the transonic phenomena in a nozzle 10 furthermore the stability of the transonic shock is also proven when the upstream supersonic flow is a small steady perturbation for the uniform supersonic flow and the corresponding pressure at the exit has a small perturbation the main ingredients of our analysis are a generalized hodograph transformation and multiplier methods for elliptic equation with mixed boundary conditions and comer singularities

reasoning about functional and full hierarchical dependencies over partial relations we study the implication problem for the combined class of functional and full hierarchical dependencies in the presence of sql s not null constraints two different notions of implication are addressed one where a dependency is implied by the given set of dependencies plus the underlying schema and one where a dependency is implied by the given set of dependencies alone we establish axiomatizations for both notions of implication and reveal deep relationships between them

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

supersonic flow onto a solid wedge we consider the problem of two dimensional supersonicflow onto a solid wedge or equivalently in a concave corner formed by two solid walls for mild corners there are two possible steady state solutions one with a strong and one with a weak shock emanating from the corner the weak shock is observed in supersonic flights a longstanding natural conjecture is that the strong shock is unstable in some sense we resolve this issue by showing that a sharp wedge will eventually produce weak shocks at the tip when accelerated to a supersonic speed more precisely we prove that for upstream state as initial data in the entire domain the timedependent solution is self similar with a weak shock at the tip of the wedge we construct analytic solutions for self similar potential flow both isothermal and isentropic with arbitrary 1 in the process of constructing the self similar solution we develop a large number of theoretical tools for these elliptic regions these tools allow us to establish large data results rather than a small perturbation we show that the wave pattern persists as long as the weak shock is supersonic supersonic when this is no longer true numerics show a physical change of behavior in addition we obtain rather detailed information about the elliptic region including analyticity as well as bounds for velocity components and shock tangents c 2007 wiley periodicals inc

two dimensional subsonic euler flows past a wall or a symmetric body the existence and uniqueness of two dimensional steady compressible euler flows past a wall or a symmetric body are established more precisely given positive convex horizontal velocity in the upstream there exists a critical value rho rm cr such that if the incoming density in the upstream is larger than rho rm cr then there exists a subsonic flow past a wall furthermore rho rm cr is critical in the sense that there is no such subsonic flow if the density of the incoming flow is less than rho rm cr the subsonic flows possess large vorticity and positive horizontal velocity above the wall except at the corner points on the boundary moreover the existence and uniqueness of a two dimensional subsonic euler flow past a symmetric body are also obtained when the incoming velocity field is a general small perturbation of a constant velocity field and the density of the incoming flow is larger than a critical value the asymptotic behavior of the flows is obtained with the aid of some integral estimates for the difference between the velocity field and its far field states

fuzzy loss less decompositions in databases in this paper we deal with the problem of defining projection and join operators in the framework of a fuzzy relational database we study the properties of such operators relating to the concept of fuzzy functional dependency there are two main properties to achieve on the one hand if a relation r satisfies a dependency between two sets of attributes x and y then we want to preserve this dependency in the fuzzy projection over xy of r on the other hand we want to test a fuzzy dependency just by looking at this projection therefore such a projection operator must allow us to store the information conveyed in r into a separate relation with fewer tuples in order to define the criterion for fuzzy dependency we shall need to extend a resemblance relation defined for crisp data to the fuzzy case finally we shall introduce a fuzzy join operator which will allow us to recover the information given in a relation from its projections

upper and lower images of a fuzzy set induced by a fuzzy relation applications to fuzzy inference and diagnosis in fuzzy set theory the image of a fuzzy set induced by a fuzzy relation is usually obtained by a sup t norm composition this corresponds to the upper image which gathers the elements in relation with at least one element of the fuzzy set however the dual point of view leading to the definition of the lower image as the fuzzy set of elements in relation with all the elements of the fuzzy set whose image is computed is not often considered fuzzy sets and fuzzy relations depending on the situations can be interpreted either in a conjunctive manner or as subsets of mutually exclusive possible values for variables whose precise values are ill known disjunctive view the applications of upper and lower images are investigated in both interpretations the generalized modus ponens used in fuzzy rule based systems corresponds to the disjunctive view the interest of upper and lower images is also emphasized for diagnosis problems where the conjunctive interpretation is encountered

