weighted minimum and maximun operations in fuzzy sets theory abstract this short note comments on the interpretation of weighted minimum and maximum operations introduced in a previous paper as medians and corrects a misleading statement about it

on sugeno integral as an aggregation function the sugeno integral for a given fuzzy measure is studied under the viewpoint of aggregation in particular we give some equivalent expressions of it we also give an axiomatic characterization of the class of all the sugeno integrals some particular subclasses such as the weighted maximum and minimum functions are investigated as well

pictorial representations of fuzzy connectives part ii cases of compensatory operators and self dual operators abstract as the continuation of part i in which pictorial representations of t norms t conorms and averaging operators were made with the aid of a computer this paper discusses compensatory operators and proposes generalized compensatory operators which can be obtained from averaging operators self dual operators are discussed which can be defined by using t norms t conorms and averaging operators finally symmetric sums are reviewed which are also self dual operators the pictorial representations of these operators are also made

distributed adaptive coordination for multiple lagrangian systems under a directed graph without using neighbors velocity information in this paper we study the distributed coordination problem for multiple lagrangian systems in the presence of parametric uncertainties under a directed graph without using neighbors velocity information in the absence of communication we consider two cases namely the distributed containment control problem with multiple stationary leaders and the leaderless synchronization problem in both cases distributed adaptive control algorithms without using neighbors velocity information are proposed the control gains in the algorithms are varying with distributed updating laws furthermore necessary and sufficient conditions on the directed graph are presented respectively such that all followers converge to the stationary convex hull spanned by the stationary leaders asymptotically in the containment control problem and the systems synchronize asymptotically in the leaderless synchronization problem finally simulation examples are provided to show the effectiveness of the proposed control algorithms

models to determine parameterized ordered weighted averaging operators using optimization criteria this paper proposes a general optimization model for determining ordered weighted averaging owa operators and three specific models for generating monotonic and symmetric owa operators as well as those with any function shape in these models entropy and variance concepts are generalized as general dispersion indices for use in the objective functions while the ordinary orness level constraints are used in the constraint equations as a special case we define an orness function for monotonic owa operators which measures the closeness of the aggregation value to the maximum value and a medianness function for symmetric owa operators which measures the closeness of the aggregation value to the median value we also extend the commonly used models for determining owa operators under given orness values to determine monotonic owa operators with given orness function values and symmetric owa operators with given medianness function values analytical solutions and properties of these models are discussed we also provide analytical solutions of the maximum entropy and minimum variance problems with given linear medianness values by setting different forms of the objective function and constraints the parameterized owa operator family elements can achieve various distributions in any desired shape two examples are given to show the owa operator elements distributed in quadratic and gaussian distribution function shapes

random generation of k interactive capacities abstract the theory of capacities provides powerful formal methodology to account for criteria dependencies in multiple criteria decision problems the discrete choquet and sugeno integrals aggregate criteria valuations accounting for criteria synergies and redundancies we address an important problem of randomly generating capacities of special classes for simulation studies and for capacity learning through evolutionary algorithms we discuss two efficient methods suitable for k interactive capacities the results are supported by the extensive numerical evidence and provide a useful tool for large scale simulations

minimum variance capacity identification abstract in the framework of multi criteria decision making whose aggregation process is based on the choquet integral we present a maximum entropy like method enabling to determine if it exists the least specific capacity compatible with the initial preferences of the decision maker the proposed approach consists in solving a strictly convex quadratic program whose objective function is equivalently either the opposite of a generalized entropy measure or the variance of the capacity the application of the proposed approach is illustrated on two examples

