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

reduction of attributes in averaged similarities abstract similarity relations may be constructed from a set of fuzzy attributes each fuzzy attribute generates a simple similarity and these simple similarities are combined into a complex similarity afterwards the representation theorem establishes one such way of combining similarities while averaging them is a different and more realistic approach in applied domains in this paper given an averaged similarity by a family of attributes we propose a method to find families of new attributes having fewer elements that generate the same similarity more generally the paper studies the structure of this important class of fuzzy relations

a unified approach for the formulation of interaction problems by the boundary element method a unified formulation is presented based on boundary element method in a form suitable for performing the interaction analyses by substructure method for solid solid and soil structure problems the proposed formulation permits the evaluation of all the elements of impedance and input motion matrices simultaneously at a single step in terms of system matrices of the boundary element method without solving any special problem such as unit displacement or load problem as required in conventional methods it eliminates further the complicated procedure and the need for using scattering analysis in the evaluation of input motion functions to explain the formulation it is first given for an inclusion interacting with an infinite surrounding medium under the influence of a seismic input where both the inclusion and surrounding medium are treated as viscoelastic it is shown that the formulation for a rigid inclusion may be obtained from that for flexible inclusion as a special case through a transformation then the formulation is extended to other types of interaction problems a multi inclusion problem and an interaction problem involving a foundation embedded in a viscoelastic half space it is found that the proposed formulation remains essentially the same for all kinds of interaction problems and it can be used not only in regular interaction analysis but also in the analysis involving diffraction of waves in a medium containing holes copyright 2005 john wiley sons ltd

l fuzzy closure systems this paper studies the generalization of fuzzy closure operators and fuzzy closure systems introduced by belohlavek in 2001 and introduces the concepts of strong l fuzzy closure systems and strong l fuzzy closure operators it is shown that a strong l fuzzy closure system is precisely the fuzzy system in opposition to the crisp system and a strong l fuzzy closure operator is a suitable closure operator that has a close relation to a strong l fuzzy closure system it is also shown that there is a galois correspondence between the category of strong l fuzzy closure system spaces and that of strong l fuzzy closure spaces

a comparison of localized finite element formulations for two dimensional wave diffraction and radiation problems two of the most promising localized finite element methods are compared the boundary series element method in which a series of eigenfunctions is used to represent the far field solution and the boundary integral element method in which an integral equation is satisfied at the boundary between localized finite element and outer regions the methods are applied to water of arbitrary depth the theory of the two methods is summarized and typical numerical results are discussed consideration is given to the well known hydrodynamical reciprocal relations and to the phenomenon of irregular frequencies the relative merits of the two methods are established

fuzzy relations and fuzzy groups abstract given a group s we consider fuzzy relations on s that is maps from s s into 0 1 of particular interest is to investigate conditions under which the fuzzy relation becomes a fuzzy subgroup on s s we prove that if is a fuzzy subset of s and is the strongest fuzzy relation on s that is a fuzzy relation on then is a fuzzy subgroup if and only if is a fuzzy subgroup a number of other results are obtained about the interrelationships between fuzzy relations on s including the weakest fuzzy relation and fuzzy subgroups on s s

a restricted second order logic for finite structures we introduce a restricted version of second order logic so in which the second order quantifiers range over relations that are closed under the equivalence relation k of k variable equivalence for some k this restricted second order logic is an effective fragment of the infinitary logic l which differs from other such fragments in that it is not based on a fixpoint logic we explore the relationship of so with fixpoint logics showing that its inclusion relations with these logics are equivalent to problems in complexity theory we also look at the expressibility of np complete problems in this logic

fuzzy groups some group theoretic analogs abstract we introduce the concepts of 1 order of a fuzzy subgroup of a finite group 2 a fuzzy abelian group and 3 a fuzzy solvable group we obtain some results involving these notions which are analogs of results from group theory also we prove analogs of two basic theorems of group theory namely cayley s theorem and lagrange s theorem

a relationship between equality relations and the t redundancy of fuzzy partitions and its application to sugeno controllers abstract the question whether a family of fuzzy subsets can be transformed by a multiplicative function is investigated in order to minimize its t l redundancy and in order to get a family of fuzzy points with respect to some equality relation

