a unifying study between modal like operators topologies and fuzzy sets the paper presents the essential connections between modal like operators topologies and fuzzy sets we show for example that each fuzzy set determines a preorder and an alexandrov topology and that similar correspondences hold also for the other direction further a category for preorder based fuzzy sets is defined and it is shown that its equivalent subcategory of representatives is isomorphic to the categories of preordered sets and alexandrov spaces moreover joins meets and complements for the objects in this category of representatives are determined this suggests how to define for fuzzy subsets of a certain universe the lattice operations in a canonical way

a note on specialization l preorder of l topological spaces l fuzzifying topological spaces and l fuzzy topological spaces it is shown that for any spatial frame l i e l is a complete lattice generated by the set of all prime elements both the specialization l preorder of l topological spaces introduced by lai and zhang fuzzy preorder and fuzzy topology fuzzy sets and systems 157 2006 1865 1885 and that of l fuzzifying topological spaces introduced by fang and qiu fuzzy orders and fuzzifying topologies internat j approx reasoning 48 2008 98 109 are special cases of that of l fuzzy topological spaces introduced by fang i fuzzy alexandrov topologies and specialization orders fuzzy sets and systems 158 2007 2359 2374

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

implication structures fuzzy subsets and enriched categories we show that there are natural ways to make a fuzzy set into an enriched category and that in doing so some basic results in fuzzy set theory are applications of enriched category theory thus we argue that the theory of enriched categories is a useful tool for fuzzy set theorists

partial ordering in l underdeterminate sets abstract the purpose of this paper is to improve results on fuzzy partial orderings obtained by zadeh in 9 we overcome the difficulties connected with the axioms of antisymmetry and linearity moreover if the underlying lattice l is a complete residuated lattice we establish a szpilrajn theorem i e any l fuzzy partial ordering has a linear extension in opposition to zadeh s our point of view is that an axiom of antisymmetry without a reference to a concept of equality is meaningless therefore we first introduce the category lus cf 2 which can be considered as a mathematical model of fuzzy equality and subsequently we specify the axioms of l fuzzy partial orderings with respect to the frame given by lus the axioms we use clearly display the usefulness of having a zadeh like complementation and as a consequence the usefulness of a positivistic and nonintuitionistic frame of study an example concerning l rn which we give clearly shows that the lus version of the szpilrajn theorem cannot be reduced to a fuzzification of an already existing theorem but provides us with additional information

a comparative study of ideals in fuzzy orders abstract this paper presents a comparative study of three kinds of ideals in quantale valued order theory forward cauchy ideals generated by forward cauchy nets flat ideals and irreducible ideals main results include necessary and sufficient conditions for forward cauchy ideals to be flat or irreducible for integral quantales

enriched categories and many valued preorders a question from programming arises if bitstring x compares with bitstring y to some degree and if bitstring y satisfies predicate a to some degree then how should the possibility be mathematically modeled that bitstring x satisfies predicate a to at least some degree related to both and mathematically modeling this question is surprisingly intricate when the underlying conjunctions e g of predicates are non commutative potential applications of this question occur in data mining a field in which pattern matching is important and commonly used this paper uses ideas from enriched categories over monoidal categories to address such issues and enable pattern matching techniques to extend to many valued contexts equipped with non commutative conjunctions first we consider the notion of a set enriched by a po monoid l which turns out to be a set equipped with an l valued preorder second we extend the notion of enriched functors to formulate the appropriate definition of variable basis morphisms between preordered sets over different lattice theoretic bases third we construct the notion of topological systems enriched with many valued preorders and use their extent spaces to motivate and formulate enriched or preordered topological spaces the compatibility or enrichment axioms for such systems and spaces model the programming question stated above using non commutative tensor products en route are determined a number of related notions and results many valued antisymmetry characterizes the l t0 separation axiom many valued preorders are categorically topological and many valued partial orders are monotopological enriched topological spaces form a topological category a large inventory of example classes is provided including programming examples and an extensive discussion of examples based on the l spectra of complete po groupoids and each of these related developments is provided a suitable lattice theoretic and categorical foundation

the categorical topology approach to fuzzy topology and fuzzy convergence it is the purpose of this paper to have a look at fuzzy topology from the point of view of categorical topology we first look at interesting subcategories of fts and determine whether they are bireflective and or coreflective we also describe the set of all subcategories of fts which are at the same time bireflective and coreflective due to the fact that top is one of these subcategories of fts ffs itself can be neither cartesian closed nor extensional we therefore secondly construct a supercategory of bts which is a topological quasitopos the construction of this quasitopos is based on the theory of convergence in fts

triangular norms position paper ii general constructions and parameterized families this second part out of three of a series of position papers on triangular norms for part i see triangular norms position paper i basic analytical and algebraic properties fuzzy sets and systems in press deals with general construction methods based on additive and multiplicative generators and on ordinal sums also included are some constructions leading to non continuous t norms and a presentation of some distinguished families of t norms

closedness of the category of liminf complete fuzzy orders it is shown that the category of liminf complete fuzzy orders and liminf continuous maps valued in the complete residuated lattice based on a continuous t norm on the unit interval is monoidal closed and that this category is cartesian closed if and only if the t norm is the minimum