optimization over state feedback policies for robust control with constraints this paper is concerned with the optimal control of linear discrete time systems subject to unknown but bounded state disturbances and mixed polytopic constraints on the state and input it is shown that the class of admissible affine state feedback control policies with knowledge of prior states is equivalent to the class of admissible feedback policies that are affine functions of the past disturbance sequence this implies that a broad class of constrained finite horizon robust and optimal control problems where the optimization is over affine state feedback policies can be solved in a computationally efficient fashion using convex optimization methods this equivalence result is used to design a robust receding horizon control rhc state feedback policy such that the closed loop system is input to state stable iss and the constraints are satisfied for all time and all allowable disturbance sequences the cost to be minimized in the associated finite horizon optimal control problem is quadratic in the disturbance free state and input sequences the value of the receding horizon control law can be calculated at each sample instant using a single tractable and convex quadratic program qp if the disturbance set is polytopic or a tractable second order cone program socp if the disturbance set is given by a 2 norm bound

an axiomatic approach of the discrete sugeno integral as a tool to aggregate interacting criteria in a qualitative framework we present a model allowing us to aggregate decision criteria when the available information is of a qualitative nature the use of the sugeno integral as an aggregation function is justified by an axiomatic approach it is also shown that the mutual preferential independence of criteria reduces the sugeno integral to a dictatorial aggregation

brief optimizing the end point state weighting matrix in model based predictive control in this paper a linear model based predictive control mpc algorithm is presented for which nominal closed loop stability is guaranteed the input is obtained by minimizing a quadratic performance index over a finite horizon plus an end point state eps penalty subject to input state and output constraints under certain conditions the weighting matrix in the eps penalty enables one to specify an invariant ellipsoid in which the input state and output constraints are satisfied in existing mpc algorithms this weighting matrix is calculated off line the main contribution of this paper is to incorporate the calculation of the eps weighting matrix into the on line optimization problem of the controller the main advantage of this approach is that a natural and automatic trade off between feasibility and optimality is obtained this is demonstrated in a simulation example

importance weighting and andness control in de morgan dual power means and owa operators abstract importance weighted aggregation plays a central role in utilization of information resources for information retrieval and fusion pattern and object recognition decision making etc a class of aggregation operators of particular interest is formed by the aggregation operators between the min minimum and the max maximum the so called averaging operators two key issues in the choice of such an operator for a given application are the kind of importance weighting and the andness minness of the operator two main kinds of importance weighting for such operators namely multiplicative and implicative are proposed and discussed the purpose of this paper is to facilitate the choice and application of such operators through providing a systematization of their classes according to their behavior and equipping some classical averaging operators namely the power means and the owa operators with importance weighting schemes and direct parametric andness control for both kinds of importance weighting for increased efficacy and for symmetric behavior by andness and orness 1 andness at the same degree of both measures the two classes of averaging operators are applied in a de morgan dual form the main issue in the choice of underlying the classical averaging operator appears to be the computational cost of its application

efficient robust predictive control predictive constrained control of time varying and or uncertain linear systems has been effected through the use of ellipsoidal invariant sets kothare et al 1996 linear matrix inequalities lmis have been used to design a state dependent state feedback law that maintains the state vector inside invariant feasible sets for the purposes of prediction however at each time instant the state feedback law is assumed constant in addition due to the large number of lmis involved online computation becomes intractable for anything other than small dimensional systems here we propose an approach that deploys a fixed state feedback law but introduces extra degrees of freedom through the use of perturbations on the fixed state feedback law the problem is so formulated that all demanding computations can be performed offline leaving only a simple optimization problem to be solved online over and above the very significant reduction in computational cost the extra degrees of freedom allow for better performance and wider applicability

a note on a generalized frank functional equation abstract we study a generalized frank functional equation in the broader framework of associative aggregation functions and show that up to the two projections we obtain exactly the same set of solutions as in the original paper by m j frank aequationes mathematicae 19 1979

