about simple fuzzy control and fuzzy control based on fuzzy relational equations abstract the paper discusses fuzzy controllers based on fuzzy relational equations in the case when fuzzy controllers inputs are exact godelian implication and minimum function as t norm are considered fuzzy relational equation with sup t composition results in plausible control and adjoint equation results in the simple fuzzy control min max inference method computation of fuzzy relations is not necessary relation between fuzzy plausible control and simple fuzzy control is discussed control algorithms are compared on simulation example

algorithms for solving fuzzy relational equations in a probabilistic setting abstract we discuss methods suitable for finding approximate solutions to fuzzy relational equations defined in finite universe of discourse and taking the form of either a system of equations x k r y k k 1 2 k with r being unknown fuzzy relation or a single equation x r y with x being looked for the key idea of the proposed algorithms is to incorporate some statistics concerning the solution of a single equation and utilize it in the final process of approximation of the unknown fuzzy relation set numerical considerations support the established algorithms

cusp geometry of fibered 3 manifolds let f be a surface and suppose that varphi colon f to f is a pseudo anosov homeomorphism fixing a puncture p of f the mapping torus m m varphi is hyperbolic and contains a maximal cusp c about the puncture p we show that the area and height of the cusp torus partial c is equal to the stable translation distance of varphi acting on the arc complex scr a f p up to an explicitly bounded multiplicative error our proof relies on elementary facts about the hyperbolic geometry of pleated surfaces in particular the proof of this theorem does not use any deep results from teichm uller theory kleinian group theory or the coarse geometry of scr a f p a similar result holds for quasi fuchsian manifolds n cong f times bbb r in that setting we find a combinatorial estimate for the area and height of the cusp annulus in the convex core of n up to explicitly bounded multiplicative and additive error as an application we show that covers of punctured surfaces induce quasi isometric embeddings of arc complexes

non lerfness of arithmetic hyperbolic manifold groups and mixed 3 manifold groups we will show that for any noncompact arithmetic hyperbolic m manifold with m 3 and any compact arithmetic hyperbolic m manifold with m 4 that is not a 7 dimensional one defined by octonions its fundamental group is not locally extended residually finite lerf the main ingredient in the proof is a study on abelian amalgamations of hyperbolic 3 manifold groups we will also show that a compact orientable irreducible 3 manifold with empty or tori boundary supports a geometric structure if and only if its fundamental group is lerf

convexly combined fuzzy relational equations and several aspects of their application to fuzzy information processing abstract this paper presents some theoretical results on a set of the convexly combined fuzzy relational equations represented in the form x k 2 x k r y k k 1 2 k where x k and y k denote fuzzy sets r and 2 fuzzy relations the sup min compositional operator the inf max one and a fuzzy convex combinator whose complement is furthermore we propose a method to formulate the fuzzy information processing approximately by means of the convexly combined fuzzy relational equations focusing our attention on the modeling of fuzzy input output systems normality of fuzzy sets characterizing fuzzy input fuzzy logical aspects of systems and association between fuzzy information finally it is suggested that the proposed method is suitable for the modelling of several types of fuzzy systems

separable subsets of gferf negatively curved groups a word hyperbolic group g is called gferf if every quasiconvex subgroup coincides with the intersection of finite index subgroups containing it we show that in any such group the product of finitely many quasiconvex subgroups is closed in the profinite topology on g

infinite fuzzy relational equations on a complete brouwerian lattice abstract let i be a finite and j an infinite index sets a a ij i j and b b i i i a given matrix and a column vector with elements from a complete brouwerian lattice in this paper the problem of a minimal solution of a fuzzy relational equation a x b where is the sup inf composite operation is investigated

solvability and unique solvability of max min fuzzy equations abstract the problem of solvability and the problem of unique solvability of a fuzzy relation equation in an arbitrary max min algebra are considered and corresponding necessary and sufficient conditions are presented the results allow to solve both problems by an o mnp algorithm where m n p are the dimensions of the corresponding relations in the equation the existence of the greatest and of the least solution is also considered