damage analysis and dynamic response of elasto plastic laminated composite shallow spherical shell under low velocity impact based on the elasto plastic mechanics the damage analysis and dynamic response of an elasto plastic laminated composite shallow spherical shell under low velocity impact are carried out in this paper firstly a yielding criterion related to spherical tensor of stress is proposed to model the mixed hardening orthotropic material and accordingly an incremental elasto plastic damage constitutive relation for the laminated shallow spherical shell is founded when a strain based hashin failure criterion is applied to assess the damage initiation and propagation secondly using the presented constitutive relations and the classical nonlinear shell theory a series of incremental nonlinear motion equations of orthotropic moderately thick laminated shallow spherical shell are obtained the questions are solved by using the orthogonal collocation point method newmark method and iterative method synthetically finally a modified elasto plastic contact law is developed to determine the normal contact force and the effect of damage geometrical parameters elasto plastic contact and boundary conditions on the contact force and the dynamic response of the structure under low velocity impact are investigated

interpolation of fuzzy data analytical approach and overview we propose a general framework for the interpolation problem our framework stems from the classical elaboration of the problem we introduce the notion of an interpolating fuzzy function and show how this function can be characterized we examine and analyze previously published fuzzy interpolation algorithms to choose those algorithms that can be represented analytically we also propose an analytic solution of the interpolation problem that unifies various algorithmic approaches

a comparative study of variable precision fuzzy rough sets based on residuated lattices abstract although qiao and hu intended to propose granular variable precision l fuzzy rough sets based on residuated lattices l actually denotes a doubly residuated lattice with an involutive negation however there exist doubly residuated lattices without involutive negations this paper presents a comparative study of variable precision fuzzy rough sets based on residuated lattices in which we compare variable precision l fuzzy rough sets with the preexisting models a variable precision upper l fuzzy rough approximation operator is proposed with l fuzzy granules based on l fuzzy implication on a residuated lattice l instead of a doubly residuated lattice the variable precision upper l fuzzy rough approximation operator is investigated with respect to different l fuzzy relations regardless of proposing an involutive negation on a residuated lattice

fundamental study complete and directed complete ω categories let w be a commutative unital quantale complete and directed complete w categories are the core objects in quantitative domain theory this paper based on the theory of f completeness for enriched categories presents a systematic investigation of completeness and directed completeness of w categories

connecting fuzzy preorders fuzzy consequence operators and fuzzy closure and co closure systems abstract the relations between fuzzy preorders fuzzy consequence operators fuzzy closure systems and co closure systems lattice structures are studied given a continuous t norm we will prove that the complete lattice of all fuzzy preorders is isomorphic with a subfamily of the complete lattice of fuzzy consequence operators moreover we will show that it is possible to embed both structures in the class of fuzzy closure systems by a lattice dual monomorphism between semilattices a solution to the following open problem when two families of fuzzy possible valuations produce the same fuzzy implication relation is given concept of interior operator of a fuzzy consequence operator is suggested and a characterization of the previous open problem through interior operator is shown

the l ordered semigroups based on l partial orders abstract fuzzy frame valued ordered semigroups are investigated with the orders being l partial orders in this framework l left resp l right ideals l bi ideals and l quasi ideals of an l ordered semigroup are discussed the idea of which is applied to the characterizations of regular and duo l ordered semigroups in addition the relationship between an l ordered semigroup and an l topological semigroup is studied as a consequence an isomorphism between the category of l ordered semigroups and the category of l topological semigroups with the topologies being l t 0 and alexandrov is obtained

granular variable precision l fuzzy rough sets based on residuated lattices abstract firstly as for the beginning of this paper we introduce the granular variable precision l fuzzy rough sets based on residuated lattices with arbitrary l fuzzy relations and then the equivalent expressions for the lower and upper approximation operators are given with l fuzzy implications and l fuzzy coimplications on arbitrary l fuzzy relations which can calculate the lower and upper approximation operators efficiently finally some basic properties of the granular variable precision l fuzzy rough sets on residuated lattices are investigated and the conclusions on the granular variable precision fuzzy rough sets are generalized into the situations of the truth values set becoming residuated lattices

fixed points and generators of fuzzy relations abstract the fixed points of a t indistinguishability operator are characterized as its generators in the sense of the representation theorem of valverde the geometric description of the set of fixed points of a reflexive and symmetric fuzzy relation based on this characterization gives a way to explicitly calculate it

the aggregation of transitive fuzzy relations revisited abstract in this paper we consider the problem of aggregating a collection of transitive fuzzy binary relations in such a way that the aggregation process preserves transitivity specifically we focus our efforts on the characterization of those functions that aggregate a collection of fuzzy binary relations which are transitive with respect to a collection of t norms preserving the transitivity we characterize them in terms of triangular triplets further the relationship between triangular triplets the monotonicity of the aggregation function and an appropriate dominance notion is explicitly stated special attention is paid to a few classes of transitive fuzzy binary relations that are relevant in the literature concretely we describe in terms of triangular triplets those functions that aggregate a collection of fuzzy pre orders fuzzy partial orders relaxed indistinguishability relations indistinguishability relations and equalities a surprising relationship between functions that aggregate transitive fuzzy relations into a t m transitive fuzzy relation and those that aggregate relaxed indistinguishability relations is shown a few consequences of the new results are also provided for those cases in which all the t norms of the given collection are the same some celebrated results are retrieved as a particular case from the exposed theory

