on fuzzy subgroups abstract in this communication we prove that n g where n g is the set of all fuzzy normal subgroups of g is a commutative idempotent semisimple semigroup also we give a fuzzy analog of the following well known result if g is a group h l and k are subgroups of g such that h l g and k g then l hk h l k

on l subsets and tl subalgebras this is a continuation of yu s 1993 work on tl subalgebras we define and discuss another kind of homomorphism and isomorphism of tl subalgebras where t is an arbitrary infinitely distributive t norm on a given complete brouwerian lattice l we also give two methods for generating tl subalgebras

stabilized finite element methods based on multiscale enrichment for the stokes problem this work concerns the development of stabilized finite element methods for the stokes problem considering nonstable different or equal order of velocity and pressure interpolations the approach is based on the enrichment of the standard polynomial space for the velocity component with multiscale functions which no longer vanish on the element boundary on the other hand since the test function space is enriched with bubble like functions a petrov galerkin approach is employed we use such a strategy to propose stable variational formulations for continuous piecewise linear in velocity and pressure and for piecewise linear piecewise constant interpolation pairs optimal order convergence results are derived and numerical tests validate the proposed methods

stabilized multiscale finite element method for the stationary navier stokes equations abstract in the paper a stabilized multiscale finite element method for the stationary incompressible navier stokes equations is considered the method is a petrov galerkin approach based on the multiscale enrichment of the standard polynomial space enriched with the unusual bubble functions which no longer vanish on every element boundary for the velocity space the stability of the p 1 p 0 triangular element or the q 1 p 0 quadrilateral element is established and the optimal error estimates of the stabilized multiscale finite element method for the stationary navier stokes equations are obtained

an unusual stabilized finite element method for a generalized stokes problem an unusual stabilized finite element is presented and analyzed herein for a generalized stokes problem with a dominating zeroth order term the method consists in subtracting a mesh dependent term from the formulation without compromising consistency the design of this mesh dependent term as well as the stabilization parameter involved are suggested by bubble condensation stability is proven for any combination of velocity and pressure spaces under the hypotheses of continuity for the pressure space optimal order error estimates are derived for the velocity and the pressure using the standard norms for these unknowns numerical experiments confirming these theoretical results and comparisons with previous methods are presented

convergence analysis of a new multiscale finite element method with the element for the incompressible flow abstract in this paper we propose a new multiscale finite element method for the stationary navier stokes problem this new method for the lowest order finite element pairs p 1 p 0 is based on the multiscale enrichment and derived from the navier stokes problem itself therefore the new multiscale finite element method better reflects the nature of the nonlinear problem the well posedness of this new discrete problem is proved under the standard assumption meanwhile convergence of the optimal order in h 1 norm for velocity and l 2 norm for pressure is obtained especially via applying a new dual problem for the incompressible navier stokes problem and some techniques in the process for proof we establish the convergence of the optimal order in l 2 norm for the velocity finally numerical examples confirm our theory analysis for this new multiscale finite element method and validate the high effectiveness of this new method

formulas on the lattice of fuzzy subalgebras in universal algebra we study what first order sentences give the equivalence in the meaning that holding on the lattice of subuniverses implies holding on that of fuzzy subalgebras and vice versa we introduce the notions of transferable form and strict transferable form of open formulas and show that universal sentences whose matrixes are of the former type and existential sentences whose matrixes are of the latter type give the equivalence for every abstract algebra after that we study the case when sentences are general for the purpose we examine skolem normal forms of given sentences

beyond pressure stabilization a low order local projection method for the oseen equation this work proposes a new local projection stabilized finite element method lps for the oseen problem the method adds to the galerkin formulation new fluctuation terms that are symmetric and easily computable at the element level proposed for the pair 1 l l 0 1 when the pressure is continuously or discontinuously approximated well posedness and error optimality are proved in addition we introduce a cheap strategy to recover an element wise mass conservative velocity field in the discontinuous pressure case a property usually neglected in the stabilized finite element context numerics validate the theoretical results and show that the present method improves accuracy to represent boundary layers when compared with alternative approaches