fully distributed flocking with a moving leader for lagrange networks with parametric uncertainties this paper addresses the leader follower flocking problem with a moving leader for networked lagrange systems with parametric uncertainties under a proximity graph here a group of followers move cohesively with the moving leader to maintain connectivity and avoid collisions for all time and also eventually achieve velocity matching in the proximity graph the neighbor relationship is defined according to the relative distance between each pair of agents each follower is able to obtain information from only the neighbors in its proximity involving only local interaction we consider two cases i the leader moves with a constant velocity and ii the leader moves with a varying velocity in the first case a distributed continuous adaptive control algorithm accounting for unknown parameters is proposed in combination with a distributed continuous estimator for each follower in the second case a distributed discontinuous adaptive control algorithm and estimator are proposed then the algorithm is extended to be fully distributed with the introduction of gain adaptation laws in all proposed algorithms only one hop neighbors information e g the relative position and velocity measurements between the neighbors and the absolute position and velocity measurements is required and flocking is achieved as long as the connectivity and collision avoidance are ensured at the initial time and the control gains are designed properly numerical simulations are presented to illustrate the theoretical results

extreme points of some families of non additive measures non additive measures are a valuable tool to model many different problems arising in real situations however two important difficulties appear in their practical use the complexity of the measures and their identification from sample data for the first problem additional conditions are imposed leading to different subfamilies of non additive measures related to the second point in this paper we study the set of vertices of some families of non additive measures namely k additive measures and p symmetric measures these extreme points are necessary in order to properly apply a new method of identification of non additive measures based on genetic algorithms whose cross over operator is the convex combination we solve the problem through techniques of linear programming

dominance of capacities by k additive belief functions in this paper we deal with the set of k additive belief functions dominating a given capacity we follow the line introduced by chateauneuf and jaffray for dominating probabilities and continued by grabisch for general k additive measures first we show that the conditions for the general k additive case lead to a very wide class of functions and this makes that the properties obtained for probabilities are no longer valid on the other hand we show that these conditions cannot be improved we solve this situation by imposing additional constraints on the dominating functions then we consider the more restrictive case of k additive belief functions in this case a similar result with stronger conditions is proved although better this result is not completely satisfactory and as before the conditions cannot be strengthened however when the initial capacity is a belief function we find a subfamily of the set of dominating k additive belief functions from which it is possible to derive any other dominant k additive belief function and such that the conditions are even more restrictive obtaining the natural extension of the result for probabilities finally we apply these results in the fields of social welfare theory and decision under risk

constrained linear quadratic regulation the paper is a contribution to the theory of the infinite horizon linear quadratic regulator lqr problem subject to inequality constraints on the inputs and states extending an approach first proposed by sznaier and damborg 1987 a solution algorithm is presented which requires solving a finite number of finite dimensional positive definite quadratic programs the constrained lqr outlined does not feature the undesirable mismatch between open loop and closed loop nominal system trajectories which is present in the other popular forms of model predictive control mpc that can be implemented with a finite quadratic programming algorithm the constrained lqr is shown to be both optimal and stabilizing the solution algorithm is guaranteed to terminate in finite time with a computational cost that has a reasonable upper bound compared to the minimal cost for computing the optimal solution inherent to the approach is the removal of a tuning parameter the control horizon which is present in other mpc approaches and for which no reliable tuning guidelines are available two examples are presented that compare constrained lqr and two other popular forms of mpc the examples demonstrate that constrained lqr achieves significantly better performance than the other forms of mpc on some plants and the computational cost is not prohibitive for online implementation

robust model predictive control of constrained linear systems with bounded disturbances this paper provides a novel solution to the problem of robust model predictive control of constrained linear discrete time systems in the presence of bounded disturbances the optimal control problem that is solved online includes uniquely the initial state of the model employed in the problem as a decision variable the associated value function is zero in a disturbance invariant set that serves as the origin when bounded disturbances are present and permits a strong stability result namely robust exponential stability of the disturbance invariant set for the controlled system with bounded disturbances to be obtained the resultant online algorithm is a quadratic program of similar complexity to that required in conventional model predictive control