essential closed surfaces in bounded 3 manifolds a question dating back to waldhausen 10 and discussed in various contexts by thurston see 9 is the problem of the extent to which irreducible 3 manifolds with infinite fundamental group must contain surface groups to state our results precisely it is convenient to make the definition that a map i s 9 m of a closed orientable connected surface s is essential if it is injective at the level of fundamental groups and the group i rr1 s cannot be conjugated into a subgroup 7rr com of rr m where om is a component of om this latter condition is equivalent to the statement that the image of the surface s cannot be freely homotoped into om one of the main results of this paper is the following

unattainable solutions of a fuzzy relation equation in a fuzzy relation equation the properties of the solution set have been investigated especially when the basic spaces are all finite sets however when the basic spaces are infinite a few properties are known in this paper we use the concepts of attainability and unattainability of a solution to clarify some properties of the solution set and show the condition for existence of a partially attainable solution and an unattainable one

free vibration analysis of a uniform cantilever beam with point masses by an analytical and numerical combined method abstract the natural frequencies and mode shapes of a uniform cantilever beam carrying any number of concentrated masses were determined by using an analytical and numerical combined method anc method the eigenvalue equation was first derived analytically by using the expansion theorem and then the eigenvalues and eigenvectors were calculated numerically in comparison with the general finite element method fem the anc method has the advantage that there is no necessity to derive the property matrices of each beam element and then to develop the overall ones of the entire beam in comparison with the transfer matrix method tmm the anc method requires no tedious matrix multiplication so that some computer time may be saved the anc method is also better than the pure analytical closed form method since instead of a few special cases a uniform beam carrying any number of point masses of various magnitudes or distributions along the beam length can be easily solved besides by using the anc method there is no difficulty in taking more modes in the mode superposition equation and hence more higher mode natural frequencies of better accuracy may be obtained

fuzzy relational equation with defuzzification algorithm for the largest solution this paper provides an algorithm for solving a new fuzzy relational equation including defuzzification an input fuzzy set is first transformed into an internal fuzzy set by a fuzzy relation and then an element giving the largest membership value is selected from the support set as an output our purpose is to obtain the internal fuzzy relation from pairs of input fuzzy sets and output set elements these relational equations are classified into two types called type i and type ii in the text depending on where internal fuzzy sets are defuzzified discussions in this paper are done on the largest solutions of these problems algorithms to obtain the largest solutions are shown as well as some propositions and numerical examples

shrinkwrapping and the taming of hyperbolic 3 manifolds we introduce a new technique for finding cat 1 surfaces in hyperbolic 3 manifolds we use this to show that a complete hyperbolic 3 manifold with finitely generated fundamental group is geometrically and topologically tame

some properties of sup min fuzzy relational equations on infinite domains abstract this paper deals with a sup min fuzzy relational equation on infinite domains some properties of its solution set will be obtained in particular a necessary and sufficient condition describing the attainable solution resp the unattainable solution is formulated in the end the solution set will be given under some conditions

lower solutions of systems of fuzzy equations lower solutions of a system of fuzzy equations are determined by lower solutions of each equation the result is applied to fuzzy relation equations so that they are decomposed to simple fuzzy relation equations

an algorithm for solving fuzzy relation equations with max t composition operator this paper studies the problem of solving a max t composite finite fuzzy relation equation where t is a special class of pseudo t norms if the equation is solvable then its set of feasible solutions is determined by the greatest solution and a finite number of minimal solutions some necessary conditions are presented for the minimal solutions in terms of the maximum solution and zero value under these conditions some minimal solutions of the system can be obtained easily some procedures are also proposed in order to simplify the original system the simplified system is then decomposed if possible into several subsystems with smaller dimensions which are very easy to solve furthermore a method is presented to solve each subsystem by combining the method and those procedures an efficient algorithm is proposed to obtain the set of feasible solutions of the original system two examples are also given to illustrate the algorithm

minimal genus in 4 manifolds with a free circle action abstract let n be a closed irreducible 3 manifold and assume n is not a graph manifold we improve for all but finitely many s 1 bundles m over n the adjunction inequality for the minimal complexity of embedded surfaces this allows us to completely determine the minimal complexity of embedded surfaces in all but finitely many s 1 bundles over a large class of 3 manifolds

