time synchronization in wsns with random bounded communication delays recently it was pointed out that many popular consensus based time synchronization algorithms such as average timesynch ats are all divergent in a network with arbitrarily small random communication delays under any interconnection topology this note proposes a least squares estimation based time synchronization lsts for short algorithm this algorithm modifies the ats algorithm in relative drift estimator low pass filter and consensus protocol by analyzing the mathematic model of the algorithm it is proved that lsts ensures asymptotic convergence of the drift estimation and boundedness of the global time synchronization error under random bounded communication delays if the network topology satisfies some connectedness conditions

some notes on equivalent fuzzy sets and fuzzy subgroups this paper discusses the problems of equivalent fuzzy sets and fuzzy subgroups first a critical discussion of previous results by murali and makamba is provided second this paper discusses the conditions under which the equivalence relation of fuzzy sets can be equivalently described by their level sets it also suggests that the equivalence approach to the classification of fuzzy subgroups is suitable only for finite groups and proposes a new definition for the classification of fuzzy subgroups s equivalence showing that any two fuzzy subgroups of an infinite cyclic group with infinite membership values are s equivalent

alternative characterizations for the representation of families of sets by fuzzy sets we investigate the representation of a given family of sets by a fuzzy set in such a way that the level sets of the fuzzy set are precisely the given sets this concept of representation is widely used in the literature for the classification and study of fuzzy structures on the same underlying set negoita and ralescu obtained two theorems both giving necessary and sufficient conditions one called the representation theorem and the second called the generalized representation theorem our aim in this paper is to take a closer look at both theorems hence establishing some equivalent forms and several constructive remarks including some directions for future investigations

equivalent finite fuzzy sets and stirling numbers in this paper we study the number of k level equivalence classes of fuzzy subsets of a finite set of n elements under a natural equivalence this number is related to stirling numbers viewing fuzzy subsets as functions from a set into the unit interval we also associate a kernel partition with every equivalence class of fuzzy subsets after some elementary properties of the equivalence we provide a recurrence relation and a generating function concerning the number of k level fuzzy subsets using stirling numbers

classifying and counting fuzzy normal subgroups by a new equivalence relation abstract the main goal of this paper is to give an explicit formula for the number of fuzzy normal subgroups of some finite non abelian groups by using the new equivalence relation presented in fuzzy sets and systems 289 2016 113 121 precisely for a group g this new equivalence is induced by an action of the automorphism group a u t g associated with g on the lattice of fuzzy normal subgroups of g in fact this new equivalence relation generalizes the natural equivalence relation defined on the lattice of fuzzy normal subgroups

general form of lattice valued fuzzy sets under the cutworthy approach in this note a new solution of problem of synthesis of fuzzy sets is presented in other words necessary and sufficient conditions are formulated under which for a given family of subsets f of a set x and a fixed complete lattice l there is a fuzzy set m x l such that the collection of cuts of m coincides with f moreover it is proved that the general form of lattice valued fuzzy sets considering families of cuts are the type of fuzzy sets having the codomain 0 1 c for a suitable chosen cardinal c

aggregation of fuzzy subgroups abstract given an aggregation function and two fuzzy subgroups of a group this study investigates whether the aggregation of them is also a fuzzy subgroup it is proven that if the cardinal of the group is a prime power then it is always a fuzzy subgroup for a general group it is proven that the existence of a binary relation between the fuzzy subgroups determines if their aggregation is a fuzzy subgroup moreover given two fuzzy subgroups if the aggregation of them is a fuzzy subgroup for some strictly monotone aggregation function then it is a fuzzy subgroup for any aggregation function the present study also examines conditions on the aggregation function that characterise the case where the aggregation of two arbitrary fuzzy subgroups is also a fuzzy subgroup

on flags and fuzzy subspaces of vector spaces this paper deals with fuzzy subspaces of a vector space in terms of flags we define the operations sum product tensor product hom and intersection of fuzzy subspaces and in each case we characterise the corresponding flag some of these have been considered in the literature in different context the novelty of this paper is in the use of flags as primary tool to study fuzzy subspaces

fuzzy subgroups having the property ii abstract in 3 the notion of the property of a fuzzy subgroup of a group which is a more fuzzified notion of the notion of a generalized characteristic fuzzy subgroup of a finite group is introduced in this paper we show that a generalized characteristic fuzzy subgroup of any group has always the property