on the relationship between limit spaces many valued topological spaces and many valued preorders let l 1 be a residuated complete lattice with the underlying lattice l a meet continuous lattice this paper presents a systematic investigation of the interrelationship between the categories of limit spaces l topological spaces and l preorders the results exhibit a close connection between these different mathematical structures

efficient design of high complexity cosine modulated filter banks using 2 m th band conditions this paper presents several new properties of biorthogonal cosine modulated filter banks cmfbs and efficient algorithms for designing cmfbs with a very large number of subbands and very long filters for a biorthogonal cmfb we find the periodicity and symmetry of its overall transfer function and aliasing transfer functions which can be efficiently computed based on a decimated uniform discrete fourier transform dft analysis filter bank by exploiting gradient information and 2m th band conditions efficient algorithms are proposed for designing both orthogonal and biorthogonal cmfbs in addition an efficient matrix inversion algorithm with o n 2 complexity is also presented several numerical examples and comparisons with many other existing methods are included to demonstrate the design performance and efficiency of the algorithms

fuzzy topological spaces with conical neighborhood systems abstract for a commutative integral and meet continuous quantale q a cns space is defined to be a q topological space such that the q neighborhood system of each point is a conical q filter these spaces reduce to fuzzy t locality spaces in the case that the quantale is the unit interval endowed with a left continuous t norm t and reduce to probabilistic q topological spaces in the case that q is an mv algebra for a continuous quantale q a necessary and sufficient condition is obtained for the category of cns spaces to be simultaneously reflective and coreflective in the category of stratified q topological spaces this result provides an interesting example of the interaction between properties of the quantale q and that of q topological spaces

on the construction of fuzzy betweenness relations from metrics abstract we consider the problem of constructing a fuzzy betweenness relation from a metric more precisely given a continuous archimedean triangular norm we present two construction methods for a fuzzy betweenness relation from a metric by making use of the pseudo inverse of either a continuous additive generator or a continuous multiplicative generator of the triangular norm in case the metric is bounded and given a 1 lipschitz continuous triangular norm we present a third construction method for a fuzzy betweenness relation from a metric by making use of the residual implication of the triangular norm since the ukasiewicz and product triangular norms are both continuous archimedean and 1 lipschitz continuous all three construction methods may be used interestingly the construction method based on the residual implication is proved to coincide with that based on a continuous additive generator for the ukasiewicz triangular norm and with that based on a continuous multiplicative generator for the product triangular norm we end by noting that all three construction methods result in a fuzzy prebetweenness relation when considering a pseudometric instead of a metric

kernel systems on l ordered sets abstract this paper presents fuzzy versions of kernel operators and kernel systems on l ordered sets and establishes a one to one correspondence between them

on the topological properties of fuzzy rough sets this paper is devoted to the discussion of the relationship between fuzzy rough set models and fuzzy topologies on a finite universe the tc axiom for fuzzy topology is proposed it is proved that the set of all lower approximation sets based on a reflexive and transitive fuzzy relation consists of a fuzzy topology which satisfies tc axiom and conversely a fuzzy topology which obey tc axiom is just the set of all lower approximation sets under a reflexive and transitive fuzzy relation that is to say there exists a one to one correspondence between the set of all reflexive and transitive fuzzy relations and the set of all fuzzy topologies which satisfy tc axiom

a stone type duality for st0 stratified alexandrov l topological spaces abstract we show that for every complete lattice a both the set of completely prime elements and the set of completely coprime elements are one to one corresponding to ch a the set of complete lattice homomorphisms from a to the two element lattice 2 a complete lattice is called completely generated a cg lattice for short if it is generated by the set of completely prime elements or equivalently by the set of completely coprime elements then we restudy the duality between the category of t 0 alexandrov topological spaces and the category of cg lattices by means of ch a with these preparations for a frame l as the truth value table we introduce s t 0 separation axiom for stratified alexandrov l topological spaces and finally establish a duality between the category of s t 0 stratified alexandrov l topological spaces and the category of completely generated complete l ordered sets we also investigate some properties of the s t 0 axiom for example it is hereditary by closed subspaces and productive

fuzzy rough sets fuzzy preorders and fuzzy topologies this paper shows that observations made by different authors at different times regarding one to one correspondence between the family of fuzzy preorders on a nonempty set and the family of all fuzzy topologies on this set satisfying certain extra conditions are essentially equivalent

near perfect reconstruction pseudo qmf banks a novel approach to the design of m channel pseudo quadrature mirror filter qmf banks is presented in this approach the prototype filter is constrained to be a linear phase spectral factor of a 2mth band filter as a result the overall transfer function of the analysis synthesis system is a delay moreover the aliasing cancellation ac constraint is derived such that all the significant aliasing terms are canceled consequently the aliasing level at the output is comparable to the stopband attenuation of the prototype filter in other words the only error at the output of the analysis synthesis system is the aliasing error which is at the level of stopband attenuation using this approach it is possible to design a pseudo qmf bank where the stopband attenuation of the analysis and thus synthesis filters is on the order of spl minus 100 db moreover the resulting reconstruction error is also on the order of spl minus 100 db several examples are included