the homomorphic image of a fuzzy subgroup is always a fuzzy subgroup let l be a completely distributive complete lattice with universal bound 0 and 1 and x any group we will prove that the image of a fuzzy group x l under a homomorphism f x y is always a fuzzy group without any restriction on and f

fuzzy homomorphisms of algebras in this paper we consider fuzzy relations compatible with algebraic operations which are called fuzzy relational morphisms in particular we aim our attention to those fuzzy relational morphisms which are uniform fuzzy relations called uniform fuzzy relational morphisms and those which are partially uniform f functions called fuzzy homomorphisms both uniform fuzzy relations and partially uniform f functions were introduced in a recent paper by us uniform fuzzy relational morphisms are especially interesting because they can be conceived as fuzzy congruences which relate elements of two possibly different algebras we give various characterizations and constructions of uniform fuzzy relational morphisms and fuzzy homomorphisms we establish certain relationships between them and fuzzy congruences and we prove homomorphism and isomorphism theorems concerning them we also point to some applications of uniform fuzzy relational morphisms

the join of fuzzy algebraic substructures of a group and their lattices this is a continuation of work in previous papers n ajmal and k v thomas fuzzy sets and systems 58 1993 217 inform sci 76 1994 1 here we provide a common technique of constructing the join of fuzzy substructures consequently it leads to the formation of various types of lattices and sublattices of fuzzy substructures of a group including those of normal and quasinormal fuzzy subgroups a lattice theoretic relationship of these sublattices is established moreover we present simple and direct proofs for the fact that the lattice of fuzzy normal subgroups is modular

a contribution to the theory of fuzzy subgroups abstract in this paper we continue our study in order to give a partial answer to the question suggested by asaad in 1991 what can be said about the structure of a group g when the information are known about the structure of a fuzzy subgroup a of g and viceversa

the free product of fuzzy subgroups abstract an associative product to be called the free product of fuzzy sets in a semigroup is defined which lies between sup min and sup max products it behaves nicely for characteristic functions and fuzzy point sets and simulates all the standard results for the product of two subgroups of a group instead of fuzzy invariance which is too strong only a milder form of relative fuzzy invariance is used to establish fuzzy subgroupness of the product which is intimately connected with the necessity of two fuzzy subgroups to commute lastly under a slightly restricted situation the free product induces a fuzzy subgroup on a quotient group it is suggested that the product be tested for a suitable definition of a fuzzy topological group an analysis of its deeper aspects is forthwith

characterizations of l convex spaces via domain theory abstract we provide some new characterizations of l convex spaces by using the way below relation in domain theory for this purpose we first study the notion of domain finiteness in the lattice valued case and then introduce three kinds of spaces algebraic l closure spaces restricted l hull spaces and l entailment spaces these three spaces are shown to be categorically isomorphic to l convex spaces additionally we introduce the notion of l polytopes and prove that a subcollection of a dense l convex structure is a base if and only if it contains all l polytopes these results indicate that in the study of the theory of fuzzy convex spaces fuzzy domain theory has important applications

tl subrings and tl ideals part 1 basic concepts abstract in 25 27 we put forward a rudimentary frame of the theory of tl subalgebras in 26 we established a theory of tl subgroups and tl subgroups in this paper we will continue our work in concern with basic ideas provided in 25 27 introduce the notions of tl subrings and tl ideals of a ring and study some of their properties where t is an arbitrary infinitely distributive t norm on a given complete brouwerian lattice l

on fuzzy quotient rings induced by fuzzy ideals abstract in this paper we define fuzzy quotient rings induced by fuzzy ideals and study the relation between fuzzy quotient rings and fuzzy ideals

an extension principle for closure operators this led several authors to investigate the closure systems and the closure operators in the framework of fuzzy set theory the resulting researches give an elegant and powerful treatment of notions such as those of fuzzy w x subalgebras necessity measures and envelopes for example see 1 4 and w x 11 let s be any set and denote by p s and f s the class of the subsets and the class of the fuzzy subsets of s respectively in this paper we propose an extension principle enabling us to extend any classical operator j p s a p s to an operator j f s a f s in such a way that j is a closure operator if and only if j is a closure operator also we