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

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

fuzzy normal subgroups and fuzzy cosets abstract we introduce here the notion of 1 i a fuzzy normal subgroup and 2 ii a fuzzy coset we prove that for a group g a fuzzy subgroup is fuzzy normal if and only if it is constant on the conjugate classes of g further we show that the level subgroups of a fuzzy normal subgroup are all normal we obtain several results which are analogs of some basic theorems of group theory in particular a fuzzy version of lagrange s theorem is established

existence and uniqueness of fuzzy ideals let r be a commutative ring the idea of identifying a fuzzy ideal of r with its corresponding chain of level ideals and its range of values although widely used in the literature for the study of fuzzy ideals has never been investigated in a general setting before we investigate in this paper the more general problem of characterization of all those fuzzy ideals that can be identified with a given arbitrary family c of subsets of r together with a given arbitrary subset s of 0 1 necessary and sufficient conditions for the existence and uniqueness of such fuzzy ideals are established in particular we obtain that uniqueness always holds true for artinian rings moreover examples are presented to further support our results and shed more light on the above mentioned problem of identification we finish by raising a natural question that is left as an open problem for further investigation

some characterizations of fuzzy subgroups abstract we show that if a fuzzy subgroup can be written as the intersection of all its minimal fuzzy p subgroups or the intersection of all its minimal fuzzy p subgroups then some properties of the fuzzy subgroup characterize the properties of all its minimal fuzzy p subgroups or all its minimal fuzzy p subgroups and investigate interrelationships among some properties of fuzzy subgroups

fuzzy ideals and fuzzy semiprime ideals some ring theoretic analogues abstract an attempt is made to examine the algebraic nature of fuzzy semiprime ideals under homomorphisms also the fuzzy nil radical of the nth power of a fuzzy prime ideal is studied and a sufficient condition for a fuzzy ideal to be fuzzy maximal is given

fuzzy sylow subgroups abstract an attempt is made to define a fuzzy sylow p subgroup of a finite group some basic results regarding sylow p subgroups are extended to the fuzzy setting in particular fuzzy versions of sylow s theorems are obtained

e e v q fuzzy normal quasinormal and maximal subgroups abstract the notions of and q fuzzy normality and quasinormality for a q fuzzy subgroup are introduced the notions of an q fuzzy core subgroup and an q fuzzy p sylow subgroup are also introduced and some fundamental properties are dealt with q fuzzy normality and q fuzzy quasinormality are found to be more generalised concepts than those introduced by others a detailed study with a fuzzy maximal subgroup is incorporated with the limitation of this concept

distributivity in lattices of fuzzy subgroups the main goal of this paper is to study the finite groups whose lattices of fuzzy subgroups are distributive we obtain a characterization of these groups which is similar to a well known result of group theory

on the number of fuzzy subgroups of finite abelian groups the main goal of this paper is to give an explicit formula for the number of fuzzy subgroups of a finite cyclic group by using a similar method some important steps in counting the number of fuzzy subgroups of a finite elementary abelian p group are also made

fuzzy subgroup some characterizations ii abstract we consider an analysis of fuzzy subgroups in terms of the corresponding family of level subgroups given a finite chain of subgroups of a group g we prove that there exists a fuzzy subgroup of g whose level subgroups are exactly the subgroups of this chain as a corollary we obtain an interpretation of the number of chains of subgroups of a group g in which a subgroup h is a member when the group g is a supersolvable group some further interpretation of this number is obtained

on an equivalence of fuzzy subgroups ii this paper forms a sequel to the paper on an equivalence of fuzzy subgroups i here we determine the number of distinct equivalence classes of fuzzy subgroups of g z p 1 z p n where p 1 p 2 p n are distinct primes we introduce the notion of a keychain of a chain of length n 1 and index of a keychain in order to determine the number of fuzzy subgroups of g we achieve this by using induction on the index of a keychain