evaluating flexible criteria on uncertain data abstract modern information management systems and databases are rapidly becoming better equipped for handling data imperfections a common imperfection is uncertainty indicating that a property s exact value is not known ideally such systems can be queried uniformly using flexible criteria regardless of whether the underlying data are uncertain or not the result thereof should always be informative and intuitive and should reflect to what degree the data satisfy the criteria and to which degree this is uncertain in this work we present a novel way to evaluate flexible criteria on uncertain data the result thereof is a distribution of uncertainty over degrees of satisfaction these so called suitability distributions are first constructed for possibilistic data it is shown that they can be used in all scenarios going from regular crisp criteria on certain data to flexible criteria on uncertain data and that they seamlessly generalize other alternatives importantly their interpretation is always the same so they can be used without needing to have prior knowledge regarding the quality of the data afterwards their properties and supported operations are given next it is shown that they can also be applied more broadly for example for probabilistic data examples illustrate their rich semantics ease of use and broad applicability

the study of joins in fuzzy relational databases abstract it is often necessary to join naturally two or more fuzzy relations to answer a user s query however the result of a join may not be what one expects in this paper we study the decomposition problem of fuzzy relation schemes we show that the algorithm proposed by aho et al 1 to test lossless join decomposition for classical relations can be applied in the fuzzy domain when particularizations are induced by functional dependencies

generalizing database relational algebra for the treatment of incomplete or uncertain information and vague queries abstract this paper deals with relational databases which are extended in the sense that fuzzily known values are allowed for attributes precise as well as partial imprecise uncertain knowledge concerning the value of the attributes are represented by means of 0 1 valued possibility distributions in zadeh s sense thus we have to manipulate ordinary relations on cartesian products of sets of fuzzy subsets rather than fuzzy relations besides vague queries whose contents are also represented by possibility distributions can be taken into account the basic operations of relational algebra union intersection cartesian product projection and selection are extended in order to deal with partial information and vague queries approximate equalities and inequalities modeled by fuzzy relations can also be taken into account in the selection operation then the main features of a query language based on the extended relational algebra are presented an illustrative example is provided this approach which enables a very general treatment of relational databases with fuzzy attribute values makes an extensive use of dual possibility and necessity measures

on two dimensional sonic subsonic flow a compensated compactness framework is established for sonic subsonic approximate solutions to the two dimensional euler equations for steady irrotational flows that may contain stagnation points only crude estimates are required for establishing compactness it follows that the set of subsonic irrotational solutions to the euler equations is compact thus flows with sonic points over an obstacle such as an airfoil may be realized as limits of sequences of strictly subsonic flows furthermore sonic subsonic flows may be constructed from approximate solutions the compactness framework is then extended to self similar solutions of the euler equations for unsteady irrotational flows

subsonic sonic limit of approximate solutions to multidimensional steady euler equations a compactness framework is established for approximate solutions to subsonic sonic flows governed by the steady full euler equations for compressible fluids in arbitrary dimension the existing compactness frameworks for the two dimensional irrotational case do not directly apply for the steady full euler equations in higher dimensions the new compactness framework we develop applies for both non homentropic and rotational flows one of our main observations is that the compactness can be achieved by using only natural weak estimates for the mass balance and the vorticity along with the bernoulli law and the entropy relation through a more delicate analysis on the phase space as direct applications we establish two existence theorems for multidimensional subsonic sonic full euler flows through infinitely long nozzles