metrics and t equalities abstract the relationship between metrics and t equalities is investigated the latter are a special case of t equivalences a natural generalization of the classical concept of an equivalence relation it is shown that in the construction of metrics from t equalities triangular norms with an additive generator play a key role conversely in the construction of t equalities from metrics this role is played by triangular norms with a continuous additive generator or equivalently by continuous archimedean triangular norms these results are then applied to the biresidual operator e t of a triangular norm t it is shown that e t is a t equality on 0 1 if and only if t is left continuous furthermore it is shown that to any left continuous triangular norm t there correspond two particular t equalities on f x the class of fuzzy sets in a given universe x one of these t equalities is obtained from the biresidual operator e t t by means of a natural extension procedure these t equalities then give rise to interesting metrics on f x

lattice valued preordered sets as lattice valued topological systems this paper provides variable basis lattice valued analogues of the well known results that the construct prost of preordered sets firstly is concretely isomorphic to a full concretely coreflective subcategory of the category top of topological spaces which employs the concept of the dual of the specialization preorder and secondly is non concretely isomorphic to a full coreflective subcategory of the category topsys of topological systems of s vickers which employs the spatialization procedure for topological systems dualizing these results one arrives at the similar properties of quasi pseudo metric spaces built over locales

speech enhancement using a minimum mean square error short time spectral amplitude estimator this paper focuses on the class of speech enhancement systems which capitalize on the major importance of the short time spectral amplitude stsa of the speech signal in its perception a system which utilizes a minimum mean square error mmse stsa estimator is proposed and then compared with other widely used systems which are based on wiener filtering and the spectral subtraction algorithm in this paper we derive the mmse stsa estimator based on modeling speech and noise spectral components as statistically independent gaussian random variables we analyze the performance of the proposed stsa estimator and compare it with a stsa estimator derived from the wiener estimator we also examine the mmse stsa estimator under uncertainty of signal presence in the noisy observations in constructing the enhanced signal the mmse stsa estimator is combined with the complex exponential of the noisy phase it is shown here that the latter is the mmse estimator of the complex exponential of the original phase which does not affect the stsa estimation the proposed approach results in a significant reduction of the noise and provides enhanced speech with colorless residual noise the complexity of the proposed algorithm is approximately that of other systems in the discussed class

a method for representing boundaries in discrete element modelling part i geometry and contact detection the discrete element method for analysis of the dynamic behaviour of discontinuous media is well established however its application to engineering problems is still limited to simplified representations of structural boundaries and their kinematics in this paper a method is developed for representing three dimensional boundaries of arbitrary geometry and for modelling the interaction between boundary objects and particles within the discrete element modelling framework the approach which we term the finite wall method uses planar triangular elements to approximate the boundary surface topology any number of wall elements can be used to model the shape of the structure a contact detection scheme is presented for boundary surfaces and spheres based on a series of vector projections to reduce the problem dimensionally the algorithm employs spatial sporting to obtain the set of potential contacts between spheres and wall elements prior to contact resolution in a further stage all possible contact conditions including contact with surfaces edges and corners are explicitly determined part i of this two part series of papers describes the finite wall method for representation of surface geometry and fully elaborates the method for detecting and resolving contact between boundary wall elements and spheres in part ii the finite wall method is extended to apply kinematics to linearly independent boundary objects using combinations of translational and rotational motion an approach is developed for coupling the dem with the fem for the purpose of optimising the design of structures which are dynamically interacting with particulate media copyright 2001 john wiley sons ltd

on the structure of f indistinguishability operators abstract some properties concerning the structure of f indistinguishability operators are analyzed it is shown that any of such operators is generated by a family of fuzzy subsets this result since it gives the way to construct f indistinguishabilities facilitates new applications of fuzzy relations the links between f indistinguishability operators and a kind of generalized metrics in the unit interval which are also explored are used to define the canonical generators of an f indistinguishability operator that is the fuzzy partition associated with the operator

on relationships among fuzzy approximation operators fuzzy topology and fuzzy automata the fuzzy approximation operator associated with an approximation space x r turns out to be a saturated kuratowski fuzzy closure operator on x precisely when the relation r on x is reflexive and transitive it is shown that all the level topologies of the fuzzy topology so obtained on x coincide these observations are then applied to fuzzy automata

new results on single axioms for l fuzzy rough approximation operators abstract this paper further studies axiomatic characterizations of l fuzzy rough sets where l denotes a residuated lattice single axioms for upper l fuzzy rough approximation operators are investigated in two different approaches which describe upper l fuzzy approximation operators with ordinary l fuzzy operations and l fuzzy product operation respectively we characterize upper l fuzzy rough approximation operators by only one axiom with ordinary l fuzzy operations when the l fuzzy relation is euclidean as well as the composition of euclidean with serial resp reflexive we also discuss the single axioms for upper l fuzzy rough approximation operators with l fuzzy product operation on arbitrary l fuzzy relations that are not limited as either general l fuzzy relations or symmetric l fuzzy relations the single axioms for lower l fuzzy rough approximation operators are discussed with ordinary l fuzzy operations regardless of the regularity of residuated lattice l