convex regularization for high dimensional multiresponse tensor regression in this paper we present a general convex optimization approach for solving high dimensional multiple response tensor regression problems under low dimensional structural assumptions we consider using convex and weakly decomposable regularizers assuming that the underlying tensor lies in an unknown low dimensional subspace within our framework we derive general risk bounds of the resulting estimate under fairly general dependence structure among covariates our framework leads to upper bounds in terms of two very simple quantities the gaussian width of a convex set in tensor space and the intrinsic dimension of the low dimensional tensor subspace to the best of our knowledge this is the first general framework that applies to multiple response problems these general bounds provide useful upper bounds on rates of convergence for a number of fundamental statistical models of interest including multiresponse regression vector autoregressive models low rank tensor models and pairwise interaction models moreover in many of these settings we prove that the resulting estimates are minimax optimal we also provide a numerical study that both validates our theoretical guarantees and demonstrates the breadth of our framework

the maps with polynomial basis functions for solving axisymmetric time fractional equations abstract this study presents a parallel meshless approach for time fractional equations in the axisymmetric geometry in the present parallel meshless approach the method of approximate particular solutions maps in conjunction with laplace transform extended precision arithmetic epa and multiple scale technique mst is implemented in this application the laplace transform is employed to eliminate the dependence on time the maps is used to obtain the solution of time independent equation in laplace space furthermore the solution of time dependent equation is restored by stehfest s algorithm here the multiple scale technique mst and extended precision arithmetic epa are applied to alleviate the effect of an ill conditioned matrix on a numerical inverse laplace transform then multi cores parallel computing can improve effectively computing speed of the proposed meshless approach in the numerical implementation both the 2d axisymmetric equations and the original 3d equations are considered and compared

a residual local projection method for the oseen equation abstract a new residual local projection stabilized method relp is proposed as a result of an enriched petrov galerkin strategy for the oseen problem the p 12 p l pairs l 0 1 with continuous or discontinuous pressures are made stable by enhancing them with solutions of residual based local oseen problems and performing a static condensation procedure afterward this process does not involve the numerical solution of the local problems and maintains the degrees of freedom of the original spaces the method adds symmetric terms to the galerkin formulation which are easy to implement at the element level consistency well posedness and error estimates are demonstrated and an economic way to recover a locally conservative velocity field for the discontinuous pressure case is also proposed extensive numerical experiments attest the theoretical results and compare the relp method to previously existing alternatives

tensor products of semilattices and fuzzy ideals we study complete fuzzy ideals on semilattices from the point of view of tensor products of semilattices we show that the lattice of all complete fuzzy ideals on a semilattice is an extension of tensor product we define the notion of semicomplete bi ideals and show that the lattice of all fuzzy ideals on a distributive lattice is isomorphic to the lattice of all semicomplete bi ideals moreover we show that the lattice of all complete fuzzy ideals on a distributive algebraic lattice is distributive

normalization of fuzzy algebras in this work the notion of fuzzy algebra is investigated given an algebra a and a poset s a fuzzy algebra over a is an s set f over the base set a of a such that every cut x a f x a a s is a subalgebra of a some consequences are derived a particular notion of equivalence between two fuzzy algebras is studied which is more perspicuous than the notion of isomorphism a set of properties which appear to be desirable for a fuzzy algebra is settled the main theorem of the paper says that every fuzzy algebra is normalizable i e another fuzzy algebra may be constructed which is equivalent to the former and which satisfies all the desired properties

fuzzy subinclines ideals of incline algebras the fuzzification of subinclines ideals in inclines are considered and some related properties are investigated we also state the product of fuzzy subinclines ideals and the projections of fuzzy subinclines ideals we discuss fuzzy relations fuzzy characteristic subinclines ideals