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

dynamic analysis of linear viscoelastic cylindrical and conical helicoidal rods using the mixed fem abstract the objective of this study is to investigate the influence of the rotary inertia on dynamic behavior of linear viscoelastic cylindrical and conical helixes by means of the laplace transform mixed finite element formulation and solution the element matrix is based on the timoshenko beam theory the influence of rotary inertias is considered in the dynamic analysis which is original in the literature rectangular sine and step type of impulsive loads are applied on helices having rectangular cross sections with various aspect ratios the kelvin and standard models are used for defining the linear viscoelastic material behavior and by means of the correspondence principle the elastic viscoelastic analogy the material parameters are replaced with their complex counterparts in the laplace domain the analysis is carried out in the laplace domain and the results are transformed back to time space numerically by modified durbin s algorithm first the solution algorithm is verified using the existing open sources in the literature and afterwards some benchmark examples such as conical viscoelastic rods are handled

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

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

towards the theory of m approximate systems fundamentals and examples the concept of an m approximate system is introduced basic properties of the category of m approximate systems and in a natural way defined morphisms between them are studied it is shown that categories related to fuzzy topology as well as categories related to rough sets can be described as special subcategories of the category of m approximate systems

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

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

an automata theoretic approach to branching time model checking translating linear temporal logic formulas to automata has proven to be an effective approach for implementing linear time model checking and for obtaining many extensions and improvements to this verification method on the other hand for branching temporal logic automata theoretic techniques have long been thought to introduce an exponential penalty making them essentially useless for model checking recently bernholtz and grumberg 1993 have shown that this exponential penalty can be avoided though they did not match the linear complexity of non automata theoretic algorithms in this paper we show that alternating tree automata are the key to a comprehensive automata theoretic framework for branching temporal logics not only can they be used to obtain optimal decision procedures as was shown by muller et al but as we show here they also make it possible to derive optimal model checking algorithms moreover the simple combinatorial structure that emerges from the automata theoretic approach opens up new possibilities for the implementation of branching time model checking and has enabled us to derive improved space complexity bounds for this long standing problem

lattices of fuzzy subgroupoids fuzzy submonoids and fuzzy subgroups we redefine the sup min product of fuzzy subsets and discuss the redefined sup min products of fuzzy subgroupoids fuzzy submonoids and fuzzy subgroups in addition we study lattice structures of the lattices of fuzzy subgroupoids fuzzy submonoids and fuzzy subgroups

the logic of tied implications part 1 properties applications and representation a conjunction t ties an implication operator a if the identity a a a b z a t a b z holds a a abdel hamid n n morsi associatively tied implications fuzzy sets and systems 136 2003 291 311 we study the class of tied adjointness algebras which are five connective algebras on two partially ordered sets in which the implications are tied by triangular norms this class contains besides residuated implications several other implications employed in fuzzy logic nevertheless we show that the algebraic inequalities of residuated algebras remain true for our tied implications but in forms that distribute roles over the five connectives of the algebra we apply the properties of tied implications to a generalized modus ponens inference scheme with two successive rules we prove its equivalence to a scheme with one compound rule when both schemata are interpreted by the compositional rule of inference and all connectives are taken from one tied adjointness algebra then we quote another application of this rich theory a notion of many valued rough sets which exhibit the basic mathematical behaviour of the rough sets of pawlak a comparator h is said to be prelinear if it satisfies h y z h z y 1 for all y z hajek we introduce prelinear tied adjointness algebras in which two comparators are prelinear we provide a representation of those algebras as subdirect products of tied adjointness chains on the lines of hajek s representation of bl algebras but our representations are more economical because we employ minimal prime filters on residuated lattices only rather than all prime filters

