numerical computations of coarsening in the one dimensional cahn hilliard model of phase separation time dependent solutions of the cahn hilliard equation are studied numerically in particular heteroclinic orbits which connect different equilibrium solutions at t and t are sought thus boundary value problems in space time are computed this computation requires an investigation of the stability of equilibria since projections onto the stable and unstable manifolds determine the boundary conditions at t and t this stability analysis is then followed by solution of the appropriate boundary value problem in space time the results obtained cannot be found by standard initial value simulations by specifying the two steady states at t appropriately it is possible to find orbits reflecting a given degree of coarsening over the time evolution this gives a clear picture of the dynamic coarsening admissible in the equation it also provides an understanding of orbits on the global attractor for the equation

an efficient numerical method for the solution of sliding contact problems in this paper an efficient numerical method to solve sliding contact problems is proposed explicit formulae for the gauss jacobi numerical integration scheme appropriate for the singular integral equations of the second kind with cauchy kernels are derived the resulting quadrature formulae for the integrals are valid at nodal points determined from the zeroes of a jacobi polynomial gaussian quadratures obtained in this manner involve fixed nodal points and are exact for polynomials of degree 2n 1 where n is the number of nodes from this gauss jacobi quadrature the existing gauss chebyshev quadrature formulas can be easily derived another apparent advantage of this method is its ability to capture correctly the singular or regular behaviour of the tractions at the edge of the region of contact also this analysis shows that once if the total normal load and the friction coefficient are given the external moment m and contact eccentricity e for incomplete contact in fully sliding contact are uniquely determined finally numerical solutions are computed for two typical contact cases including sliding hertzian contact and a sliding contact between a flat punch with rounded corners pressed against the flat surface of a semi infinite elastic solid these results provide a demonstration of the validity of the proposed method copyright 2005 john wiley sons ltd

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

spinodal decomposition for the cahn hilliard equation in higher dimensions nonlinear dynamics this paper addresses the phenomenon of spinodal decomposition for the cahn hilliard equation where n n 1 2 3 is a bounded domain with sufficiently smooth boundary and f is cubic like for example f u u u 3 based on the results of 26 the nonlinear cahn hilliard equation will be discussed this equation generates a nonlinear semiflow in certain affine subspaces of h 2 in a neighborhood u e with size proportional to e n around the constant solution where lies in the spinodal region we observe the following behavior within a local inertial manifold containing there exists a finite dimensional invariant manifold which dominates the behavior of all solutions starting with initial conditions from a small ball around with probability almost 1 the dimension of is proportional to e n and the elements of exhibit a common geometric quantity which is strongly related to a characteristic wavelength proportional to e

weighted minimum and maximun operations in fuzzy sets theory abstract this short note comments on the interpretation of weighted minimum and maximum operations introduced in a previous paper as medians and corrects a misleading statement about it

pattern formation in a nonlinear model for animal coats abstract several models have been proposed for describing the formation of animal coat patterns we consider reaction diffusion models due to murray which rely on a turing instability for the pattern selection in this paper we describe the early stages of the pattern formation process for large domain sizes this includes the selection mechanism and the geometry of the patterns generated by the nonlinear system on one two and three dimensional base domains these results are obtained by an adaptation of results explaining the occurrence of spinodal decomposition in materials science as modeled by the cahn hilliard equation we use techniques of dynamical systems viewing solutions of the reaction diffusion model in terms of nonlinear semiflows our results are applicable to any parabolic system exhibiting a turing instability

topological microstructure analysis using persistence landscapes phase separation mechanisms can produce a variety of complicated and intricate microstructures which often can be difficult to characterize in a quantitative way in recent years a number of novel topological metrics for microstructures have been proposed which measure essential connectivity information and are based on techniques from algebraic topology such metrics are inherently computable using computational homology provided the microstructures are discretized using a thresholding process however while in many cases the thresholding is straightforward noise and measurement errors can lead to misleading metric values in such situations persistence landscapes have been proposed as a natural topology metric common to all of these approaches is the enormous data reduction which passes from complicated patterns to discrete information it is therefore natural to wonder what type of information is actually retained by the topology in the present paper we demonstrate that averaged persistence landscapes can be used to recover central system information in the cahn hilliard theory of phase separation more precisely we show that topological information of evolving microstructures alone suffices to accurately detect both concentration information and the actual decomposition stage of a data snapshot considering that persistent homology only measures discrete connectivity information regardless of the size of the topological features these results indicate that the system parameters in a phase separation process affect the topology considerably more than anticipated we believe that the methods discussed in this paper could provide a valuable tool for relating experimental data to model simulations