non standard cut classification of fuzzy sets abstract several important non standard cut sets of lattice valued fuzzy sets are investigated these are strong cuts not less and neither less nor equal cuts in each case it is proved that collection of all cuts of any lattice valued fuzzy set form a complete lattice under inclusion decomposition theorem representation by cuts is proved for neither less nor equal cuts necessary and sufficient conditions under which two lattice valued fuzzy sets with the same domain have equal families of corresponding cut sets are given

fuzzy cosets and fuzzy normal subgroups abstract in this paper besides generalizing some of the results of mukherjee and bhattacharya 9 we investigate conditions under which a homomorphic image of a fuzzy normal subgroup is fuzzy normal we also prove that a fuzzy subgroup of order p n 1 of a group of order p n is a fuzzy normal subgroup if p is a prime

fuzzy characteristic subgroups of a group abstract a fuzzy characteristic subgroup of a group is characterized in terms of its level subgroups without any restriction on the order of the underlying group

consensus conditions of multi agent systems with time varying topologies and stochastic communication noises this paper investigates the average consensus problem of first order discrete time multi agent networks in uncertain communication environments each agent can only use its own and neighbors information to design its control input to attenuate the communication noises a distributed stochastic approximation type protocol is used by using probability limit theory and algebraic graph theory consensus conditions for this kind of protocols are obtained a for the case of fixed topologies a necessary and sufficient condition for mean square average consensus is given which is also sufficient for almost sure consensus b for the case of time varying topologies sufficient conditions for mean square average consensus and almost sure consensus are given respectively especially if the network switches between jointly containing spanning tree instantaneously balanced graphs then the designed protocol can guarantee that each individual state converges both almost surely and in mean square to a common random variable whose expectation is right the average of the initial states of the whole system and whose variance describes the static maximum mean square error between each individual state and the average of the initial states of the whole system

analysis of the level subgroups of a fuzzy group abstract since the level subgroups of a fuzzy subgroup of a group fail to classify certain subgroups of the group which crop up naturally an open level subgroup is defined these are further subdivided into tangible and hidden subgroups a tangible subgroup can be realized as a level subgroup defined by a positive image point in the unit interval whereas a hidden subgroup cannot be so expressed a necessary and sufficient condition to identify a hidden subgroup through a particular type of a limiting point of the image set is established the usefulness of the open level subgroups of a fuzzy group is demonstrated by factorizing an open level subgroup of the product of two fuzzy subgroups of a group as defined by liu by the corresponding open level subgroups of the individual fuzzy subgroups it is shown that every hidden subgroup of the product fuzzy subgroup is the product of a hidden subgroup and an open level subgroup of the individual fuzzy subgroups lastly the adjustible and the non adjustible subgroups which appear like ghost images all along the chain of level subgroups are detected and analyzed

coordination and consensus of networked agents with noisy measurements stochastic algorithms and asymptotic behavior this paper considers the coordination and consensus of networked agents where each agent has noisy measurements of its neighbors states for consensus seeking we propose stochastic approximation type algorithms with a decreasing step size and introduce the notions of mean square and strong consensus although the decreasing step size reduces the detrimental effect of the noise it also reduces the ability of the algorithm to drive the individual states towards each other the key technique is to ensure a trade off for the decreasing rate of the step size by following this strategy we first develop a stochastic double array analysis in a two agent model which leads to both mean square and strong consensus and extend the analysis to a class of well studied symmetric models subsequently we consider a general network topology and introduce stochastic lyapunov functions together with the so called direction of invariance to establish mean square consensus finally we apply the stochastic lyapunov analysis to a leader following scenario

on the definition of a fuzzy subgroup abstract using the idea of quasi coincidence of a fuzzy point with a fuzzy set some new concepts of a fuzzy subgroup are introduced and their acceptibility is investigated some fundamental properties of one such viable fuzzy subgroup are obtained

some properties on fuzzy subgroups abstract in this paper the concept of homologous fuzzy subgroups of a group g is introduced and some properties on homologous fuzzy subgroups are obtained on the basis of bhattacharya and mukherjee inform sci 41 1987 77 91 and zhang and zou j fuzzy math 1 1993 571 585 the investigation of fuzzy centralizers fuzzy normalizers and fuzzy abelian subgroups is continued