brief paper distributed containment control for lagrangian networks with parametric uncertainties under a directed graph in this paper we study the distributed containment control problem for networked lagrangian systems with multiple dynamic leaders in the presence of parametric uncertainties under a directed graph that characterizes the interaction among the leaders and the followers we propose a distributed adaptive control algorithm combined with distributed sliding mode estimators a necessary and sufficient condition on the directed graph is presented such that all followers converge to the dynamic convex hull spanned by the dynamic leaders asymptotically as a byproduct we show a necessary and sufficient condition on leaderless consensus for networked lagrangian systems under a directed graph numerical simulation results are given to show the effectiveness of the proposed control algorithms

an axiomatic approach to the definition of the entropy of a discrete choquet capacity to extend the classical shannon entropy to nonadditive measures marichal recently introduced the concept of generalized entropy for discrete choquet capacities we provide a first axiomatization of this new concept on the basis of three axioms the symmetry property a boundary condition for which the entropy reduces to the shannon entropy and a generalized version of the well known recursivity property we also show that this generalized entropy fulfills several properties considered as requisites for defining an entropy like measure lastly we provide an interpretation of it in the framework of aggregation by the discrete choquet integral

construction of fuzzy σ algebras using triangular norms abstract generalizing the definitions given by the author fuzzy sets and systems4 1980 83 93 we introduce and study t fuzzy algebras t being any triangular norm the main result is that for a large class of triangular norms each t fuzzy algebra is generated i e consists of all functions x 0 1 being measurable with respect to some algebra on x

optimizing prediction dynamics for robust mpc a convex formulation is derived for optimizing dynamic feedback laws for constrained linear systems with polytopic uncertainty we show that when it exists the maximal invariant ellipsoidal set for the plant state under a dynamic feedback law incorporating any chosen static feedback gain is equal to the maximal invariant ellipsoidal set under any linear feedback law the dynamic controller and its associated invariant set define a computationally efficient robust model predictive control mpc law with prediction dynamics belonging to a polytopic uncertainty set

on the properties of owa operator weights functions with constant level of orness the result of aggregation performed by the ordered weighted averaging owa operator heavily depends upon the weighting vector used a number of methods have been presented for obtaining the associated weights in this paper we present analytic forms of owa operator weighting functions each of which has properties of rank based weights and a constant level of orness irrespective of the number of objectives considered these analytic forms provide significant advantages for generating the owa weights over previously reported methods first the owa weights can be efficiently generated by using proposed weighting functions without solving a complicated mathematical program moreover convex combinations of these specific owa operators can be used to generate the owa operators with any predefined values of orness once specific values of orness are a priori stated by the decision maker those weights have a property of constant level of orness as well finally the owa weights generated at a predefined value of orness make almost no numerical difference with maximum entropy owa weights in terms of dispersion

robust triple mode mpc this paper reviews triple mode predictive control for linear time invariant systems and then proposes a new algorithm for robust triple mode predictive control for constrained linear systems described by polytopic uncertainty models the approach significantly enlarges the feasibility region compared to recently proposed robust dual mode approaches the efficacy of the approach is demonstrated with numerical examples

fuzzy measure of fuzzy events defined by fuzzy integrals abstract we define the concept of fuzzy measure of a fuzzy event by using a general form of fuzzy integral proposed by murofushi called fuzzy t conorm integral encompassing previous definitions zadeh defined the probability measure of a fuzzy event and later the possibility measure of fuzzy event using a duality property of fuzzy t conorm integral we propose a general definition of fuzzy measure of fuzzy events which is compatible with previous definitions of zadeh and possesses all properties of a fuzzy measure in particular the duality property using our definition we examine the case of decomposable measures and belief functions a comparison with previous works is provided