algebras of fuzzy sets in this paper we investigate two kinds of algebras of fuzzy sets which are obtained by using zadeh s extension principle we give conditions under which a homomorphism between two algebras induces a homomorphism between corresponding algebras of fuzzy sets we prove that if the structure of truth values is a complete residuated lattice the induced algebra of a subalgebra of an algebra a can be embedded into the induced algebra of fuzzy sets of a for direct products we give conditions under which the direct product of algebras of fuzzy sets could be embedded into the algebra of fuzzy sets of the direct product in the case of homomorphisms and direct products the two kinds of algebras of fuzzy sets behave in different ways

an absolutely stabilized finite element method for the stokes problem on presente une formulation a elements finis absolument stabilisee pour le probleme de stokes on etablit des estimations d erreurs optimales dans la norme l 2 pour l approximation des champs de vitesses et de pressions

fuzzy quotient algebras and fuzzy factor congruences fuzzy quotient algebras are defined some homomorphism theorems are given fuzzy factor congruences and fuzzy factorable algebras are defined and some basic theorems are proved

stabilized mixed methods for the stokes problem the solution of the stokes problem is approximated by three stabilized mixed methods one due to hughes balestra and franca and the other two being variants of this procedure in each case the bilinear form associated with the saddle point problem of the standard mixed formulation is modified to become coercive over the finite element space error estimates are derived for each procedure

fuzzy krasner m n hyperrings recently krasner m n hyperrings were introduced and analyzed by mirvakili and davvaz krasner m n hyperrings are a suitable generalization of krasner hyperrings this paper concerns a relationship between fuzzy sets and hyperstructure theory it is a continuation of the ideas presented by davvaz et al 2009 b davvaz p corsini v leoreanu fotea fuzzy n ary subpolygroups computers mathematics with applications 57 2009 141 152 the aim of the paper is to introduce the notion of a fuzzy hyperideal of a krasner m n hyperring and to extend the fuzzy results to krasner m n hyperrings

hybrid chebyshev polynomial scheme for solving elliptic partial differential equations abstract in this paper we propose hybrid chebyshev polynomial scheme hcps which couples the chebyshev polynomial scheme and the method of fundamental solutions into a single matrix system this hybrid formulation requires solving only one system of equations and opens up the possibilities for solving a large class of partial differential equations in this paper we consider various boundary value problems and in particular the challenging cauchy navier equation the solution is approximated by the sum of the particular solution and the homogeneous solution chebyshev polynomials are used to approximate a particular solution of the given partial differential equation and the method of fundamental solutions is used to approximate the homogeneous solution numerical results show that our proposed approach is efficient accurate and stable

a multiscale a posteriori error estimate we introduce a hierarchic a posteriori error estimate for singularly perturbed reaction diffusion problems the estimator is based on a petrov galerkin method in which the trial space is enriched with nonpolynomial functions or multiscale functions we study the equivalence between the a posteriori estimate and the exact error in the energy norm moreover we prove a relationship between the hierarchic estimator and an explicit residual estimator the approach provides accurate estimates for the boundary layer regions which is confirmed by numerical experiments 2004 elsevier b v all rights reserved

the lattice of fuzzy ideals of a ring the set of all fuzzy ideals of a ring r is partially ordered with respect to the natural ordering of fuzzy sets in r it has been shown that this is a lattice but not a sublattice of the lattice of all fuzzy sets in r this lattice of all fuzzy ideals of r is complete distributive and bounded and has neither atoms nor dual atoms

rings with chain conditions abstract the aim of this paper is to find out some new results about fuzzy ideals to characterise artinian rings and noetherian rings by fuzzy ideals and to give alternative proofs of some well known results of artinian and noetherian rings by fuzzy ideal theoretic techniques

finite element approximation of the nonstationary navier stokes problem i regularity of solutions and second order error estimates for spatial discretization this is the first part of a work dealing with the rigorous error analysis of finite element solutions of the nonstationary navier stokes equations second order error estimates are proven for spatial discretization using conforming or nonconforming elements the results indicate a fluid like behavior of the approximations even in the case of large data so long as the solution remains regular the analysis is based on sharp a priori estimates for the solution particularly reflecting its behavior as t to 0 and as t to infty it is shown that the regularity customarily assumed in the error analysis for corresponding parabolic problems cannot be realistically assumed in the case of the navier stokes equations as it depends on nonlocal compatibility conditions for the data the results which are presented here are independent of such compatibility conditions which cannot be verified in practice