uniqueness results in the representation of families of sets by fuzzy sets the important concept of identifying a fuzzy subset of a set r with its corresponding chain of level sets is widely used in the literature we investigate in this paper the problem of characterization of all fuzzy subsets of r that can be identified with a given arbitrary family c of subsets of r together with a given arbitrary subset s of 0 1 although our main focus is on the problem of uniqueness we start by giving necessary and sufficient conditions for both existence and uniqueness of such fuzzy subsets we continue by obtaining several algebraic and topological properties under which uniqueness is guaranteed to further support our results we present some examples which we hope will shed more light on the above mentioned problem of identification we finish by raising a few natural questions that are left as open problems for further investigation

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

structural modeling and convergence analysis of consensus based time synchronization algorithms over networks this paper raises a quite general problem how to characterize necessary conditions of bounded convergence namely the divergence conditions of a consensus based time synchronization cbts algorithm over a network with random communication delays we firstly present a unified structural model of cbts algorithms then we fit different cbts algorithms such as dcts ats wmts and lsts into the same structural model with just different algorithm parameters to characterize divergence conditions we focus on the algorithm structure and algorithm parameters rather than the topology graph of the network by studying the asymptotic property of the relative drift estimation error of cbts algorithms we discover almost sure divergence conditions and mean square divergence conditions of cbts algorithms using these conditions we clearly point out that the dcts algorithm is divergent the ats algorithm is divergent almost surely the wmts algorithm is mean square divergent but the lsts overcomes all of these divergence conditions the results of this paper provide a fundamental guideline for designing future time synchronization algorithms

commutative fuzzy sets and nilpotent fuzzy groups abstract the notions of a commutative fuzzy subset and a nilpotent fuzzy subgroup are introduced and some of their properties are investigated in particular it is shown that all nilpotent groups can be characterized in terms of their nilpotent fuzzy subgroups

level subgroups and union of fuzzy subgroups abstract in this paper we investigate the conditions under which a given fuzzy subgroup of a given group can or can not be realized as a union of two proper fuzzy subgroups moreover we formulate the notion of fuzzy subgroup generated by a given fuzzy subset by level subgroups we also give characterizations of fuzzy conjugate subgroups and fuzzy characteristic subgroups by their level subgroups also we discuss the relationship between level subgroups of a given fuzzy subgroup and the level subgroups of its homomorphic image

classification of fuzzy subgroupoids of a group ii abstract the fuzzy subsets of a group under the sup min product have been classified into six successively stronger classes and their interrelationship like absorption has been studied the central fuzzy sets that commute with all fuzzy sets have been identified as a closed class a generating technique for these classes is proposed and their preservation under homomorphic images and preimages is studied the existence of certain subgroups acting as the maximal domains for members of these classes has been established

preferential normal fuzzy subgroups in this paper we consider the notion of normality on preferential fuzzy subgroups of a finite group g and define the associated concept of a normal pinned flag we discuss the preferential equality of quotients and products of normal preferential fuzzy subgroups further normalizers of fuzzy subgroups under preferential equality are briefly dealt with examples are given to illustrate the structure of preferential normal fuzzy subgroups and normal pinned flags

solutions to the seepage face model for dual porosity flows with hysteresis abstract this paper is concerned with theoretical analysis of the initial boundary value problem for the dual porosity model of darcian flows with the preisach hysteresis operator due to the presence of the so called unilateral boundary condition the problem comes as an evolution variational inequality we apply the penalty method to prove the global in time existence of the variational solution by constructing approximate solutions satisfying suitable energy type estimates

on existence of p valued fuzzy sets with a given collection of cuts a representation theorem of families of subsets by poset valued fuzzy sets is presented namely necessary and sufficient conditions are given under which for a given family of subsets f of a set x and a fixed poset p there is a fuzzy set m x p such that the collection of cuts of m coincides with f