preordered sets valued in a gl monoid let m l be a gl monoid an m valued preordered set is an l subset endowed with a reflexive and m transitive l relation it is essentially a category enriched in a quantaloid generated by m this paper presents a study of m valued preordered sets with emphasis on symmetrization and the cauchy completion the main result states that symmetrization and the cauchy completion of m valued preordered sets commute up to a natural isomorphism

finitary solvability conditions for systems of fuzzy relation equations in this paper we consider the problem of solving systems of fuzzy relation equations two types of these systems with different compositions are considered and processed simultaneously a new sufficient condition and new solvability criteria are proposed for systems of both types all these conditions are finitary and thus can be easily verified the sufficient condition and criteria of solvability characterize a relationship between a skeleton nxn matrix n is a number of equations and a vector of the right hand side

on un suitable fuzzy relations to model approximate equality in this paper we state that fuzzy equivalence relations in general are not suitable to model approximate equality since then the notion of transitivity is counter intuitive to substantiate this we investigate some of the undesirable results caused by transitivity among other things in the case of approximate reasoning we then introduce a new framework to model approximate equality i e the concept of a pseudometric based resemblance relation we go into the properties of this new kind of fuzzy relation and illustrate it by means of some examples

some results on the degree of symmetry of fuzzy relations abstract in this paper we investigate the degree of the symmetry of fuzzy relations on a set x based on the fuzzy e equality derived from uninorms with unit element e the degree of the symmetry of fuzzy relations are defined by two different approaches the type i degree of symmetry and the type ii degree of symmetry the main work of this paper include first we discuss some basic properties of those two degrees especially for the relationship between them in particular for continuous t norms we give a necessary and sufficient condition such that the type i degree of symmetry and the type ii degree of symmetry are equal and then we obtain that the type ii degree of symmetry is more appropriate to character the degree of the symmetry of fuzzy relations than the type i degree of symmetry with respect to whether they preserve the fuzzy e equalities or not in the meantime for a special case with continuous t norms we provide a necessary and sufficient condition such that the type i degree of symmetry preserves the fuzzy equalities finally for conjunctive left continuous idempotent uninorms with neutral element e 0 1 we find out a symmetric fuzzy relation s which is close enough to the given fuzzy relation r with respect to fuzzy e equality such that the degree of fuzzy e equality of s and r is the type ii degree of symmetry of r in particular we obtain analogous results for continuous t norms and one class of left continuous t norms

a general formulation of modulated filter banks this paper presents a general framework for maximally decimated modulated filter banks the theory covers the known classes of cosine modulation and relates them to complex modulated filter banks the prototype filters have arbitrary lengths and the overall delay of the filter bank is arbitrary within fundamental limits necessary and sufficient conditions for perfect reconstruction pr are derived using the polyphase representation it is shown that these pr conditions are identical for all types of modulation modulation based on the discrete cosine transform dct both dct iii dct iv and dct i dct ii and modulation based on the modified discrete fourier transform mdft a quadratic constrained design method for prototype filters yielding pr with arbitrary length and system delay is derived and design examples are presented to illustrate the tradeoff between overall system delay and stopband attenuation subchannelization

fuzzy galois connections on fuzzy sets abstract in fairly elementary terms this paper presents how the theory of preordered fuzzy sets more precisely quantale valued preorders on quantale valued fuzzy sets is established under the guidance of enriched category theory motivated by several key results from the theory of quantaloid enriched categories this paper develops all needed ingredients purely in order theoretic languages for the readership of fuzzy set theorists with particular attention paid to fuzzy galois connections between preordered fuzzy sets

fuzzy complete lattices in this paper based on l fuzzy posets previously introduced by the third author l fuzzy complete lattices are defined which are generalizations of usual complete lattices and coincide with wagner s complete and cocomplete w categories enriched over the frame l and are consequently a special kind of complete w lattices defined by lai and zhang however tarski fixed point theorem for the l fuzzy complete lattices is proved in a different way from that by lai and zhang furthermore some fuzzy powerset operators are suggested they are not only generalizations of ordinary powerset operators but also generalizations of l valued zadeh powerset operators and their properties are discussed

topological properties of the class of generators of an indistinguishability operator the present paper investigates the relations between topologies in the classical sense fuzzy topologies in lowen s sense and indistinguishability operators as well as constructing topologies and fuzzy topologies by means of indistinguishability operators furthermore as a particular consequence of the results in this paper a characterization theorem for pseudo metrizable topological spaces in the classical sense is also surprisingly obtained

some properties of m fuzzifying convexities induced by m orders abstract in this paper the notions of geometric interval spaces convex geometries and base point orders in the theory of convexity spaces are generalized to m fuzzifying convexity spaces using m fuzzifying restricted hull operators the m fuzzifying convexity spaces induced by m orders are defined conveniently then it is shown that m fuzzifying convexity spaces induced by m orders are m fuzzifying jhc and arity 2 and if the m order is strongly anti symmetric then the m fuzzifying convexity space is an m fuzzifying convex geometry and its segment operator is an m fuzzifying geometric interval operator