functional linear regression analysis for longitudinal data we propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data where both the predictor and response are functions of a covariate such as time predictor and response processes have smooth random trajectories and the data consist of a small number of noisy repeated measurements made at irregular times for a sample of subjects in longitudinal studies the number of repeated measurements per subject is often small and may be modeled as a discrete random number and accordingly only a finite and asymptotically nonincreasing number of measurements are available for each subject or experimental unit we propose a functional regression approach for this situation using functional principal component analysis where we estimate the functional principal component scores through conditional expectations this allows the prediction of an unobserved response trajectory from sparse measurements of a predictor trajectory the resulting technique is flexible and allows for different patterns regarding the timing of the measurements obtained for predictor and response trajectories asymptotic properties for a sample of n subjects are investigated under mild conditions as n oo and we obtain consistent estimation for the regression function besides convergence results for the components of functional linear regression such as the regression parameter function we construct asymptotic pointwise confidence bands for the predicted trajectories a functional coefficient of determination as a measure of the variance explained by the functional regression model is introduced extending the standard r 2 to the functional case the proposed methods are illustrated with a simulation study longitudinal primary biliary liver cirrhosis data and an analysis of the longitudinal relationship between blood pressure and body mass index

generalized fuzzy hyperideals of hyperrings the concept of quasi coincidence of a fuzzy interval value with an interval valued fuzzy set is considered in fact this is a generalized concept of the quasi coincidence of a fuzzy point with a fuzzy set by using this new idea the notion of interval valued a b fuzzy hyperideals in a hyperring is introduced and consequently a generalization of a fuzzy hyperideal is defined in this paper we study the related properties of the fuzzy hyperideals and in particular the interval valued q fuzzy hyperideals in a hyperring will be investigated moreover we also consider the concept of implication based interval valued fuzzy hyperideals in a hyperring some recent results obtained by b davvaz and j m zhan on hyperstructures are extended and consolidated

on the lattice and the algebra of fuzzy subsets of a universal algebra abstract for a given universal algebra the set of all its fuzzy subsets is endowed with two structures a structure of algebra called the fuzzy algebra or the algebra of fuzzy subsets and a structure of bounded lattice called the lattice of fuzzy subsets in this paper first of all we construct some subuniverses of this fuzzy algebra and give a way to generate such subuniverses we characterize the subuniverse generated by a fuzzy point of this fuzzy algebra some subalgebras containing the subalgebra generated by a finite set of fuzzy points of the fuzzy algebra are specified we also describe some subuniverses of the initial universal algebra induced by those of its fuzzy algebra and vice versa we then give some properties of fuzzy subalgebras of this universal algebra describe some fuzzy subalgebras generated by others fuzzy subalgebras and give a partial characterization of universal algebras in which the set of all fuzzy subalgebras is a subuniverse of their fuzzy algebras after that we characterize some properties which can be transfered between the codomain lattice of fuzzy subsets the lattice of truth values and the lattice of fuzzy subsets later we show that there exists some subsets of the set of all fuzzy subsets which can be both subuniverses of the fuzzy algebra and sublattices of the lattice of fuzzy subsets that means these subsets are endowed with a double structure like the set of all fuzzy subsets of the given universal algebra and finally we introduce the residuation of some of them by defining the residual operations in a certain way

towards multiscale functions enriching finite element spaces with local but not bubble like functions in this paper we propose a novel way via finite elements to treat problems that can be singular perturbed a reaction diffusion equation in our case we enrich the usual piecewise linear or bilinear finite element trial spaces with local solutions of the original problem as in the residual free bubble rfb setting but do not require these functions to vanish on each element edge a departure from the rfb paradigm such multiscale functions have an analytic expression for triangles and rectangles bubbles are the choice for the test functions allowing static condensation thus our method is of petrov galerkin type we perform several numerical validations which confirm the good performance of the method 2004 elsevier b v all rights reserved