quasinormality and fuzzy subgroups abstract we extend the notion of quasinormality to the fuzzy setting we prove that a fuzzy subgroup of a group is fuzzy quasinormal if and only if all its level subsets are quasinormal in the usual group theoretic sense we investigate the natures of homomorphic image and preimage of a fuzzy quasinormal subgroup moreover we introduce the notions of core of a fuzzy subgroup core free fuzzy subgroup fuzzy sylow subgroup and fuzzy maximal subgroup of a group consequently we establish that in a finite group all the fuzzy sylow subgroups of a core free fuzzy quasinormal subgroup are fuzzy quasinormal furthermore we also establish that a fuzzy maximal quasinormal subgroup with the sup property is fuzzy normal

from fuzzy sets to the decompositions of non rigid sets the concept of identifying a fuzzy subset of a set r with its collection of level sets and its collection of membership values plays an important role in many real life applications such identification is possible only if the fuzzy set can be recaptured this implies that uniqueness of the fuzzy set plays an important role it has been recently shown that in order to have uniqueness it is necessary and sufficient that the collection s of membership values of the fuzzy set be a rigid set with this in mind the authors went on to show that if s has the min max property then s is a rigid set and left the converse as an open problem we start this paper by constructing a counterexample that shows that rigid sets do not have to have the min max property we then take a closer look at non rigid sets by decomposing them into isomorphism invariant components and into s connected components in the hope of getting a characterization of non rigid sets which will lead to a characterization of rigid sets and hence of uniqueness of the fuzzy set we also investigate in the case of nonuniqueness the number of fuzzy sets corresponding to a collection of level sets and a collection of membership values

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

counting the number of fuzzy subgroups of an abelian group of order pnqm abstract in this paper we determine the number of fuzzy subgroups of g z p n z q m where p q are distinct primes and n m are any two natural numbers first we represent the number of maximal chains of g as a summation through m involving certain binomial coefficients using this concise expression we propose a combinatorial formula for the number of fuzzy subgroups of g and verify it for specific values of m and n finally we sketch a proof for the general case

an adaptive time discretization of the classical and the dual porosity model of richards equation this paper presents a numerical solution to the equations describing darcian flow in a variably saturated porous medium a classical richards equation model richards 1931 1 and an extension of it that approximates the flow in media with preferential paths a dual porosity model gerke and van genuchten 1993 8 a numerical solver to this problem the drutes computer program was developed and released during our investigation a new technique which maintains an adaptive time step defined here as the retention curve zone approach was constructed and tested the aim was to limit the error of a linear approximation to the time derivative part finally parameter identification was performed in order to compare the behavior of the dual porosity model with data obtained from a non homogenized fracture and matrix flow simulation experiment

direct products and isomorphism of fuzzy subgroups abstract the concepts of internal direct product and external direct product of fuzzy subgroups of a group are established as well as that of fuzzy isomorphism of fuzzy subgroups of possibly different groups it is shown that the internal direct product of two fuzzy subgroups of a group is isomorphic to their external direct product the fuzzy counterparts of the first and third isomorphism theorems are also proved

generalized fuzzy quotient subgroups abstract in this paper we consider the fuzzy subgroup of a given group defined by generalized triangular norms and conorms introduced by yager 1986 the definitions of a anti fuzzy subgroup and a anti pseudo fuzzy subgroup are reviewed then a generalized fuzzy cayley theorem as well as a partial generalization of fuzzy lagrange theorem are given also a unified approach for studying fuzzy quotient subgroups is discussed some correspondence theorems for several kinds of fuzzy subgroups are proved and examples of generalized triangular norms conorms are given