frontiers for propositional reasoning about fragments of probabilistic conditional independence and hierarchical database decompositions abstract conditional independence provides an essential framework to deal with knowledge and uncertainty in artificial intelligence and is fundamental in probability and multivariate statistics its associated implication problem is paramount for building bayesian networks unfortunately the problem does not enjoy an axiomatization by a finite set of horn rules and is already conp complete to decide for some fragments of conditional independencies saturated conditional independencies form an important fragment whose implication problem is decidable in almost linear time we establish an axiomatization by a finite set of horn rules for the fragment of generalized saturated conditional independencies these state the conditional independence between finitely many sets of random variables the special case of two sets captures geiger and pearl s finite axiomatization for saturated conditional independencies even for this special case our completeness proof is new the proof argument utilizes special probability models where two events have probability one half special probability models allow us to establish an equivalence between the implication of generalized saturated conditional independencies and that of formulae in a boolean propositional fragment this duality is then extended to a trinity including the implication problem of delobel s full first order hierarchical database decompositions already for the independence between two sets of random variables the dualities cannot be extended to cover conditional independencies in general or first order hierarchical decompositions

a fuzzy datalog deductive database system this paper describes a proposal for a deductive database system with fuzzy small mathsf datalog as its query language concepts supporting the fuzzy logic programming system small mathsf bousi sim small mathsf prolog are tailored to the needs of the deductive database system small mathsf des we develop a version of fuzzy small mathsf datalog where programs and queries are compiled to the small mathsf des core small mathsf datalog language weak unification and weak sld resolution are adapted for this setting and extended to allow rules with truth degree annotations we provide a public implementation in small mathsf prolog which is open source multiplatform portable and in memory featuring a graphical user interface a distinctive feature of this system is that unlike others we have formally demonstrated that our implementation techniques fit the proposed operational semantics we also study the efficiency of these implementation techniques through a series of detailed experiments moreover a database example for a recommender system is used to illustrate some of the features of the system and its usefulness

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

unfair coins and necessity measures towards a possibilistic interpretation of histograms this short note defines a bijective mapping which turns a probability measure into a possibility measure this transformation has intuitive grounds especially the converse mapping corresponds to the usual assignment of identical probability values to elementary events of a given set when no information is available

null inclusion dependencies in relational databases abstract functional dependencies fds and inclusion dependencies inds are the most fundamental integrity constraints that arise in practice in relational databases we introduce null inclusion dependencies ninds to cater for the situation when a database is incomplete and contains null values we show that the implication problem for ninds is the same as that for inds we then present a sound and complete axiom system for null functional dependencies nfds and ninds and prove that the implication problem for nfds and ninds is decidable and exptime complete by contrast when no nulls are allowed this implication problem is undecidable this undecidability result has motivated several researchers to restrict their attention to fds and noncircular inds in which case the implication problem was shown to be exptime complete our results imply that when considering nulls in relational database design we need not assume that ninds are noncircular

on a weak solution for a transonic flow problem on essaie d etablir l existence de solutions faibles pour un ecoulement stationnaire bidimensionnel irrotationnel compressible non visqueux dans un canal de longueur infinie ou autour d un profil aerodynamique la vitesse de l ecoulement etant donnee a l infini

measuring properties of fuzzy sets a general technique and its use in fuzzy query evaluation abstract a fuzzy set can be viewed as a weighted max combination or as a convex combination of a family of nested ordinary sets the latter point of view allows the interpretation of a fuzzy set as a consonant random set then any numerical set function applied to a fuzzy set leads to a result which is a random number the expectation attached to this random number provides a scalar evaluation of the fuzzy set with respect to the considered set function this approach is very general and can be used for various kinds of measurements cardinality confidence measures attached to the occurrence of events diameter or perimeter of a fuzzy region distance between two sets etc also the fuzziness of the set to evaluate naturally induces a fuzzy set of possible evaluations and expected values of the lower and upper bounds of this fuzzy set of numbers can be computed the weighted max combination view which leads to another type of scalar evaluation is also briefly discussed in this paper the above approach is more particularly applied to the treatment of queries asking for some global evaluation of a set of items specified by means of a fuzzy property this kind of query can be managed by languages like sql in case of a crisp set of items when this set is fuzzily specified a scalar answer can still be provided as well as a fuzzy valued or interval valued one if we want to keep track of the effect of the fuzziness of the query the case where the data base contains precise information but also the more general case of fuzzy information data bases are considered