on some systems of simultaneous equations in a completely distributive lattice abstract we discuss some systems of simultaneous equations in a completely distributive lattice l when the unknowns are regarded as elements of l we obtain necessary and sufficient conditions for the systems to have a solution in addition we consider an application for systems of fuzzy relation equations

on some finite fuzzy relation equations abstract we give a necessary and sufficient condition for the resolution of a new type of finite fuzzy relation equation whose set of solutions is entirely characterized an example of application to approximate reasoning is also given

t eigen fuzzy sets abstract this paper concerns the study of the solutions of sup t equations such that atr a where t is a triangular norm and r is a fuzzy relation by generalizing a result from sanchez 12 we determine the greatest t eigen fuzzy set of a fuzzy relation a t eigen fuzzy set of r being a fuzzy set a which is a solution of atr a we also study some algebraic properties for the class of the t eigen sets of a fuzzy relation and for the set of fuzzy relations leaving invariant a given fuzzy set finally properties related with the transitive closure are established

optimization of fuzzy relation equations with max product composition abstract an optimization problem with a linear objective function subject to a system of fuzzy relation equations using max product composition is considered since the feasible domain is non convex traditional linear programming methods cannot be applied we study this problem and capture some special characteristics of its feasible domain and the optimal solutions some procedures for reducing the original problem are presented the problem is transformed into a 0 1 integer program which is then solved by the branch and bound method for illustration purpose an example of the procedures is provided

an exact generalised function approach to frequency response analysis of beams and plane frames with the inclusion of viscoelastic damping abstract this paper concerns the frequency response analysis of beams and plane frames with an arbitrary number of kelvin voigt viscoelastic dampers typical external and internal dampers are considered as grounded translational tuned mass rotational and axial dampers for bending and axial vibrations respectively using the theory of generalised functions within a 1d formulation of equations of motion exact closed form expressions are derived for beam dynamic green s functions and frequency response functions under arbitrary polynomial load for any number of dampers for a plane frame exact global frequency response matrix and load vector are built with size depending only on the number of beam to column nodes for any number of dampers and point polynomial loads along the frame members from the nodal displacement solution the exact frequency response in all frame members is also obtained in closed analytical form numerical applications show many of the advantages of the proposed method

strict preference relations based on weak t norms abstract in this paper we introduce and investigate weak t norms and related concepts in order to give a general representation of valued strict preference relations associated with a given valued preference relation all the well known forms of valued strict preference relations are particular cases of our results moreover when some types of rationality assumptions are made our unified approach seems to be the only possible one

method of solution to fuzzy equations in a complete brouwerian lattice abstract up to now how to solve a fuzzy relation equation in a complete brouwerian lattice is still an open problem as di nola et al point out to this problem the key problem is whether there exists a minimal element in the solution set when a fuzzy relation equation is solvable in this paper we first show that there is a minimal element in the solution set of a fuzzy relation equation a x b where a a 1 a 2 a n and b are known and x x 1 x 2 x n t is unknown when its solution set is nonempty and b has an irredundant finite join decomposition further we give the method to solve a x b in a complete brouwerian lattice under the same conditions finally a method to solve a more general fuzzy relation equation in a complete brouwerian lattice when its solution set is nonempty is also given under similar conditions

generalized solvability criteria for fuzzy equations abstract recently e sanchez has given a necessary and sufficient condition for the existence of a solution of a fuzzy a x c with the extension of a given binary operation in the universe of discourse using many valued logic we generalize this result and get a characterization also of the cases if a x c has only nearly a solution additionally we consider fuzzy relation equations and get similar results