extension principles for fuzzy set theory in several cases we show that it is possible to extend a notion in classical mathematics by identifying each fuzzy subset with the continuous chain of its closed cuts and by applying this notion to these cuts in particular this idea is applied to extend functions from subsets into subsets for instance closure operators and functions from sets into real numbers for instance measures

numerical representation of transitive fuzzy relations we show that there exists a continuous fuzzy quasi order r on the set of real numbers r such that for any fuzzy quasiorder r on a finite set x there is a mapping f x r such that r x y r f x f y for all x y x

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

comparing fuzzy and crisp deduction systems abstract the connections between the fuzzy deduction systems and the crisp deduction systems are examined we show that there is a natural way to associate to every fuzzy deduction system a crisp deduction system and to every crisp deduction system a fuzzy deduction system

galois connections among fuzzy groups similarities distances given a set s we define galois connections between the lattices of the fuzzy subgroups of transformations in s the lattice of the similarities in s and the lattice of the distances in s

fuzzy submonoids fuzzy preorders and quasi metrics let l be a residuated lattice then given a monoid m we define a galois connection from the lattice of the compatible l preorders in m and the lattice of l submonoids of m given a set s we define a galois connection between the lattice of the l preorders in s and the lattice of l submonoids of the monoid ss i a link with the notion of quasi metric is also established

fuzzy counterparts of hull operators and interval operators in the framework of l convex spaces abstract for fuzzy counterparts of hull operators and interval operators two types of fuzzy hull operators and one type of fuzzy interval operators are proposed firstly the concept of l hull operators is introduced and the resulting category is shown to be isomorphic to that of l convex spaces secondly considering the graded inclusions of l subsets the notion of l ordered hull operators is presented which is shown to be categorically isomorphic to strong l convex structures finally the concept of l interval operators is introduced and it is shown that there is a galois correspondence between the category of l interval spaces and that of l convex spaces in particular the category of arity 2 l convex spaces can be reflectively embedded into that of l interval spaces

maxima and minima in fuzzified linear orderings the paper studies the notions of fuzzy maxima minima suprema and infima in the setting of fuzzified linear orderings the main result shows that in fuzzified linear orders satisfying certain reasonable assumptions the fuzzy maxima and minima of all non empty fuzzy sets are non empty

on fuzzy ideals and fuzzy bi ideals in semigroups abstract in this paper we give some properties of fuzzy ideals and fuzzy bi ideals of semigroups and characterize semigroups that are left duo left simple and semilattices of subsemigroups in terms of fuzzy ideals and fuzzy bi ideals

a characterization of fuzzy subgroups abstract an ordinary subgroup of a group g is 1 a subset of g 2 closed under the group operation in a fuzzy subgroup it is precisely these two notions that lose their deterministic character a fuzzy subgroup of a group g associates with each group element a number the larger the number the more certainly that element belongs to the fuzzy subgroup the closure property is captured by the inequality x y t x y in a rosenfeld s original definition t was the function minimum however any t norm t provides a meaningful generalization of the closure property two classes of fuzzy subgroups are investigated the fuzzy subgroups in one class are subgroup generated those in the other are function generated each fuzzy subgroup in these classes satisfies the above inequality with t given by t a b max a b 1 0 while the two classes look different each fuzzy subgroup in either is isomorphic to one in the other it is shown that a fuzzy subgroup satisfies the above inequality with t minimum if and only if it is subgroup generated of a very special type finally these notions are applied to some abstract pattern recognition problems

on fuzzy regular subsemigroups of a semigroup abstract since a rosenfeld proposed the concept of fuzzy subgroup in 1971 there has been considerable development of fuzzy algebra in particular n kuraki discussed fuzzy biideals and the fuzzy semiprime ideal of a semigroup we introduce the concepts of fuzzy regular subsemigroups fuzzy weakly regular subsemigroups fuzzy completely regular subsemigroups and fuzzy weakly completely regular subsemigroups and investigate some of their algebraic properties