steady subsonic ideal flows through an infinitely long nozzle with large vorticity in this paper the existence uniqueness and far field behavior of a class of subsonic flows with large vorticity for the steady euler equations in infinitely long nozzles are established more precisely for any given convex horizontal velocity of incoming flow in the upstream there exists a critical value mcr if the mass flux is larger than mcr then there exists a unique smooth subsonic euler flow through the infinitely long nozzle this well posedness result is proved by a new observation for the method developed in xie and xin siam j math anal 42 751 784 2010 to deal with the euler system furthermore the optimal convergence rates of the subsonic flows at far fields are obtained via the maximum principle and an elaborate choice of the comparison functions

an extended version of the fuzzy relational database model abstract the fuzzy relational database model proposed by buckles and petry is a formal method for organizing and using fuzzy information in relational databases the model possesses two key properties that hold for classical relational databases no two tuples have identical interpretations and each relational algebra operation has a unique result the original fuzzy relational database model was based on similarity relations which were defined on finite scalar domains buckles and petry later extended the model to incorporate fuzzy number domains this extension was done without loss of consistency with the representation or the relational algebra in a recent paper we have extended the original model to proximity relations which generalize similarity relations the key properties of buckles and petry s model are preserved in the extension in this work we demonstrate that the existence of partitions on finite scalar domains in the fuzzy relational model is the key to preserving the important properties of the classical relational model we explain how proximity relations defined on finite scalar domains are used to partition the domains further we show that normal fuzzy sets can be employed as domain values these fuzzy sets become members of fi nite scalar domains and their characteristic functions are employed in generating the proximity relations of the fuzzy relational database model

an extension of classical functional dependency dynamic fuzzy functional dependency abstract relational data model has constituted an incontestable success in database history in this context a lot of attention has been paid to functional dependencies due to their paramount importance in the design of relational database for about fifteen years several attempts to formalize soft real world constraints imposed on the data has been made leading to the emergence of the concept of fuzzy functional dependency in this paper an overview of the different proposals of the fuzzy functional dependency is presented a new extension of classical functional dependency based on the lukasiewicz implication is presented and called dynamic fuzzy functional dependency the associated axiomatic system is introduced and proved to be sound

fuzzy division in fuzzy relational databases an approach an approach to calculate the relational division in fuzzy databases is presented starting with the gefred model the tuples of the division are obtained with a possibility degree that indicates the extent to which they comply with the relational division requisites the results obtained are those expected a priori furthermore in order to formalize this method of fuzzy relational division two new operators are defined which may be useful in other operations the qualified fuzzy intersection and the generalized fuzzy projection with group functions some examples are included in order to clarify the method proposed here and the defined operators a comparison with other fuzzy division approaches that appear in the literature is included too

on the existence of solutions to a one dimensional degenerate nonlinear wave equation abstract this paper is concerned with the degenerate initial boundary value problem to the one dimensional nonlinear wave equation u t t 1 u a u x x which arises in a number of various physical contexts the global existence of smooth solutions to the degenerate problem was established under relaxed conditions on the initial boundary data by the characteristic decomposition method moreover we show that the solution is uniformly c 1 continuous up to the degenerate boundary and the degenerate curve is c 1 continuous for 0 min a 1 a 1 1 a

fuzzy functional dependencies and independencies in extended fuzzy relational database models abstract in this paper we have considered data dependencies more specifically restricted fuzzy functional dependencies in the framework of extended fuzzy relational database model a formal system is presented for the derivation of fuzzy functional dependencies which is both sound and complete the problem of lossless join decomposition is discussed in the framework of extended fuzzy relational model then we introduce a formal statement of fuzzy functional independency which expresses the fact that the corresponding restricted fuzzy functional dependency is not a legitimate constraint of the real world a formal system is presented for the derivation of restricted fuzzy functional dependencies and independencies the various problems such as the membership problem the contradiction problem and the problem of canonical represents are discussed a cover called minimal cover of restricted fuzzy functional independencies is shown to be unique