dynamic analysis of a uniform cantilever beam carrying a number of elastically mounted point masses with dampers abstract the free and forced vibration analyses of a uniform cantilever beam carrying a number of spring damper mass systems with arbitrary magnitudes and locations were made by means of the analytical and numerical combined method ancm first of all a method was presented to replace each spring damper mass system by a massless equivalent spring damper system with effective spring constant keffand effective damping coefficient ceffso that the ancm is available for the title problem next the equation of motion for the constrained beam with spring damper mass systems attached was derived by using the natural frequencies and normal mode shapes of the unconstrained beam without carrying any attachments incorporating the expansion theorem finally the eigenvalues and the forced vibration responses of the constrained beam were determined by conventional numerical methods to confirm the reliability of the presented theory all the numerical results obtained from the ancm were compared with the corresponding ones obtained from the conventional finite element method fem and good agreement was achieved the influence of the damping magnitude of each spring damper mass system on the eigenvalues and the forced vibration responses of the constrained beam was studied because the order of the overall property matrices for the equation of motion of the constrained beam derived from the ancm is much lower than that from the conventional fem the storing memory and the cpu time required by the ancm are much less than those required by the fem

approximate solutions of fuzzy relational equations in the previous chs we have discussed various problems concerning solutions of fuzzy relation equations obviously an underlying assumption is that there exists a nonempty set of solutions a situation may occurr and indeed it is quite common in which no solution exists nevertheless even in this case one might be interested to obtain an approximate solution and know to which extent it can be viewed as a solution this stream of investigations is particularly interesting for applicational purposes contrary to the topics already discussed in the previous chs this is a field of research which has not been developed enough so far it concerns studies on solvability properties of fuzzy relation equations in this ch we shall try to answer by using several techniques the following basic question how difficult is it to attain a situation in which the system of equations has solutions and then how to measure this property

łukasiewicz transform and its application to compression and reconstruction of digital images we define the lukasiewicz transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an mv algebra then we describe the lukasiewicz transform based ltb algorithm for image processing demonstrating its applicability

specificity shift in solving fuzzy relational equations abstract studied is a system of n fuzzy relational equations with a max t composition x k r y k where the input output fuzzy sets x k and y k are available while the fuzzy relation r needs to be determined the solution to these equations is derived through a new paradigm of specificity shift the main objective is to modify a level of specificity of the fuzzy sets relational constraint so that the modified constraints allow for the use of some standard theoretical results of the theory of fuzzy relational equations that otherwise would have been found totally unjustifiable in more detail the specificity of the available input fuzzy sets becomes gradually increased while an opposite tendency is observed for the output fuzzy sets the optimization of the specificity levels is discussed in detail numerical studies are also included finally the use of the specificity shift is discussed in a conjunction with the exploitation of standard gradient based techniques

novel neural algorithms based on fuzzy d rules for solving fuzzy relation equations part iii abstract in this paper we first design a fuzzy neuron which possesses some generality this fuzzy neuron is founded by replacing the operators of the traditional neuron with a pair of abstract fuzzy operators as which we call fuzzy neuron operators for example it may be or etc it is an extended fuzzy neuron and a network composed o such neurons is an extended fuzzy neural network then we discuss the relationship between the fuzzy neuron operators and t norm and t conorm and point out fuzzy neuron operators are based on t norm but much wider than t norm in this paper we will emphatically discuss a two layered network and its training algorithm which will have to satisfy a set of various operators this work is very related to solving fuzzy relation equations so it can be used to resolve fuzzy relation equations furthermore the new fuzzy neural algorithm is found to be stronger than other existing methods to some degree some simulation results will be reported in detail

mixed 3 manifolds are virtually special letm be a compact oriented irreducible 3 manifold which is neither a graph manifold nor a hyperbolic manifold we prove that 1m is virtually special

resolution of finite fuzzy relation equations abstract general schemes for solving fuzzy relation equations with finite sets are derived in this paper the relationship between the results derived here and those of previous publications regarding this subject is also discussed

design of fuzzy logic controllers based on generalized t operators abstract since zadeh first proposed the basic principle of fuzzy logic controllers in 1968 the min and max operators have been popular in the design of fuzzy logic controllers in this paper the general concept of t operators is introduced into the conventional design methods for fuzzy logic controllers so that a general and flexible methodology for the design of these fuzzy logic controllers is available then by computer simulations studies are made so as to determine the relations between the various t operators and the performance of a fuzzy logic controller it is concluded that the performance of the fuzzy logic controller for a given class of plants very much depends upon the choice of the t operators

