dual fuzzy neighbourhood spaces i abstract a fuzzy neighbourhood space fns is determined by means of a system of fuzzy neighbourhoods of the ordinary points of that space we provide a general method for constructing bases for all fuzzy neighbourhood systems in a natural way from the fuzzy topologies of a special type of fuzzy topological spaces fts s which we call the fuzzy neighbourhood base spaces this construction is shown to be functorial of those new fts s the full subcategory of dual fuzzy neighbourhood spaces is shown to be isomorphic to the category of fns s and a fns will coincide with its dual fts iff it is topologically generated

fast distributed average consensus algorithms based on advection diffusion processes distributed consensus algorithms have recently gained large interest in sensor networks as a way to achieve globally optimal decisions in a totally decentralized way that is without the need of sending all the data collected by the sensors to a fusion center however distributed algorithms are typically iterative and they suffer from convergence time and energy consumption in this paper we show that introducing appropriate asymmetric interaction mechanisms with time varying weights on each edge it is possible to provide a substantial increase of convergence rate with respect to the symmetric time invariant case the basic idea underlying our approach comes from modeling the average consensus algorithm as an advection diffusion process governing the homogenization of fluid mixtures exploiting such a conceptual link we show how introducing interaction mechanisms among nearby nodes mimicking suitable advection processes yields a substantial increase of convergence rate moreover we show that the homogenization enhancement induced by the advection term produces a qualitatively different scaling law of the convergence rate versus the network size with respect to the symmetric case

stochastic bounded consensus tracking of second order multi agent systems with measurement noises based on sampled data with general sampling delay this paper is devoted to the stochastic bounded consensus tracking problems of second order multi agent systems where the control input of each agent can only use the information measured at the sampling instants from its neighbors or the virtual leader with a time varying reference state the measurements are corrupted by random noises and the signal sampling process induces the small sampling delay the augmented matrix method the probability limit theory and some other techniques are employed to derive the necessary and sufficient conditions guaranteeing the mean square bounded consensus tracking we show that the convergence of the proposed protocol simultaneously depends on the constant feedback gains the network topology the sampled period and the sampling delay and that the static consensus tracking error depends on not only the above mentioned factors but also the noise intensity and the upper bound of the velocity and the acceleration of the virtual leader the obtained results cover no sampling delay as its one special case simulations are provided to demonstrate the effectiveness of the theoretical results

self organization in systems of self propelled particles we investigate a discrete model consisting of self propelled particles that obey simple interaction rules we show that this model can self organize and exhibit coherent localized solutions in one and in two dimensions in one dimension the self organized solution is a localized flock of finite extent in which the density abruptly drops to zero at the edges in two dimensions we focus on the vortex solution in which the particles rotate around a common center and show that this solution can be obtained from random initial conditions even in the absence of a confining boundary furthermore we develop a continuum version of our discrete model and demonstrate that the agreement between the discrete and the continuum model is excellent

axiomatizations of the shapley value for games on augmenting systems this paper deals with cooperative games in which only certain coalitions are allowed to form there have been previous models developed to confront the problem of unallowable coalitions games restricted by a communication graph were introduced by myerson and owen in their model the feasible coalitions are those that induce connected subgraphs another type of model is introduced in gilles owen and van den brink in their model the possibilities of coalition formation are determined by the positions of the players in a so called permission structure faigle proposed another model for cooperative games defined on lattice structures we introduce a combinatorial structure called augmenting system which is a generalization of the antimatroid structure and the system of connected subgraphs of a graph in this framework the shapley value of games on augmenting systems is introduced and two axiomatizations of this value are showed

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

consensus in a heterogeneous influence network we consider a dynamical network model in which a number of agents all move on the plane with the same constant absolute velocity at each time step each agent s direction is updated as the average of its direction plus the directions of other agents who can influence it the influencing capability of each agent is represented by its influencing radius which is randomly chosen according to a power law distribution with a scaling exponent between 2 and ensuremath infty as the value of the scaling exponent decreases the radius distribution becomes more heterogeneous and the network becomes much easier to achieve direction consensus among agents due to the leading roles played by a few hub agents furthermore almost all agents will finally move in the same desired direction in a strong heterogeneous influence network if and only if a small fraction of hub agents can be controlled to move in the desired direction these results also reflect the robust yet fragile feature of a heterogeneous influence network

games with fuzzy authorization structure a cooperative game consists of a set of players and a characteristic function which determines the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate regardless of the actions that the other players take it is often assumed that the players are free to participate in any coalition but in some situations there are dependency relationships among the players that restrict their capacity to cooperate within some coalitions those relationships must be taken into account if we want to distribute the profits fairly in this respect several models have been proposed in literature in all of them dependency relationships are considered to be complete in the sense that either a player is allowed to fully cooperate within a coalition or they cannot cooperate at all nevertheless in some situations it is possible to consider another option that a player has a degree of freedom to cooperate within a coalition a model for those situations is presented