alexandroff l co topological spaces this article is concerned with alexandroff l topological spaces and l co topological spaces where l is a commutative unital quantale on one hand an example is given to show that there is a finite strong l topological space that is not alexandroff on the other hand it is proved that every finite strong l co topological space is alexandroff and that the category of alexandroff strong l co topological spaces is the coreflective hull of the subcategory of finite strong l co topological spaces in the category of strong l co topological spaces so the results illustrate an essential difference between topology and co topology in the many valued setting

on many valued stratified l fuzzy convergence spaces based on complete residuated lattices the relations between stratified l fuzzy convergence spaces and enriched l fuzzy topological spaces are studied it is shown that as a reflective subcategory the category of enriched l fuzzy topological spaces can embedded in the category of stratified l fuzzy convergence spaces also the specialization l preorder of stratified l fuzzy convergence spaces is investigated

a 3 d discrete element method for dry granular flows of ellipsoidal particles abstract we use 3 d discrete element method dem to simulate dry granular flows of non spherical particles in our simulation code non spherical particles are represented by clusters of spheres for contact detection and for contact force calculation for particles in contact the normal force displacement nfd model is simulated by a partially latching spring system whereas the tangential force displacement tfd model is simulated by an incremental relation that corresponds to a simplification of the mindlin and deresiewicz r d mindlin h deresiewicz asme j appl mech 20 1953 327 344 contact mechanics theory to establish the validity of the simulation procedure benchmark tests such as superball and superbean simulations were carried out we present various results obtained from the simulation of ellipsoidal particles flowing down a chute having a bumpy bottom these ellipsoidal particles had their physical properties obtained from experiments

an enriched category approach to many valued topology in this paper we discuss a basic question in fuzzy set theory what is a many valued topology on a set x an answer is presented by interpreting the axioms two logical formulas for classical topological spaces in the fuzzy setting making use of the intrinsic fuzzy partial order on the fuzzy power set of x as preparation a systematic investigation of fuzzy partial orders is presented from the viewpoint of enriched category theory

fuzzy t transitive relations eigenvectors and generators abstract after some preliminaries the set of generators of a generalized equality relation t indistinguishability operator is studied this set is identified with the set of the eigenvectors of the relation the relation between the fuzzy and metric topologies derived from these equalities is stablished the concept of basis is introduced and the construction of a procedure in order to calculate explicitly a basis of a t indistinguishability operator for t archimedean is proposed

representations and constructions of similarity based fuzzy orderings this contribution advocates the dissemination of similarity based fuzzy orderings a generalized concept of fuzzy orderings which appears to be unavoidable as soon as the classical correspondences between preorderings equivalence relations and orderings are taken into account in contrast to earlier papers on the topic this paper is focused on representation and construction results which once more demonstrate the feasibility of the proposed concept

perfect reconstruction filter banks with rational sampling factors an open problem namely how to construct perfect reconstruction filter banks with rational sampling factors is solved such filter banks have n branches each one having a sampling factor of p i qi and their sum equals one in this way the well known theory of filter banks with uniform band splitting is extended to allow for nonuniform divisions of the spectrum this can be very useful in the analysis of speech and music the theory relies on two transforms the first transform leads to uniform filter banks having polyphase components as individual filters the other results in a uniform filter bank containing shifted versions of same filters this in turn introduces dependencies in design and is left for future work as an illustration several design examples for the 2 3 1 3 case are given filter banks are then classified according to the possible ways in which they can be built it is shown that some cases cannot be solved even with ideal filters with real coefficients

fuzzy preorder and fuzzy topology this paper presents by means of alexandrov topology for fuzzy preordered sets and specialization order for fuzzy topological spaces a systematic investigation of the interrelationship between fuzzy preordered sets topological spaces and fuzzy topological spaces

a survey of fuzzifications of frames the papert papert isbell adjunction and sobriety this paper gives a survey of fuzzifications of frames the papert papert isbell adjunction between the categories of topological spaces and locales as well as the related concept of sobriety it then establishes categorical isomorphisms between yao l frames zhang liu l frames and l algebras lastly it studies the relationships between l sobriety modified l sobriety and i l sobriety the obtained results suggest that modified l sobriety is the most fruitful notion between the above concepts of lattice valued sobriety

new analytical and numerical results for two dimensional contact profiles recently a generalized coulomb law for elastic bodies in contact has been developed by the author which assumes that the tangential traction is the difference of the slip stress of the contact and the stick area whereby each stick area corresponds to a smaller contact area it holds for multiple contact regions also several applications for elastic half planes half spaces thin and thick layers and impact problems have been published for plane contact of equal bodies with friction it provides exact solutions and the interior stress field can be expressed with analytical results in closed form in this article a singular superposition of flat punch solutions is outlined in which the punches are aligned with an edge of the contact area it is shown that this superposition satisfies coulomb s inequalities directly and new results for the muskhelishvili potentials of several profiles are presented it is illustrated how problems of singularity and multi valuedness of complex functions can be solved in closed form and the chebyshev approximation used by earlier authors can be avoided for comparison some previous solutions for symmetric profiles are appended some results for the interior stress field the pressure the frictional traction and the surface displacements are compared with fem solutions of an equivalent problem the small differences between both methods show characteristic features of the fem model and the theoretical assumptions and are shortly explained further this example can be used as benchmark test for fem and bem programs