an approach to solve division like queries in fuzzy object databases the division operator is well known in the context of fuzzy relational databases fuzzy approaches to this operator can be found in the literature to solve flexible queries these approaches try to compute to which extent each element of a candidate set is connected with a given fuzzy set of elements this kind of queries is also interesting in the framework of fuzzy object databases where the management of complex objects instead of plain tuples causes additional difficulties the presence of fuzzily described objects in the database makes necessary to use suitable operators that take into account the resemblance that governs the comparison in the underlying reference universe in this paper we propose a method to solve this type of queries founded on the use of fuzzy inclusion operators we study two different alternatives for the way resemblance is considered and we also analyze the role of cardinality in the process

on the use of interpolative quadratures for hypersingular integrals in fracture mechanics the implementation of finitepart integration of hypersingular boundary integrals is discussed in the context of the applications in engineering fracture mechanics the approach uses a formulation o

unexpectedly linear behavior for the cahn hilliard equation this paper gives theoretical results on spinodal decomposition for the cahn hillard equation we prove a mechanism which explains why most solutions for the cahn hilliard equation starting near a homogeneous equilibrium within the spinodal interval exhibit phase separation with a characteristic wavelength when exiting a ball of radius r namely most solutions are driven into a region of phase space in which linear behavior dominates for much longer than expected the cahn hilliard equation depends on a small parameter epsilon modeling the atomic scale interaction length we quantify the behavior of solutions as epsilon rightarrow 0 specifically we show that most solutions starting close to the homogeneous equilibrium remain close to the corresponding solution of the linearized equation with relative distance o epsilon 2 n 2 up to a ball of radius r in the h 2 omega norm where r is proportional to epsilon 1 rho n 4 as epsilon to 0 here n in 1 2 3 denotes the

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

frictional contact problem for a rigid cylindrical stamp and an elastic layer resting on a half plane abstract the frictional contact problem for a layer resting on a homogeneous half plane is handled using linear elasticity theory in this study the layer is in contact with a rigid cylindrical stamp that is on the layer and applies a concentrated force in the normal and tangential directions friction between the component couples of layer stamp and layer half plane is taken into account the problem is reduced to a system of singular integral equations in which the contact pressures and the contact areas are the unknowns and it is treated using fourier transforms and the boundary conditions for the problem the system of singular integral equations is solved numerically using the gauss jacobi integration formula with equilibrium and consistency conditions numerical results for the contact pressures and the contact areas are given as a solution for both the frictional and the frictionless cases this work is the first study that investigates the effect of friction on the receding contact problem of a layer and a half plane with two contact areas

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

axiomatisation of fuzzy multivalued dependencies in a fuzzy relational data model the concept of fuzzy multivalued dependencies fmvds is introduced it is concluded that fmvds are more generalised than classical multivalued dependencies a set of sound and complete inference rules similar to armstrong s axioms are proposed to derive more dependencies from a given set of fmvds with reference to fmvds inter relationships between two tuple subrelations and the relation to which they belong have been established the proof procedures for the inference rules are based on these relationships

maximum norms of random sums and transient pattern formation many interesting and complicated patterns in the applied sciences are formed through transient pattern formation processes in this paper we concentrate on the phenomenon of spinodal decomposition in metal alloys as described by the cahn hilliard equation this model depends on a small parameter and one is generally interested in establishing sharp lower bounds on the amplitudes of the patterns as the parameter approaches zero recent results on spinodal decomposition have produced such lower bounds unfortunately for higher dimensional base domains these bounds are orders of magnitude smaller than what one would expect from simulations and experiments the bounds exhibit a dependence on the dimension of the domain which from a theoretical point of view seemed unavoidable but which could not be observed in practice in this paper we resolve this apparent paradox by employing probabilistic methods we can improve the lower bounds for certain domains and remove the dimension dependence we thereby obtain optimal results which close the gap between analytical methods and numerical observations and provide more insight into the nature of the decomposition process we also indicate how our results can be adapted to other situations

the set of fuzzy rational numbers and flexible querying a fuzzy bag is a bag in which each occurrence of an element is associated with a grade of membership this notion can be viewed as a generalization of the concepts of set fuzzy set and bag the set of fuzzy integers n f provides a general characterization in which all these different concepts are treated in a uniform way and can then be composed in the field of databases the use of fuzzy bags is motivated by their ability to manage both quantities and preferences however n f becomes too restricted a framework when dealing with queries based on difference or division operations so a more general structure based on the set of fuzzy relative integers z f in which exact differences can be performed has been first developed in this paper we carry on with this approach and we extend z f to the set of fuzzy rational numbers q f this context leads to define a closed system of multiplicative operations and allows to perform exact divisions applied to flexible querying of databases q f and the notion of division on fuzzy numbers allow to generalize the relational division they define a sound basis for queries involving ratios between quantities

prevalence a translation invariant almost every on infinite dimensional spaces we present a measure theoretic condition for a property to hold almost everywhere on an infinite dimensional vector space with particularemphasis on function spaces such as c k and l p like the concept of lebesgue almost every on an infinite dimensional spaces our notion of prevalence is translation invariant instead of using a specific measure on the entire space we define prevalence in terms of the class of all probability measures with compact support prevalence is a more appropriate condition than the topological concepts of open and dense or generic when one desires a probabilistic result on the likelihood of a given property on a function space