on matrix equations in a class of complete and completely distributive lattices matrix equations of the form ax b and ya b are considered in a class of complete and completely distributive lattices where the multiplication operation of matrices is defined either by the max min or by the min max way necessary and sufficient conditions for the solvability of the equations are obtained and for the solvable case the entire solution set and the largest solution are determined by using relative pseudo or relative lower pseudocomplements in lattices the results are seen to be a generalization of 4 5 6 and in a sense also an extension of 3 as an application the g inverse and thierrin vagner inverses of matrices are considered

fuzzy relation equations for coding decoding processes of images and videos we adopt fuzzy relation equations with continuous triangular norms for compression decompression processes of grey images colour images in the rgb space and frames of videos by comparing the results of the reconstructed images with standard methods like jpeg and mpeg 4 any image is subdivided in blocks and each block is coded decoded using arbitrary fuzzy sets as coders in the fuzzy equations we evaluate the peak signal to noise ratio psnr on the decompressed images for several values of the compression rates as measure of the quality of images and frames reconstructed the original frames of a video are classified in intra frames and predictive frames by using a similarity measure based on the well known lukasiewicz t norm

coxeter groups are virtually special abstract in this paper we prove that every finitely generated coxeter group has a finite index subgroup that is the fundamental group of a special cube complex some consequences include every f g coxeter group is virtually a subgroup of a right angled coxeter group every word hyperbolic coxeter group has separable quasiconvex subgroups

on direct and inverse problems for fuzzy equation systems with tolerances abstract we investigate the resolution of fuzzy relational equation systems with tolerances which are a certain extension of fuzzy equations considered f i in 3 5 the extension of the concept of higashi and klir 3 enables us to describe the set of solutions to our problem for given tolerances by means of posets in a second part we investigate an inverse problem given upper lower tolerances how to determine lower upper tolerances such that the arising problem becomes consistent numerical examples are given

pseudo t norms and implication operators direct products and direct product decompositions in this paper we further study the pseudo t norms and implication operators on a complete brouwerian lattice and discuss their direct products and direct product decompositions

solving nonlinear optimization problems with fuzzy relation equation constraints abstract an optimization model with a nonlinear objective function subject to a system of fuzzy relation equations is presented since the solution set of the fuzzy relation equations is in general a non convex set when it is not empty conventional nonlinear programming methods are not ideal for solving such a problem in this paper a genetic algorithm ga is proposed this ga is designed to be domain specific by taking advantage of the structure of the solution set of fuzzy relation equations the individuals from the initial population are chosen from the feasible solution set and are kept within the feasible region during the mutation and crossover operations the construction of test problems is also developed to evaluate the performance of the proposed algorithm

fuzzy function as an approximate solution to a system of fuzzy relation equations this paper is mostly focused on the problem of approximate solvability of a system of fuzzy relation equations however we put a new light on this problem connecting it with the interpolation of a fuzzy function we introduce a notion of fuzzy function and its representation by fuzzy relation we demonstrate how problems of interpolation and approximation of fuzzy functions are connected with solvability of systems of fuzzy relation equations first we explain the general framework and then we prove some results related to the problem of the best approximation in particular we have shown that fuzzy relations introduced by sanchez and mamdani are the best approximations in certain approximation spaces

further relation equations with equality and difference composition operators in this ch we will introduce other composition operators which have a plausible logical interpretation they will be called equality and difference operator respectively we first define a notion of equality and difference of any two grades of membership of a fuzzy set and of a fuzzy relation in the sequel this concept will be utilized to form the respective composition operators and the related fuzzy equations afterwards we provide a method of resolution of these equations characterizing completely the set of the solutions all the fuzzy sets involved are defined on finite sets and with membership values in 0 1

fuzzy relation equations on a finite set abstract the family of all the solutions of a fuzzy relation equation on a finite set is considered it is characterized by the set of all the lower solutions which can be obtained by a combinatorial algorithm

vibration analysis for a coupled beam sdof system by using the recurrence equation method this paper presents the vibration analysis of a coupled system composed of a beam and a single degree of freedom sdof system the harmonic responses of this kind of system are formulated by means of the recurrence equation method in addition the natural characteristics of the system are also analyzed numerical examples of the undamped system are given and compared with the published results and an excellent correlation shows that the study work in this paper is correct