fuzzy relation equations and inequalities with two unknowns and their applications abstract in this paper we study several types of systems of fuzzy relation equations and inequalities composed of a given family of fuzzy relations between two sets and two unknown fuzzy relations on these sets solutions to these systems are pairs of fuzzy relations on the underlying sets and can be ordered coordinatewise we show that solutions to each of these systems form a complete lattice and provide procedures for computing the greatest solution which is less than or equal to a given pair of fuzzy relations we also demonstrate the application of solutions to these systems in data reduction

quantitative domains via fuzzy sets part ii fuzzy scott topology on fuzzy directed complete posets this paper pursues an investigation on quantitative domains via fuzzy sets initiated by the first author this time we define an l topology called the fuzzy scott topology on fuzzy dcpos and investigate its properties scott convergence of stratified l filters is also defined and studied we show that a fuzzy dcpo x e is continuous if and only if for any stratified l filter on x scott convergence coincides with the convergence with respect to the fuzzy scott topology at last we show that the category of fuzzy dcpos with fuzzy scott continuous maps is cartesian closed

laplacian matrices and alexandrov topologies of digraphs abstract we explore the spectral properties of digraph laplacians and how they relate to topological properties of digraphs such as openness closure and strong connectedness under the alexandrov topology

an elastoplastic contact force displacement model in the normal direction displacement driven version we present an elastoplastic normal forcedisplacement nfd model for spheres in collision among several possible applications of this model are the granularflow simulations using a discreteelement

on ordered categories as a framework for fuzzification of algebraic and topological structures using the framework of ordered categories the paper considers a generalization of the fuzzification machinery of algebraic structures introduced by rosenfeld as well as provides a new approach to fuzzification of topological structures which amounts to fuzzifying the underlying set of a structure in a suitably compatible way leaving the structure itself crisp the latter machinery allows the so called double fuzzification i e a fuzzification of something that is already fuzzified

low delay nonuniform pseudo qmf banks with application to speech enhancement this paper presents a method for designing low delay nonuniform pseudo quadrature mirror filter qmf banks this method is motivated by the work of li nguyen and tantaratana in which the nonuniform filter bank is realized by combining an appropriate number of adjacent sub bands of a uniform pseudo qmf bank in prior work the prototype filter of the uniform pseudo qmf bank was constrained to have linear phase and the overall delay associated with the filter bank was often unacceptably large for filter banks with a large number of sub bands this paper proposes a pseudo qmf filter bank design technique that significantly reduces the delay by relaxing the linear phase constraints an example in which an oversampled critical band nonuniform filter bank is designed and applied to a two state modeling speech enhancement system is presented in this paper comparison of the performance of this system to competing methods employing tree structured linear phase multiresolution analysis indicates that the approach described in this paper strikes a good balance between system performance and low delay

completely lattice l ordered sets with and without l equality a relationship between l order based on an l equality and l order based on crisp equality is explored in detail this enables to clarify some properties of completely lattice l ordered sets and generalize some related assertions namely belohlavek s main theorem of fuzzy concept lattices is generalized as well as his theorem dealing with dedekind macneille completion analogously completion of an l ordered set via completely lattice l ordered set of all down l sets is described

quantale valued dissimilarity abstract inspired by the theory of apartness relations of scott we establish a positive theory of dissimilarity valued in an involutive quantale q without the aid of negation it is demonstrated that a set equipped with a q valued dissimilarity is precisely a symmetric category enriched in a subquantaloid of the quantaloid of back diagonals of q interactions between q valued dissimilarities and q valued similarities which are equivalent to q valued equalities in the sense of hohle kubiak are investigated with the help of lax functors in particular it is shown that similarities and dissimilarities are interdefinable if q is a girard quantale with a hermitian and cyclic dualizing element

normal and tangential force displacement relations for frictional elasto plastic contact of spheres abstract in this paper we present the data obtained from numerical experiments that are at the foundation of our successful elasto plastic force displacement fd models in both the normal direction and tangential direction of spheres in collision we also present in detail how these data were obtained our numerical experiments are in the form of frictional elasto plastic finite element analysis of spherical particles in contact we use the numerical experiments to observe the behavior of various quantities involved in the contact e g contact area radius contact curvature stresses fd relations etc this observation has helped us to devise an accurate and consistent model for frictional elasto plastic contact of spherical particles that are used in granular flow simulations that may involve tens of thousands of these particles

i fuzzy alexandrov topologies and specialization orders the aim of this paper is to investigate the relationships between certain generalized topological structures and fuzzy order structures on a universe set x in details a fuzzy preordered relation induces an i fuzzy alexandrov topology and an i fuzzy topology induces a fuzzy preordered relation which turns out to be a specialization order in i fuzzy setting in addition the representation theorem of fuzzy preorders by i fuzzy topologies is obtained these results coincide with the conclusions obtained in literature in the version of two valued logic