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

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

monte carlo simulations for spinodal decomposition this paper addresses the phenomenon of spinodal decomposition for the cahn hilliard equation namely we are interested in why most solutions to the cahn hilliard equation which start near a homogeneous equilibrium u 0 in the spinodal interval exhibit phase separation with a characteristic wavelength when exiting a ball of radius r in a hilbert space centered at u 0 there are two mathematical explanations for spinodal decomposition due to grant and to maier paape and wanner in this paper we numerically compare these two mathematical approaches in fact we are able to synthesize the understanding we gain from our numerics with the approach of maier paape and wanner leading to a better understanding of the underlying mechanism for this behavior with this new approach we can explain spinodal decomposition for a longer time and larger radius than either of the previous two approaches a rigorous mathematical explanation is contained in a separate paper our approach is to use monte carlo simulations to examine the dependence of r the radius to which spinodal decomposition occurs as a function of the parameter e of the governing equation we give a description of the dominating regions on the surface of the ball by estimating certain densities of the distributions of the exit points we observe and can show rigorously that the behavior of most solutions originating near the equilibrium is determined completely by the linearization for an unexpectedly long time we explain the mechanism for this unexpectedly linear behavior and show that for some exceptional solutions this cannot be observed we also describe the dynamics of these exceptional solutions

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

spinodal decomposition for the cahn hilliard equation in higher dimensions part i probability and wavelength estimate this paper is the first in a series of two papers addressing the phenomenon of spinodal decomposition for the cahn hilliard equation where is a bounded domain with sufficiently smooth boundary and f is cubic like for example f u u u3 we will present the main ideas of our approach and explain in what way our method differs from known results in one space dimension due to grant 26 furthermore we derive certain probability and wavelength estimates the probability estimate is needed to understand why in a neighborhood of a homogeneous equilibrium u0 of the cahn hilliard equation with mass in the spinodal region a strongly unstable manifold has dominating effects this is demonstrated for the linearized equation but will be essential for the nonlinear setting in the second paper 37 as well moreover we introduce the notion of a characteristic wavelength for the strongly unstable directions

relaxing constraints in enhanced entity relationship models using fuzzy quantifiers while various articles about fuzzy entity relationship er and enhanced entity relationship eer models have recently been published not all examine how the constraints expressed in the model may be relaxed in this paper our aim is to relax the constraints which can be expressed in a conceptual model using the modeling tool so that these constraints can be made more flexible we will also study new constraints that are not considered in classic eer models we use the fuzzy quantifiers which have been widely studied in the context of fuzzy sets and fuzzy query systems for databases in addition we shall examine the representation of these constraints in an eer model and their practical repercussions the following constraints are studied the fuzzy participation constraint the fuzzy cardinality constraint the fuzzy completeness constraint to represent classes and subclasses the fuzzy cardinality constraint on overlapping specializations fuzzy disjoint and fuzzy overlapping constraints on specializations fuzzy attribute defined specializations fuzzy constraints in union types or categories and fuzzy constraints in shared subclasses we shall also demonstrate how fuzzy min max notation can substitute the fuzzy cardinality constraint but not the fuzzy participation constraint all these fuzzy constraints have a new meaning they offer greater expressiveness in conceptual design and are included in the so called fuzzy eer model

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

second phase spinodal decomposition for the cahn hilliard cook equation we consider the dynamics of a nonlinear partial differential equation perturbed by additive noise assuming that the underlying deterministic equation has an unstable equilibrium we show that the nonlinear stochastic partial differential equation exhibits essentially linear dynamics far from equilibrium more precisely we show that most trajectories starting at the unstable equilibrium are driven away in two stages after passing through a cylindrical region most trajectories diverge from the deterministic equilibrium through a cone shaped region which is centered around a finite dimensional subspace corresponding to strongly unstable eigenfunctions of the linearized equation and on which the influence of the nonlinearity is surprisingly small this abstract result is then applied to explain spinodal decomposition in the stochastic cahn hilliard cook equation on a domain g this equation depends on a small interaction parameter e 0 and one is generally interested in asymptotic results as e 0 specifically we show that linear behavior dominates the dynamics up to distances from the deterministic equilibrium which can reach e 2 dim g 2 with respect to the h 2 g norm