issues on adjointness in multiple valued logics we contribute to the theory of implications and conjunctions related by adjointness in multiple valued logics we suggest their use in zadeh s compositional rule of inference to interpret generalized modus ponens inference schemata we provide new complete characterizations of implications that distinguish left arguments implications that satisfy the exchange principle divisible conjunctions commutative conjunctions associative conjunctions and triangular norms we also introduce and characterize pseudo strict and pseudo continuous implications and conjunctions and we explore the close relationship between these two notions

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 semiprime ideals in semigroups abstract in this paper we shall introduce the notion of fuzzy semiprimality in a semigroup which is an extension of semiprimality in it and characterize a semigroup that is a semilattice of simple semigroups in terms of fuzzy semiprimality

new results in fuzzy clustering based on the concept of indistinguishability relation the issue of validity in clustering is considered and a definition of fuzzy r cluster that extends e ruspini s definition 1982 is proposed this definition is based on an indistinguishability relation based on the concept of t norm the fuzzy r cluster s metrical properties are studied through the dual concept of t conorm that leads to g pseudometrics from the concept of g pseudometric fuzzy r clusters and fuzzy cluster coverages are defined the authors propose a measure of cluster validity based on the concept of fuzzy coverage the basic idea of the approach presented is that the smaller the difference between the degrees of membership and the degrees of indistinguishability the better the clustering

the structure of decomposable indistinguishability operators decomposable fuzzy relations are studied symmetric fuzzy relations are proved to be generated by a single fuzzy subset for archimedean t norms decomposable indistinguishability operators generate special kinds of betweenness relations that characterize them a new way to generate indistinguishability operators coherent with the underlying ordering structure of the real line is given in the sense that this structure is compatible with the betweenness relation generated by the relation is developed

handling the valuation of the predicates in a fuzzy model given a fuzzy model and therefore a graded valuation of the predicates several handlings of such a valuation are possible for example we can change the set of truth values modify the scale cut the predicates and identify truth values in this exploratory paper we analyze some of the properties preserved under these handlings to do this we refer to an approach to fuzzy semantics in which the valuation structures can vary freely inside a given type

state space boundary element finite element coupling for fluid structure interaction analysis state space coupling is a new approach for handling computational fluid structure interaction problems in the low to medium frequency range the method is based on standard boundary element bem and finite element fem discretizations of the acoustic and structural domains respectively the implicit frequency dependence of a traditional acoustic impedance matrix is made explicit through a power series expansion on circular frequency and considering time harmonic motion once expanded the acoustic energy of the fluid is directly coupled to that of the structure via hamilton s principle the coupled system is then recast in a canonical state space form which is also in the form of a standard eigenvalue problem solution of this system produces a series of complex eigenvalues and eigenvectors which represent a modal decomposition of the fluid loaded structure biorthogonality properties of the state space eigensystem allow for an uncoupled modal solution of the forced problem results for a submerged spherical shell and a finite plate in an infinite ridged baffle are given to illustrate the state space approach

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

fuzzy closure operators closure operators and closure systems play a significant role in both pure and applied mathematics in the framework of fuzzy set theory several particular examples of closure operators and systems have been considered e g so called fuzzy subalgebras fuzzy congruences fuzzy topology etc recently fuzzy closure operators and fuzzy closure systems themselves i e operators which map fuzzy sets to fuzzy sets and the corresponding systems of closed fuzzy sets have been studied by gerla et al see e g 3 4 6 7 as a matter of fact a fuzzy set a is usually defined as a mapping from a universe set x into the real interval 0 1 in the above mentioned works therefore the structure of truth values of the logic behind is fixed to 0 1 equipped usually with minimum as the operation corresponding to logical conjunction as it appeared recently in the investigations of fuzzy logic in narrow sense 9 10 i e fuzzy logic as a many valued logical calculus there are several logical calculi formalizing the intuitive idea of fuzzy reasoning which are complete with respect to the semantics over special structures of truth values among these structures the most general one is that of a residuated lattice it is worth noticing that residuated lattices introduced originally in 12 as an abstraction in the study of ideal systems of rings have been proposed as a suitable structure of truth values by goguen in 8 from this point of view the need for a general notion of a fuzzy closure concept becomes apparent the aim of this paper is to outline a general theory of fuzzy closure operators and fuzzy closure systems in the next section we introduce the necessary concepts in section 3 fuzzy closure operators and systems are