one to one correspondence between fuzzifying topologies and fuzzy preorders this paper is devoted to the discussion of the relationship between fuzzifying topologies and fuzzy relations a saturated fuzzifying topology can be generated by a reflexive fuzzy relation and conversely a fuzzy preorder can be generated by a fuzzifying topology in fact there exists a one to one correspondence between the set of all saturated fuzzifying topologies and that of all fuzzy preorders

an accurate elasto plastic frictional tangential force displacement model for granular flow simulations displacement driven formulation we present in this paper the displacement driven version of a tangential force displacement tfd model that accounts for both elastic and plastic deformations together with interfacial friction occurring in collisions of spherical particles this elasto plastic frictional tfd model with its force driven version presented in l vu quoc l lesburg x zhang an accurate tangential force displacement model for granular flow simulations contacting spheres with plastic deformation force driven formulation journal of computational physics 196 1 2004 298 326 is consistent with the elasto plastic frictional normal force displacement nfd model presented in l vu quoc x zhang an elasto plastic contact force displacement model in the normal direction displacement driven version proceedings of the royal society of london series a 455 1991 4013 4044 both the nfd model and the present tfd model are based on the concept of additive decomposition of the radius of contact area into an elastic part and a plastic part the effect of permanent indentation after impact is represented by a correction to the radius of curvature the effect of material softening due to plastic flow is represented by a correction to the elastic moduli the proposed tfd model is accurate and is validated against nonlinear finite element analyses involving plastic flows in both the loading and unloading conditions the proposed consistent displacement driven elasto plastic nfd and tfd models are designed for implementation in computer codes using the discrete element method dem for granular flow simulations the model is shown to be accurate and is validated against nonlinear elasto plastic finite element analysis

the relationship between l fuzzy rough set and l topology various fuzzy generalizations of rough approximations have been proposed in the literature this paper is devoted to the discussion of the relationship between l fuzzy rough sets and l topologies on an arbitrary universe finally one to one correspondence between the set of all reflexive transitive l relations and the set of all alexandrov l topologies is obtained

a non commutative and non idempotent theory of quantale sets in fuzzy set theory non idempotency arises when the conjunction is interpreted by arbitrary t norms there are many instances in mathematics where set theory ought to be non commutative and or non idempotent the purpose of this paper is to combine both ideas and to present a theory of non commutative and non idempotent quantale sets among other things standard concepts like fuzzy preorders and fuzzy equivalence relations will be exhibited as special cases more specifically the category q set is investigated where q is an arbitrary involutive quantale objects quantale sets are pairs consisting of a set and a q valued equality with a suitable symmetry axiom three important properties of q set are shown it is complete cocomplete and has the epi extremal mono factorization property its subcategory s q set of separated quantale sets is reflective in q set and shares the same fundamental properties with q set in particular s q set is also a complete and cocomplete epi extremal mono category the objects of the category q set are interesting categories in their own right two categorical frameworks for objects of q set are exhibited first it is shown that q valued equalities arise from q valued preorders with self adjoint extents by symmetrization which leaves q valued equalities invariant here sets with quantale preorders are shown to be b categories with base b being a specific quantaloid the second approach is based on involutive quantaloids a combination of two well known things quantaloids and ordered categories with involution in this context quantale sets are precisely symmetric b categories w r t appropriately chosen quantaloid b with involution further the cauchy completion preserves the symmetry axiom for a large class of involutive quantales which include quantic frames our non commutative generalization of frames and all left continuous t norms there exist at least two monads on q set the singleton monad and quasi singleton monad which are of special interest for fuzzy set theory the kleisli category associated with the singleton monad is the non commutative and non idempotent analogue of higgs topos while the eilenberg moore category of the quasi singleton monad permits the internalization of lukasiewicz negation as truth arrow finally an application of quantale sets to c algebras is given and the change of base is treated

fuzzy betweenness relations and their connection with fuzzy order relations abstract fuzzy relations and in particular fuzzy order relations have been largely studied since zadeh first introduced the concept back in 1971 bearing in mind that betweenness relations and their relationship with order relations have historically attracted the attention of mathematicians it is very surprising that the study of fuzzy betweenness relations has had a very limited scientific reach so far and barely no attention has been given to their relationship with fuzzy order relations in this manuscript we study fuzzy betweenness relations in depth and discuss their connection with both schools of thought in the study of fuzzy order relations the already mentioned one introduced by zadeh and the one initiated by hohle and blanchard and popularized by bodenhofer

towards probabilistic partial metric spaces diagonals between distance distributions abstract the quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories motivated by the categorical interpretation of partial metric spaces we are led to investigate the quantaloid of diagonals between distance distributions which is expected to establish the categorical foundation of probabilistic partial metric spaces observing that the quantale of distance distributions w r t an arbitrary continuous t norm is non divisible we precisely characterize diagonals between distance distributions and prove that one step functions are the only distance distributions on which the set of diagonals coincides with the generated down set

a short note on l fuzzy approximation spaces and l fuzzy pretopological spaces in this note we investigate the relationship between l fuzzy pretopological spaces and l fuzzy approximation spaces based on the reflexive l fuzzy relations from a categorical viewpoint

sobriety of quantale valued cotopological spaces abstract for each commutative and integral quantale making use of the fuzzy order between closed sets a theory of sobriety for quantale valued cotopological spaces is established based on irreducible closed sets