fuzzy logics as families of bivaluated logics abstract in this paper we will prove the equivalence between l valued logics and l indexed families of bivaluated logics it is also proved that this equivalence can be used as a tool for checking compactness and decidability properties of a l valued logic

a posteriori error estimation for stabilized mixed approximations of the stokes equations the practical implementation of the lowest order pl p0 linear velocity constant pressure finite element method for the steady state incompressible navier stokes equations is addressed in this work three different types of a posteriori error indicator are introduced and each is shown to be equivalent to the discretization error our numerical results show that these indicators can be used to drive an adaptive refinement process which is specially tailored to create grids which conform to the requirements of the local stabilization it is also shown that the indicators provide an effective method for detecting local singularities in the flow solution

analysis on the method of fundamental solutions for biharmonic equations abstract in this paper the error and stability analysis of the method of fundamental solution mfs is explored for biharmonic equations the bounds of errors are derived for the fundamental solutions r 2 ln r in bounded simply connected domains and the polynomial convergence rates are obtained for certain smooth solutions the bounds of condition number are also derived to show the exponential growth rates for disk domains numerical experiments are carried out to support the above analysis which is the first time to provide the rigorous analysis of the mfs using r 2 ln r for biharmonic equations

the lattices of fuzzy subgroups and fuzzy normal subgroups abstract here we discuss various types of sublattices of the lattice of fuzzy subgroups of a given group we prove that a special class of fuzzy normal subgroups constitutes a modular sublattice of the lattice of fuzzy subgroups

analysis of locally stabilized mixed finite element methods for the stokes problem in this paper a locally stabilized finite element formulation of the stokes problem is analyzed a macroelement condition which is sufficient for the stability of locally stabilized mixed methods based on a piecewise constant pressure approximation is introduced by satisfying this condition the stability of the qi po quadrilateral and the pi po triangular element can be established

stability of finite elements under divergence constraints a finite dimensional stability test for checking velocity pressure finite element trial spaces is presented applications are made to a new class of element pairs proposed in this paper as well as to existing spaces

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

fuzzy nil radicals and fuzzy semiprimary ideals of rings abstract an attempt is made to define a fuzzy semiprimary ideal by using the idea of the fuzzy nil radical of a fuzzy ideal the level ideals of a such a fuzzy ideal are examined and the ring of fuzzy cosets of such a fuzzy ideal is studied the algebraic nature of such fuzzy ideals under homomorphisms is also ascertained

a two level method with backtracking for the navier stokes equations we consider a two level method for resolving the nonlinearity in finite element approximations of the equilibrium navier stokes equations the method yields l2 and h1 optimal velocity approximations and an l2 optimal pressure approximation the two level method involves solving one small nonlinear coarse mesh system one oseen problem hence linear with positive definite symmetric part on the fine mesh and one linear correction problem on the coarse mesh the algorithm we study produces an approximate solution with the optimal asymptotic in h accuracy for any fixed reynolds number we do not consider the behavior of the error for fixed h as re rightarrow infty i e for flows in transition to turbulence

virtual bubbles and galerkin least squares type methods ga l s abstract the equivalence between stabilized finite element methods or galerkin least squares tyoe methods ga l s and the standard galerkin method with bubble functions is established in an abstract framework the results are applicable to various finite element spaces including high order elements and applications to the advective diffusive model and to the stokes problem are presented illustrating the potential of the abstract theory introduced here

the lattice of fuzzy normal subgroups is modular abstract we have introduced and discussed in a recent paper 2 various sublattices such as lf lt and lfnt of the lattice l of fuzzy subgroups of a given group in particular we proved that the sublattice lfn of fuzzy normal subgroups with finite range and tip t is a modular sublattice of l here we remove all the restrictions on the choice of fuzzy normal subgroups and prove that the class of all fuzzy normal subgroups ln forms the modular sublattice of l as a tool we prove an important result that the fuzzy subgroups generated by a pair of fuzzy normal subgroups of a group is fuzzy normal