three dimensional full euler flows in axisymmetric nozzles abstract in this paper we consider global subsonic compressible flows through general infinitely long nozzles the flow is governed by the steady full euler equations we find a new invariant along streamline take advantages of this we reformulate the full euler system into quasilinear second order equations of stream function with the upstream condition and the solid wall boundary condition we obtain the existence uniqueness asymptotic behavior and the critical mass flux

a flexible bipolar querying approach with imprecise data and guaranteed results in this paper we propose an approach to query a database when the user preferences are bipolar i e express both constraints and wishes about the desired result and the data stored in the database are imprecise results are then completely ordered with respect to these bipolar preferences giving priority to constraints over wishes additionally we propose a treatment that allows us to guarantee that any query will return a result even if no element satisfies all constraints specified by the user such a treatment may be useful when user s constraints are unrealistic i e cannot be all satisfied simultaneously and when the user desires a guaranteed result the approach is illustrated on a real world problem concerning the selection of optimal packaging for fresh fruits and vegetables

interaction of four rarefaction waves in the bi symmetric class of the two dimensional euler equations the global existence and structures of solutions to multi dimensional unsteady compressible euler equations are interesting and important open problems in this paper we construct global classical solutions to the interaction of four orthogonal planar rarefaction waves with two axes of symmetry for the euler equations in two space dimensions in the case where the initial rarefaction waves are large the bi symmetric initial data is a basic type of four wave two dimensional riemann problems the solutions in this case are continuous bounded and self similar and we characterize how large the rarefaction waves must be we use the methods of hodograph transformation characteristic decomposition and phase space analysis we resolve binary interactions of simple waves in the process

functional dependencies and constraints on null values in database relations database relations with incomplete information are considered the no information interpretation of null values is adopted due to its characteristics of generality and naturalness coherently with the framework and its motivation two meaningful classes of integrity constraints are studied a functional dependencies which have been widely investigated in the classical relational theory and b constraints on null values which control the presence of nulls in the relations specifically three types of constraints on null values are taken into account nullfree subschemes existence constraints disjunctive existence constraints and the interaction of each of them with functional dependencies is studied in each of the three cases the inference problem is solved the complexity of the algorithms for its solution analyzed and the existence of a complete axiomatization discussed

multivalued dependencies in fuzzy relational databases abstract we show that by using the theory of possibility distribution multivalued dependencies in fuzzy relations can be expressed in the frame work of particularization another definition of functional dependencies in a fuzzy relation is given in terms of fuzzy hamming weight we have also discussed the validity of inference rules for multivalued dependencies in fuzzy relations

fuzzy information in extended fuzzy relational databases abstract the queries on type 2 fuzzy relational databases may get non reasonable answers and as pointed out by buckles a tuple s membership value is not static but is a measure of the appropriateness of that tuple to a given query here we use two supplementary attributes r and i e to model the concepts of fuzziness and uncertainty respectively we also use these two attribute values to compute the appropriateness of a tuple to a given query in this paper the proposed fuzzy relational model is defined by first order logical in our proposed model the classical properties of the database which are 1 database interpretation being redundant free being uniquely determined and 2 the well definedness of relational algebra are preserved for the fuzzy relational algebra therefore the proposed fuzzy relational model can capture more meaning than the conventional approaches and is more suitable to handle the real life application