fuzzy t locality spaces abstract a lowen fuzzy topological space is said to be localizable at points if it is completely determined in some prescribed manner by a system of fuzzy neighbourhoods called here fuzzy localities of its ordinary points we introduce for each lower semicontinuous triangular norm t a new type of those spaces which we call fuzzy t locality spaces the particularity of a fuzzy t locality space is that its fuzzy interior operator is obtained from its t locality system through a definition of fuzzy containment of fuzzy sets that employs the t residuated implication operator the origins of this new theory lie in the theory of probabilistic metric spaces indeed fuzzy t locality spaces provide a fuzzy topological framework for a naturally defined notion of metric t continuity of functions between probabilistic t metric spaces in a manner described in the last two sections of this article before that we establish characterizations and aspects of good behaviour for fuzzy t locality spaces including that every t locality system has an open basis we briefly study their level topologies and we show that all topologically generated spaces are fuzzy t locality spaces we prove that the category t fls of fuzzy t locality spaces and continuous functions between them is a topological category we show that it is closed in fts under the formation of optimal lifts of sources we provide a condition on t under which t fls becomes closed in fts also under the formation of co optimal lifts of sinks

average consensus in networks of multi agents with both switching topology and coupling time delay abstract this paper is devoted to the study of the average consensus problem in directed networks of agents with both switching topology and time delay the stability analysis is performed based on a proposed lyapunov krasovskii function sufficient conditions in terms of linear matrix inequalities lmis are given to guarantee the average consensus under arbitrary switching of the network topology even if the time delay is time varying numerical simulations show the effectiveness of our theoretical results

enhancing the convergence efficiency of a self propelled agent system via a weighted model we investigate a weighted self propelled agent system wherein each agent s direction is determined by its spatial neighbors directions with exponential weights according to the neighbor numbers in order to describe the fact that some agents with more neighbors might have larger influence on its neighbors we introduce a scaling exponent of the neighbor number between 0 and ensuremath infty when the exponent is equal to 1 the convergence efficiency is enhanced in our simulation furthermore as the exponent increases i e the effect of weight becomes stronger the network of agents becomes easier to achieve direction consensus

adaptive velocity strategy for swarm aggregation collective behaviors of biological swarms have attracted significant interest in recent years but much attention and efforts have been focused on constant speed models in which all agents are assumed to move with the same constant speed one limitation of the constant speed assumption without attraction function is that global convergence is quite difficult or even practically impossible to achieve if the speed is relatively fast in this paper we propose an adaptive velocity model in which each agent not only adjusts its moving direction but also adjusts its speed according to the degree of direction consensus among its local neighbors one important feature of the adaptive velocity model is that the speeds of all agents are adaptively tuned to the same maximum constant speed after a short transient process the adaptive velocity strategy can greatly enhance the global convergence probability and thus provides a powerful mechanism for coordinated motion in biological and technological multiagent systems

on two types of stable subconstructs of fts abstract in the topological construct fts of fuzzy topological spaces and continuous functions the subconstructs t fls of fuzzy t locality spaces and t fns of fuzzy t neighbourhood spaces are simultaneously bireflective and bicoreflective in fts for certain infinite sets of triangular norms t we identify their stabilizing total fuzzy topologies t fls and t fns on 0 1 in the sense of lowen and wuyts 1993 the special case of t min has already been dealt with by lowen and wuyts we also establish a symmetrically defined order reversing bijection between t fns and a basis for t fls

accelerating consensus of self driven swarm via adaptive speed abstract in recent years the well developed vicsek model has attracted more and more attention unfortunately in depth research on its convergence speed is not yet completed in this paper we investigate some key factors governing the convergence speed of the vicsek model with the assistance of extensive numerical simulations a significant phenomenon surfaces that the convergence time scales obeys a power law with r 2 ln n with r and n being the horizon radius and the number of particles respectively to further accelerate the convergence procedure we propose a kind of improved vicsek model with self driven particles governed by variational speeds which can remarkably shorten the convergence time of the standard vicsek model

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

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

a note on fuzzy neighbourhood base spaces abstract fuzzy neighbourhood base spaces fnbs introduced by morsi are a special type of stratified i topological spaces si top previously denoted as fuzzy topological spaces fts we introduce further characterizations of fnbs in terms of level sets also we construct stable subconstructs of si top in the sense of lowen and wuyts stable subconstructs of fts i j fuzzy math 1 3 1993 475 489 whose corresponding total stratified i topologies are generated by elements of i i which are greater than id i the maximal objects of such stable subconstructs have weaker properties than that of the ascending chain property and then these objects give rise to fuzzy neighbourhood base spaces therefore special types of fuzzy neighbourhood base spaces are constructed