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

on a fuzzy bipolar relational algebra this paper presents an extension of relational algebra suitable for the handling of bipolar concepts the type of queries considered involves two parts a first one which expresses a possibly flexible constraint and a second one that corresponds to a possibly flexible wish the framework considered is that of bipolar fuzzy relations where each tuple is associated with a pair of satisfaction degrees

semantics of quotient operators in fuzzy relational databases abstract the quotient operator plays an important role for query evaluation in relational databases its extension to fuzzy databases raises the question of the intended interpretation of the intermediary degrees attached to the items in the fuzzy relations this note points out that the fuzzy quotient operator should be defined in slightly different ways depending on the possible interpretations of the degrees levels of satisfaction of a gradual property levels of importance of a required property uncertainty pertaining to the membership of an element to a subset

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

tolerant division queries and possibilistic database querying this article is situated in the framework of the relational model of data and it focuses on two quite orthogonal issues even if one may reasonably think that they can be mixed together the first topic is concerned with non traditional queries called flexible or fuzzy queries the key idea here is to introduce preferences inside queries addressed to a database thanks to fuzzy predicates so doing the user can express that some values are preferred to others but also that some criteria are more important than others this idea of preferences is especially illustrated with several extensions of the division operation the second question tackled is about the handling and querying of possibilistic databases basically a possibilistic database is similar to a regular one except that some attribute values are ill known and represented as possibility distributions in such a case it turns out that the set of queries that can be posed to the database with acceptable performances is significantly reduced with respect to the usual relational algebra however it is shown that diverse types of queries of interest against possibilistic databases can be envisaged

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 extended fuzzy relational model with proximity relations in this paper shenoi and melton s model of fuzzy relational database is considered proximity relation being an important tool of the model is characterized theoretically an optimal distribution in 0 1 and consequently the domain partition are defined and studied with examples on fuzzy queries

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

fuzzy relational compositions abstract this paper investigates the fuzzy relational compositions defined by bandler and kohout it is indicated that these compositions have to be modified in order to capture the desired interpretation several alternative definitions are suggested and discussed the paper concludes with an overview of the properties of these improved fuzzy relational compositions

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

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

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

retrieving images in fuzzy object relational databases using dominant color descriptors in this paper a fuzzy approach for image retrieval on the basis of color features is presented the proposal deals with vagueness in the color description and introduces the use of fuzzy database models to store and retrieve imprecise data to face the color description the concept of dominant fuzzy color is proposed using linguistic labels for representing the color information in terms of hue saturation and intensity to deal with fuzzy data in our database model we use a general approach which can support the manipulation of fuzzy objects in an object relational database system this allows the retrieval of images by performing flexible queries on the database

flexible queries in relational databases the example of the division operator abstract allowing for flexible queries enables database users to express preferences inside minimal requirements and if necessary priorities inside compound queries in other words clear cut properties can be refined by ordering the interpretations compatible with them according to user s preferences often the representation of these preferences can be viewed as modelling linguistic like terms in requests in this paper the theoretical issues raised by the introduction of flexible queries are studied in the case of the division operator in the framework of fuzzy sets and possibility theory the notion of division is well known in the context of regular relations and the extension of this operation to fuzzy relations induced by the flexible queries is investigated several types of extended divisions can be envisaged depending on the meaning of the grades attached to the tuples of the fuzzy relations degree of fulfillment of gradual properties level of importance of components in a query or uncertainty pervading data we focus on the first two meanings which are associated with different multiple valued logic implications and we examine their properties and their expression in the framework of an extended sql like language where no specific construct for the division is available

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

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

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

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

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

fundamental formulation for frictional contact problems of coated systems abstract the plane problem about surface loading of an elastic layer perfectly bonded to an elastically dissimilar half plane is considered the fundamental solutions for concentrated forces acting perpendicular and parallel to the layer surface are obtained the stress and displacement fields in the coating layer and the substrate due to these concentrated forces are found on the basis of these expressions the fundamental integral equations are obtained which describe the frictional contact between an elastic body and a coated substrate from the fundamental integral equations a series of integral equations for special cases are deduced corresponding to practical contact situations finally the numerical results for a typical example are given to demonstrate the validity of the fundamental equations and numerical procedures given in this paper

spinodal decomposition for the cahn hilliard cook equation this paper gives theoretical results on spinodal decomposition for the stochastic cahn hilliard cook equation which is a cahn hilliard equation perturbed by additive stochastic noise we prove that most realizations of the solution which start at a homogeneous state in the spinodal interval exhibit phase separation leading to the formation of complex patterns of a characteristic size