flexible queries on relational databases using fuzzy logic and ontologies combines fuzzy logic and semantic techniques to perform flexible queries in a relational database alternative method to fuzzy logic to execute flexible queries on non scalar attributes answers are ordered according with the accomplishment degree to the query ontologies are used as an attribute domain frame to return semantically similar information to the query fuzzy logic are used on scalar attributes nowadays there are many proposals that allow users to perform fuzzy queries on relational databases regardless of these proposals fuzzy queries are really useful on scalar values where fuzzy sets can be adjusted to the user needs and domains but non scalar values are a more complex task here we extend non scalar attribute management in fuzzy queries with the use of ontologies thus we allow to compute this kind of queries not only with the similarity relationships defined explicitly on a fuzzy set but with semantically interrelated terms modeled as a domain ontology as well moreover we present the architecture of a novel system that combines both techniques to return an answer as much complete as possible and ordered by a degree of accomplishment finally a qualitative and quantitative study about the use of flexible queries on relational databases is included in this work as well

a note on phillips 1991 a constrained maximum likelihood approach to estimating switching regressions abstract phillips phillips r f 1991 a constrained maximum likelihood approach to estimating switching regressions journal of econometrics 48 241 262 proposed a constrained maximum likelihood approach to estimating the parameters in a switching regression model in this note we propose a new approach which leads to a proof of a more general result than phillips s specifically we prove that the constrained mle cmle is still strongly consistent when the constant c decreases to 0 at the rate of exp n 1 2 log n as n increases to with 1 we also suggest a suitable hence c n for practice based on simulation results

fuzzy relations and fuzzy relational databases abstract this paper deals with the connections existing between fuzzy set theory and fuzzy relational databases our new result dealing with fuzzy relations is how to calculate the greatest lower bound glb of two similarity relations our main contributions in fuzzy relational databases are establishing from fuzzy set theory what a fuzzy relational database should be the result is both surprising and elegant and making fuzzy relational databases even more robust our work in fuzzy relations and in fuzzy databases had led us into other interesting problems two of which we mention in this paper the first is primarily mathematical and the second provides yet another connection between fuzzy set theory and artificial intelligence in understanding similarity relations in terms of other fuzzy relations and in making fuzzy databases more robust we work with closure and interior operators we present some important properties of these operators in establishing the connection between fuzzy set theory and artificial intelligence we show that an abstraction on a set is in fact a partition on the set that is an abstraction defines an equivalence relation on the underlying set

flexible querying in a relational framework supported by possibilistic logic traditionally flexible querying systems are supported by a logical framework that is based on satisfaction degrees alternatively certainty about query satisfaction can also be modelled by possibility and necessity measures this approach was extended by our group in order to handle the cases of missing information more adequately in this paper it is presented how our extended logical framework can be used to support flexible querying on conventional relational databases the handling of preferences both inside elementary query conditions and between query conditions is presented as well as the extension of the traditional selection projection and join operators motivated examples are provided to illustrate the used concepts

global shock waves for the supersonic flow past a perturbed cone we prove the global existence of a shock wave for the stationary supersonic gas flow past an infinite curved and symmetric cone the flow is governed by the potential equation as well as the boundary conditions on the shock and the surface of the body it is shown that the solution to this problem exists globally in the whole space with a pointed shock attached at the tip of the cone and tends to a self similar solution under some suitable conditions our analysis is based on a global uniform weighted energy estimate for the linearized problem combining this with the local existence result of chen li 1 we establish the global existence and decay rate of the solution to the nonlinear problem

comparison of fuzzy reasoning methods l a zadeh e h mamdani and m mizumoto et al have proposed methods for fuzzy reasoning in which the antecedent involves a fuzzy conditional proposition if x is a then y is b with a and b being fuzzy concepts mizumoto et al have investigated the properties of their methods in the case of generalized modus ponens this paper deals with the properties of their methods in the case of generalized modus tollens and investigates the other new fuzzy reasoning methods obtained by introducing the implication rules of many valued logic systems finally the properties of syllogism and contrapositive are investigated under each fuzzy reasoning method

incomplete conjunctive information abstract many information systems capable of handling incomplete or fuzzy information manipulate objects with single valued attributes information is then said to be disjunctive information is said to be conjunctive when pertaining to many valued attributes while a piece of incomplete disjunctive information is easily represented by means of a set of mutually exclusive possible values modeling incomplete conjunctive information theoretically leads to consider families of sets since attributes are then set valued under complete information some proposals are made in order to efficiently and rigorously represent incomplete conjunctive information and deal with query evaluation especially in the case where only upper and or lower bounds of the set of values of a many valued attribute are known applications of this approach can be expected for the processing of time intervals as well as spatial reasoning among other topics in knowledge base management