tensor regression with applications in neuroimaging data analysis classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays tensors traditional statistical and computational methods are proving insufficient for analysis of these high throughput data due to their ultrahigh dimensionality as well as complex structure in this article we propose a new family of tensor regression models that efficiently exploit the special structure of tensor covariates under this framework ultrahigh dimensionality is reduced to a manageable level resulting in efficient estimation and prediction a fast and highly scalable estimation algorithm is proposed for maximum likelihood estimation and its associated asymptotic properties are studied effectiveness of the new methods is demonstrated on both synthetic and real mri imaging data supplementary materials for this article are available online

isomorphic fuzzy groups abstract we introduce an acceptable definition of isomorphic fuzzy groups which fulfils the basic requirements the fuzzy versions of the first and the second isomorphism theorems become immediate consequences the idea is applied to the sup min product of two fuzzy subgroups of a group as an indispensable tool the characterization of a fuzzy normal subgroup of a group by the so called open level subgroups is brought forth an isomorphism between the cartesian product and the sup min product of two fuzzy subgroups of a group is demonstrated

correspondence remarks on the lattices of fuzzy subsets of a groupoid in this paper we give a necessary and sufficient condition for a groupoid d such that the sup min product is distributive over arbitrary intersection of fuzzy subsets of d and correct some results from the paper s ray the lattice of all idempotent fuzzy subsets of a groupoid fuzzy sets and systems 96 1998 239 245 also we prove that the set of all idempotent fuzzy sets forms a complete lattice which is a complete join sublattice of the lattice of all fuzzy subgroupoids this result extends the corresponding result from the above mentioned paper

a characterization of l fuzzy prime ideals abstract in this paper the concepts of a l fuzzy prime and a l fuzzy completely prime ideal are given and some fundamental lemmas are proved in particular bijections among some of the l fuzzy prime ideals of two homomorphic rings are constructed also a characterization of a l fuzzy prime ideal of a ring is given

multiple tensor on tensor regression an approach for modeling processes with heterogeneous sources of data in recent years measurement or collection of heterogeneous sets of data such as those containing scalars waveform signals images and even structured point clouds has become more common statis

computing the lattice of all fixpoints of a fuzzy closure operator we present a fast bottom up algorithm to compute all fixpoints of a fuzzy closure operator in a finite set over a finite chain of truth degrees along with the partial order on the set of all fixpoints fuzzy closure operators appear in several areas of fuzzy logic and its applications including formal concept analysis fca that we use as a reference area of application in this paper several problems in fca such as computing all formal concepts from data with graded attributes or computing non redundant bases of all attribute dependencies can be reduced to the problem of computing fixpoints of particular fuzzy closure operators associated with the input data the development of a general algorithm that is applicable in particular to these problems is the ultimate purpose of this paper we present the algorithm its theoretical foundations and experimental evaluation

tom head s join structure of fuzzy subgroups abstract tom head formulated a metatheorem in 1995 fuzzy sets and systems 73 1995 349 with an idea of directly proving the fuzzy analogs of results of classical mathematics in the process he defined a vital concept of tip extended pair of fuzzy subgroups in this paper we use this concept to define the join of fuzzy subgroups using this definition of join we have provided a much simpler and direct proof of modularity of the lattice of fuzzy normal subgroups moreover we have also demonstrated other applications regarding quasinormality and fuzzy submonoid generated by two fuzzy submonoids using the redefined sup min product due to kim inform sci 91 1996 77

probability like functionals and fuzzy logic abstract the aim of this paper is to show that fuzzy logic is a suitable tool to manage several types of probability like functionals namely we show that the superadditive functions the necessities the upper and lower probabilities and the envelopes can be considered theories of suitable fuzzy logics some general results about the compactness in fuzzy logic are also obtained

lattice of fuzzy subalgebras and closure systems in i x abstract let x be a non empty set and i be the unit interval of real numbers the elements of i x are called fuzzy subsets of x i x is a lattice with the pointwise ordering of i now if a x f is an universal algebra with a specified set f of finitary operations on x then each operation can be extended to a finitary operation on i x an element of i x is defined to be a fuzzy subalgebra of a using these extended operations we also define algebraic closure system in i x we then show that the lattice of fuzzy subalgebras of a is an algebraic closure system in i x