fuzzy subgroups some characterizations the notion of a fuzzy set was first introduced in 1965 by zadeh 12 since then the theory of fuzzy sets has gone through remarkably rapid strides with well over 4000 papers by now see for example the bibliography 3 several textbooks for example 2 and 6 and an international journal solely devoted to it s the theory has found wideranging applications in such diverse fields as automata control theory decision theory and social behavior pattern studies to name just a few for an interesting expository account see rosenfeld lo and also the book review 7 in 9 rosenfeld introduced the notion of a fuzzy group and showed that many concepts of group theory can be extended in an elementary manner to develop the theory of fuzzy groups in particular he characterized all the fuzzy subgroups of cyclic groups of prime order 9 proposition 5 101 fuzzy groups were further investigated by das in 1 where he characterized all the fuzzy subgroups of finite cyclic groups l theorem 4 21 in this connection he introduced the notion of level subgroups of a fuzzy subgroup which is based on the notion of a level subset introduced earlier by zadeh for a finite group das showed that these level subgroups of a fuzzy subgroup form a chain 1 corollary 3 11 and also constructed a fuzzy subgroup whose chain of level subgroups is maximal in the following special cases when the group is i a direct product of cyclic groups of prime orders ii abelian l theorem 3 41 we analyze the level subgroups of a fuzzy subgroup in more detail and investigate whether the family of level subgroups of a fuzzy subgroup deter

fuzzy points of equivalent fuzzy subsets a natural equivalence relation on the set of all fuzzy subsets generalizing the equality of crisp sets was recently introduced and studied in various contexts such as finite fuzzy subsets fuzzy vector space finite fuzzy subfields and in the classification of finite abelian groups in this paper we restrict this equivalence to the set of fuzzy points and study its effect on the relationship between fuzzy points and fuzzy subsets all fuzzy subsets take a finite number of membership values in the real unit interval an important tool for studying this equivalence relation is that of a keychain this notion gives rise to the idea of a pinned flag their equivalences and index of fuzzy subsets

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

uniqueness in the generalized representation by fuzzy sets the concept of representation of a given family of sets by a fuzzy set in such a way that the level sets of the fuzzy set are precisely the given sets is widely used in the literature for the classification and study of fuzzy algebraic structures on the same underlying set the problem of existence of such fuzzy sets was investigated by various authors as far as we know the problem of uniqueness of such fuzzy sets was not studied before we establish among other things necessary and sufficient conditions under which uniqueness is guaranteed in the cases of complete as well as partial representations of the level sets of the fuzzy set

short communication lattice representations of interval valued fuzzy sets in this paper a solution of the problem of the interval valued fuzzy sets synthesis is given the codomain is considered to be a lattice of intervals the necessary and sufficient conditions for a family of subsets to be a family of cut sets of an interval valued fuzzy set are given

a new equivalence relation to classify the fuzzy subgroups of finite groups in this paper a new equivalence relation for classifying the fuzzy subgroups of finite groups is introduced and studied this generalizes the equivalence relation defined on the lattice of fuzzy subgroups of a finite group that has been used in our previous papers explicit formulas for the number of distinct fuzzy subgroups with respect to the new equivalence relation are obtained in some particular cases

extensions of fuzzy deductive systems in hilbert algebras abstract let s be a hilbert subalgebra of a bounded hilbert algebra a the purpose of this paper is to give an extension of a fuzzy deductive system of s to a fuzzy deductive system e of a such that and e have the same image

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

fuzzy congruences and fuzzy normal subgroups abstract a complete description of the congruences on a group in terms of its normal subgroups can be seen in papers by a rosenfeld and w j howie in this paper we shall introduce the concept of fuzzy congruences on a groupoid and a group and characterize fuzzy congruences on a group in terms of fuzzy normal subgroups

a note on a natural equivalence relation on fuzzy power set the necessary and sufficient conditions under which two fuzzy sets with the same domain have equal families of cut sets are given consequently there is a corresponding equivalence relation on the related fuzzy power set the collection of classes under this relation can be ordered and we give a necessary and sufficient condition under which it is a lattice

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper

the stability of local properties of fuzzy relations under ordinal equivalence abstract we consider a notion of equivalence relation between fuzzy relations and its properties the relation is called ordinal equivalence since it partitions the family of fuzzy relations into equivalence classes by means of the order defined on elements of each relation we compare fuzzy relations by their membership values and as a consequence we propose two types of local properties of fuzzy relations new properties of fuzzy relations are more compatible with the ordinal equivalence relation namely they are stable in the equivalence classes moreover we study dependencies between these new properties of fuzzy relations finally notes on applications of the presented local properties and the ordinal equivalence relation are provided