dominance in the family of sugeno weber t norms the dominance relationship between two members of the family of sugeno weber t norms is proven by using a quantifier elimination algorithm further it is shown that dominance is a transitive and therefore also an order relation on this family of t norms

equality relations as a basis for fuzzy control abstract the aim of this paper is to introduce a fuzzy control model with well founded semantics in order to explain the concepts applied in fuzzy control assuming that the domains of the input and output variables for the process are endowed with equality relations that reflect the indistinguishability of values lying closely together the use of triangular and trapezoidal membership functions can be justified and max inference where is a t norm turns out to be a consequence of our model distinguishing between a functional and a relational view of the control rules it is possible to explain when defuzzification strategies like mom or coa are appropriate or lead to undesired results

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

closure systems and l subalgebras abstract let x be a set and l a class of l subsets of x l is a closure system if it is closed with respect to greatest lower bounds if is an l subset then the g l b tf of g l g is said to be generated by we examine closure systems of l subalgebras and propose formulas for the l subalgebra of a required type generated by a given l subset

normality and congruence in fuzzy subgroups abstract it is proved that normal fuzzy subgroups and fuzzy congruence relations determine each other in a group theoretic situation this is analogous to the crisp set theoretic case of groups

generalising automaticity to modal properties of finite structures we introduce a complexity measure of modal properties of finite structures which generalises the automaticity of languages it is based on graph automata like devices called labelling systems we define a measure of the size of a structure that we call rank and show that any modal property of structures can be approximated up to any fixed rank n by a labelling system the function that takes n to the size of the smallest labelling system doing this is called the labelling index of the property we demonstrate that this is a useful and fine grained measure of complexity and show that it is especially well suited to characterise the expressive power of modal fixed point logics from this we derive several separation results of modal and non modal fixed point logics some of which are already known whereas others are new

extension principles for closure operators on fuzzy sets and cuts abstract we investigate closure operators defined on various partly ordered sets of fuzzy objects including sets of all fuzzy sets with values in a complete residuated lattice and sets of all cuts systems defined in crisp sets and sets with similarity relations respectively we proved several extension theorems under which a closure operator defined on one universe can be extended to a closure operator defined on another universe we also investigate relationships between continuity of pairs of maps with respect to different closure operators

on β precision aggregation in this paper we propose an extension of the current fuzzy connectives to precision aggregators which include a certain tolerance towards noise and measurement errors in the values of the aggregated criteria when their cardinality is large to do this we have set our extension proposal in the framework of yager s mam mom and mica operators and study the properties of the new extended operators a simple example illustrates the practical use of the extended aggregators

measures of specificity over continuous spaces under similarity relations we introduce the concept of specificity and indicate its importance as a measure of uncertainty for information represented using fuzzy sets or possibility distributions we provide formal measures of specificity for variables whose domain is an interval of the real line similarity relations are discussed and formalized the class of width based similarity relations is introduced we extend the measure of specificity to allow for the effect of an underlying similarity relationship the manifestation of this extension for a number of different similarity relations is investigated particularly notable results are obtained for width based similarity relationships more generally we note the connection between the size of a granule of information and its uncertainty motivated by this we investigate the effect of a similarity relationship on the perception of distance in the underlying space and use this to develop an extension of the specificity measure