the lattice of fuzzy left right ideals of a ring is modular we use the technique of nested set to study the structure of the lattice of all fuzzy left right ideals of a given ring we give a way to depict the supremum of fuzzy left right ideals by nested set and prove that the lattice of all fuzzy left right ideals of a given ring is modular

mono unary algebras are uniquely determined by their lattices of fuzzy weak subalgebras in this paper we give an abstract characterization of the lattices that are isomorphic to the lattice of fuzzy weak subalgebras of some partial algebra and we show that from this lattice we can extract more information about the algebra than from its lattice of weak subalgebras we use it to prove that the directed graph associated to a unary partial algebra is always uniquely determined up to isomorphisms by the algebra s lattice of fuzzy weak subalgebras and in particular that if two mono unary partial algebras i e two partial algebras over a signature containing only one operation symbol which is moreover unary have their lattices of fuzzy weak subalgebras isomorphic then they are isomorphic

higher order partial least squares hopls a generalized multilinear regression method a new generalized multilinear regression model termed the higher order partial least squares hopls is introduced with the aim to predict a tensor multiway array y from a tensor x through projecting the data onto the latent space and performing regression on the corresponding latent variables hopls differs substantially from other regression models in that it explains the data by a sum of orthogonal tucker tensors while the number of orthogonal loadings serves as a parameter to control model complexity and prevent overfitting the low dimensional latent space is optimized sequentially via a deflation operation yielding the best joint subspace approximation for both x and y instead of decomposing x and y individually higher order singular value decomposition on a newly defined generalized cross covariance tensor is employed to optimize the orthogonal loadings a systematic comparison on both synthetic data and real world decoding of 3d movement trajectories from electrocorticogram signals demonstrate the advantages of hopls over the existing methods in terms of better predictive ability suitability to handle small sample sizes and robustness to noise

fuzzy congruence relations abstract if a x f is an universal algebra and if r x denotes the set of all fuzzy subsets of x x i e fuzzy relations on x then the algebraic operations fg f on x are extended to algebraic operations f on r x f is an algebra similar to a it is called relational algebra a fuzzy equivalence relation which is at the same time a fuzzy subalgebra of r x f is called a fuzzy congruence relation on x in this paper we study fuzzy congruence relations amongst other things we prove that the set of all fuzzy congruence relations on an algebra is a complete lattice and an algebraic closure system

function on function linear regression by signal compression abstractwe consider functional linear regression models with a functional response and multiple functional predictors with the goal of finding the best finite dimensional approximation to the signal part of the response function defining the integrated squared correlation coefficient between a random variable and a random function we propose to solve a penalized generalized functional eigenvalue problem whose solutions satisfy that projections on the original predictors generate new scalar uncorrelated variables and these variables have the largest integrated squared correlation coefficient with the signal function with these new variables we transform the original function on function regression model to a function on scalar regression model whose predictors are uncorrelated and estimate the model by penalized least square method this method is also extended to models with both multiple functional and scalar predictors we provide the asymptotic consistency and the corresponding convergence rates

fuzzy generalized bi ideals in semigroups abstract we introduce the concept of a fuzzy generalized bi ideal of a semigroup which is an extension of the concept of a fuzzy bi ideal and of a nonfuzzy bi ideal and a nonfuzzy ideal of a semigroup and characterize regular semigroups and both intraregular and left quasiregular semigroups in terms of fuzzy generalized bi ideals

stabilized low order finite elements for stokes equations with damping abstract in this paper we consider the stationary stokes equations with damping low order mixed finite element spaces are used to approximate the velocity and the pressure and a local pressure projection stabilization method is used for the pairs to overcome the lack of the inf sup condition the stability of this method is proved and the optimal order error estimates are derived by some nonlinear analysis techniques at last two numerical examples are implemented to test the stability and effectiveness of the proposed method