markov switching model selection using kullback leibler divergence abstract in markov switching regression models we use kullback leibler kl divergence between the true and candidate models to select the number of states and variables simultaneously specifically we derive a new information criterion markov switching criterion msc which is an estimate of kl divergence msc imposes an appropriate penalty to mitigate the over retention of states in the markov chain and it performs well in monte carlo studies with single and multiple states small and large samples and low and high noise we illustrate the usefulness of msc via applications to the u s business cycle and to media advertising

interweaving algebra and topology lattice valued topological systems this paper is primarily dedicated to understanding the natural role that topological systems and lattice valued topological systems play in understanding the relationship between algebra and topology a relationship expressed by an interweaving of embeddings of essentially algebraic and topological categories this natural role is revealed by how various categories for systems relate to locales topological spaces and various categories for lattice valued topology

proximity relations in the fuzzy relational database model abstract the fuzzy relational model of buckles and petry is a rigorous scheme for incorporating non ideal or fuzzy information in a relational database in addition to providing a consistent scheme for representing fuzzy information in the relational structure the model possesses two critical properties that hold for classical relational databases these properties are that no two tuples have identical interpretations and each relational operation has a unique result the fuzzy relational model relies on similarity relations for each scalar domain in the fuzzy database these relations are reflexive symmetric and max min transitive in addition to introducing fuzziness into the relational model each similarity relation induces equivalence classes in its domain it is the existence of these equivalence classes that provides the model with the important properties possessed by classical relational databases in this paper we extend the fuzzy relational database model of buckles and petry to deal with proximity relations for scalar domains since reflexivity and symmetry are the only constraints placed on proximity relations they generalize the notion of similarity relations we show that it is possible to induce equivalence classes from proximity relations thus the nice properties of the fuzzy relational model of buckles and petry are preserved furthermore the removal of the max min transitivity restriction also provides database users with more freedom to express their value structures

multivalued dependencies in fuzzy relational databases and lossless join decomposition abstract the fuzzy multivalued dependency is defined on the lines of classical multivalued dependency to resolve the redundancy and inconsistency in fuzzy databases the implication problem of fmvd s has been examined and a set of sound and complete inference axioms has been proposed we next examine lossless join problem of fuzzy relations in the presence of fuzzy functional depandencies and fuzzy multivalued dependencies and obtain decomposition of relation schemes

efficient refinement of uncertain data by fuzzy integrity constraints abstract fuzzy data models were proposed to handle uncertain data based on a set of fuzzy functional dependencies the fuzzy values in a fuzzy relation may be refined into clearer ones in this paper we develop efficient algorithms for the refinement process a dependency graph is defined for a set of fuzzy functional dependencies by this graph an efficient refinement sequence can be determined these algorithms are proved correct and efficient

on the impact of regular functional dependencies when moving to a possibilistic database framework this paper is situated in the area of fuzzy databases i e databases containing imprecise information more precisely it deals with the notion of a functional dependency when data involved in this type of property are possibly imprecise contrary to previous works the idea is not to fuzzify the concept of a functional dependency in the view suggested here we rather consider regular functional dependencies and we study the impact of the presence of such fds on the insertion and handling of imprecise data

non transitive fuzzy dependencies i in this work we deal with the problem of defining projection and join operators in a fuzzy database so that they allow us to compress the information given in a relation r of such a database such a compression is possible when a relation satisfies one kind of fuzzy functional dependency f f d such projection and join operators allow us to decompose the original relation r into two new relations in such a way that the amount of information to store is less than originally with r in this process of decomposition there are two main properties to be achieved on the one hand we must be able to test the fuzzy dependency just by looking at one of the projections as it has less records than r this represents a computational advantage on the other hand the join of both projections is such that we can recover the information we had in r but with fuzzier values in order to measure the degree of increasing fuzziness the concept of granularity level is used the definition of fuzzy dependency does not verify the transitivity inference axiom