a comparison of various uniformities in fuzzy topology it is known that the construct fts of stratified fuzzy topological spaces contains non trivial concretely both reflective and coreflective full subconstructs since each of these subconstructs is both initially and finally closed in fts it gives rise to a perfectly viable and autonomous theory of fuzzy topology in this paper this idea is applied to analyze the interrelations between the various notions of uniformity in fuzzy set theory the results show that these notions can be put into a coherent and clear picture if we interpret them as notions of uniformity for certain subconstructs of fts that are concretely both reflective and coreflective or some superconstructs of fuzzy topological spaces

enhancing consensus in weighted networks with coupling time delay abstract we study the consensus problem in a weighted and directed network composed of self propelled agents the weight which quantifies the relationship between the agents is adjusted according to their state incoherence to suppress the heterogeneity in state the proposed consensus protocol enhances the convergence efficiency of consensus greatly and has better performance than that of two other protocols the convergence efficiency can be further improved by adjusting the parameter of this protocol furthermore the robustness of the system against coupling time delay is significantly increased unlike most consensus acceleration methods no topological information is needed in our model networks with different stuctures are investigated to demonstrate the generality of the method

axioms for the shapley value on convex geometries the purpose of this article is an extension of shapley s value for games with restricted cooperation the classical model of cooperative game where every subset of players is a feasible coalition may be unrealistic the feasible coalitions in our model will be the convex sets i e those subsets of players belonging to a convex geometry l in the last section we apply this model to several examples about the power in the council of ministers of the european union

fuzzy t neighbourhood spaces part 2 t neighbourhood systems we explore a notion of fuzzy t neighbourhood spaces for any continuous triangular norm t and we present on this notion a unified treatment our theory on one hand generalizes the theory of lowen fuzzy sets and systems 7 1982 65 from t min to arbitrary t which has been the progenitor of this work and on the other hand it is strongly related to the theory of l neighbourhoods of hohle mathematics of fuzzy sets logic topology and measure theory kluwer academic publishers dordrecht 1999 when l is restricted to the lattice 0 1 we study the t neighbourhood bases and systems of our spaces their level topologies as well as their relationship to the lowen hohle fuzzy t uniformities j math anal appl 82 1981 370 manuscripta math 38 1982 289 and to our fuzzy t proximities introduced in part 1 we show that the nearness concept underlying a fuzzy t neighbourhood space is a fuzzy relation of closeness between its ordinary subsets and ordinary points in particular our spaces are in canonical one to one correspondence with the t probabilistic topological spaces of frank j math anal appl 34 1971 67 we demonstrate that each full subcategory t fns of fts of fuzzy t neighbourhood spaces is a topological category to do that we characterize t fns within fts and we characterize continuity of functions within t fns in terms of t neighbourhood bases

a modified vicsek model for self propelled agents with exponential neighbor weight and restricted visual field abstract large flocks of wild beings can have coordinated motion with neither leading center nor global information the vicsek model and its new versions explained such collective behavior of self propelled agents with the mechanism of un weighted influence of neighbors and global visual field gvf which may not always fit the reality in the present work we take both exponential neighbor weight enw and restricted visual field rvf into account and investigate the combinatory effect of them based on this mechanism in most cases of our simulation stationary direction consensus v a exhibits a maximum or decreases with v f and a minimum convergence time t m i n appears in rvf which demonstrates that gvf is not necessary for coordinated motion while rvf matched enw would be reasonable moreover we simulated various recipes for optimizing v a and t in unfavorable cases and found critical points separating inverse dependent variations of t the present work may be useful in improving the efficiency of direction consensus of large flocks of artificial individuals besides the understanding of biological collective motion in nature

order monotonic solutions for generalized characteristic functions abstract generalized characteristic functions extend characteristic functions of classical tu games by assigning a real number to every ordered coalition being a permutation of any subset of the player set such generalized characteristic functions can be applied when the earnings or costs of cooperation among a set of players depend on the order in which the players enter a coalition in the literature the two main solutions for generalized characteristic functions are the one of nowak and radzik 1994 shortly called nr value and the one introduced by sanchez and bergantinos 1997 shortly called sb value in this paper we introduce the axiom of order monotonicity with respect to the order of the players in a unanimity coalition requiring that players who enter earlier should get not more in the corresponding ordered unanimity game than players who enter later we propose several classes of order monotonic solutions for generalized characteristic functions that contain the nr value and sb value as special extreme cases we also provide axiomatizations of these classes

fuzzy neighborhood spaces abstract in this paper we introduce a subcategory of the category of fuzzy topological spaces and we prove basic properties of this subcategory the main idea behind these spaces is the notion of fuzzy neighborhoods which enables us to introduce a local theory of fuzzy topologies

proportional coalition values for monotonic games on convex geometries with a coalition structure abstract a new model called games on convex geometries with a coalition structure is introduced where all players and the coalition structure form a convex geometry respectively an explicit form of the proportional coalition solidarity value is given which endows each union with the solidarity value in quotient games and then allocates this value to players in a union following the proportions of their solidarity values in original games on convex geometries i e without unions meanwhile an axiomatization of this value is offered furthermore the proportional coalition shapley value is introduced its explicit form is offered and an axiomatic system is studied

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