on a degenerate mixed type boundary value problem to the 2 d steady euler equation abstract this paper is concerned with the structure of sonic supersonic solutions near sonic curves arising from the transonic channel flow problems in gas dynamics given two smooth curves one of which is a sonic curve and the other is a characteristic curve we construct a local classical supersonic solution for the two dimensional steady euler equations in the angular region a novel set of dependent and independent variables are introduced to transform the euler equations into a linear system with explicitly singularity regularity structures we use the iteration method to establish the existence and uniqueness of smooth solutions for the new system and then express the solution in terms of the original variables

on the structure of armstrong relations for functional dependencies an armstrong relation for a set of functional dependencies fds is a relation that satisfies each fd implied by the set but no fd that is not implied by it the structure and size number of tuples of armstrong relatsons are investigated upper and lower bounds on the size of minimal sized armstrong relations are derived and upper and lower bounds on the number of distinct entries that must appear m an armstrong relation are given it is shown that the time complexity of finding an armstrong relation gwen a set of functional dependencies is precisely exponential in the number of attributes also shown s the falsity of a natural conjecture which says that almost all relations obeying a given set of fds are armstrong relations for that set of fds finally armstrong relations are used to generahze a result obtained by demetrovics using quite complicated methods about the possible sets of keys for a relauon

a domain calculus for fuzzy relational databases abstract a complete relational calculus is introduced for similarity based fuzzy relational databases the ordinary domain calculus is chosen as the basis from which to develop the fuzzy counterpart because it tends to be closer to natural language than tuple calculus a constructive proof is used to show that the fuzzy relational algebra can be mapped into the calculus the proof is significant from the standpoint of demonstrating implementability of the calculus as a query language

equivalence and transformation of extended algebraic operators in fuzzy relational databases relational algebra serves as the theoretical basis for database design and queries this paper extends our efforts on fuzzy relational algebraic operations under a fuzzy relational data model namely extended possibility based model with a more general setting of fuzzy relational algebraic operators some properties of the operators are investigated including equivalent definitions and transformation rules of the operators these properties are important and desirable for processing queries in an effective and efficient manner

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

twofold fuzzy sets and rough sets some issues in knowledge representation abstract this paper deals with the representation of sets where the membership of some elements may be ill known rather than just a matter of degree as in a fuzzy set the notion of a twofold fuzzy set is introduced when the relevant information for determining the membership status is incomplete a twofold fuzzy set is made of a nested pair of fuzzy sets the one which gathers the elements which more or less necessarily belong and the one which gathers the elements which more or less possibly belong twofold fuzzy sets are compared from a frontal and from a semantical point of view with other proposals and particularly with the notion of a rough set recently introduced by pawlak set operations of twofold fuzzy sets are discussed and the cardinality of a twofold fuzzy set is defined twofold fuzzy relations are also introduced finally various applications of twofold fuzzy sets in knowledge representation are briefly discussed

gefred a generalized model of fuzzy relational databases abstract in this paper we present a fuzzy relational databases model whose main characteristics are the integration of previous models in the same framework representation capabilities for a wide series of fuzzy information and a coherent and flexible handling of it this model aims to solve each problem of representation and handling of fuzzy information taking into account its specific nature and hence it allows the user to choose the comparison operator and the fuzzy compatibility measure to be used in a query besides it permits the user to specify the precision with which the conditions involved in a query are satisfied

some properties of extended fuzzy preference relations using modalities abstract a fuzzy preference relation is extended to six kinds of relations between fuzzy sets the properties of the six extended relations are investigated especially a sufficient condition for reducing the extended relations to four kinds is discussed when fuzzy sets are bounded and normal and some examples are given to illustrate it further a sufficient condition for the extended negative relations to coincide with the extended inverse relations is described