tolerant or intolerant character of interacting criteria in aggregation by the choquet integral abstract in many multi criteria decision making problems the decision criteria present some interaction whose nature may vary from one situation to another for example some criteria may be statistically correlated thus making them somewhat redundant or opposed some others may be somewhat substitutive or complementary depending on the behavior of the decision maker some others may be decisive in the sense that the global score of any alternative obtained by aggregation is bounded by the partial score along one of them in this paper we analyze this latter form of interaction when a criterion bounds the global score from above it is called a blocker or a veto due to its rather intolerant character when it bounds the global score from below it is then called a pusher or a favor we thus investigate the tolerance of criteria or equivalently the tolerance of the weighted aggregation operator here the choquet integral that is used to aggregate criteria more specifically we propose axiomatically indices to appraise the extent to which each criterion behaves like a veto or a favor in the aggregation by the choquet integral previous to this we also propose global tolerance degrees measuring the extent to which the choquet integral is conjunctive or disjunctive

suowa operators an analysis of their conjunctive disjunctive character abstract choquet integrals mainly weighted means and owa operators are a well known family of functions widely used in several scientific fields because of this it is very important to know the behavior of these functions in order to choose the best suited operators in practical applications in this sense the analysis of the conjunctive disjunctive character is very interesting given that allow understand the behavior of functions in relation to order statistics in this paper we focus on some classes of suowa operators which are choquet integrals that simultaneously generalize weighted means and owa operators and provide conditions under which the k conjunctive or k disjunctive character of an owa operator is retained by the suowa operators associated with it of particular interest is the case where the owa operator is located between two order statistics given that we can obtain suowa operators also located between the same order statistics likewise we show closed form expressions of k conjunctiveness and k disjunctiveness indices for some specific cases of suowa operators

computationally efficient algorithms for constraint handling with guaranteed stability and near optimality predictive control strategies allow for the systematic handling of constraint performance and stability however the associated algorithms can be computational burdensome and or difficult to unravel the aim of this paper is to discuss and compare algorithms based on invariant sets which meet the additional requirement for computational simplicity there may of course be a concomitant loss of optimality but as illustrated this can be minimal and often is a small price to pay when one considers the significant improvements in efficiency

entropy of discrete choquet capacities we introduce a measure of entropy for any discrete choquet capacity and we interpret it in the setting of aggregation by the choquet integral

roughness bounds in rough set operations this paper presents some roughness bounds for rough set operations the results show that a bound of the set operation can be determined from their operand s roughnesses we prove also that this bound is not determined under some special operations

2 additive capacity identification methods from multicriteria correlation preference information the essential role of the particular families of capacities and the capacity identification methods is to help the decision maker to deal with the exponential complexity inherent in the construction process of the capacity the 2 additive capacities appear to be the most popular among the particular families of capacities since they permit to model interactions between criteria while preserving simplicity besides the preference with respect to the decision criteria most of the capacity identification methods also need to provide the desired overall evaluations of the decision alternatives in the learning set which is a time consuming task for the decision maker in this paper we propose some models to identify 2 additive capacities only from a kind of refined preference information with respect to the decision criteria called the multicriteria correlation preference information mccpi the mccpi is a group of 2 d preference information which can be described and obtained by the refined diamond diagram the common principle of the proposed models is to minimize the different kinds of deviations between the mccpi and the most desired 2 additive capacity ies a multicriteria decision making example is presented to show the feasibility of the proposed methods and a 2 d scale of the mccpi is also introduced in the further discussion of the illustrative example

more efficient predictive control an approach for constrained predictive control of linear systems or uncertain systems described by polytopic uncertainty models is presented the approach consists of in general non convex but often convex offline optimization and very efficient online optimization two examples one being a laboratory experiment compare the approach to existing approaches revealing both advantages and disadvantages

the explicit linear quadratic regulator for constrained systems we present a technique to compute the explicit state feedback solution to both the finite and infinite horizon linear quadratic optimal control problem subject to state and input constraints we show that this closed form solution is piecewise linear and continuous as a practical consequence of the result constrained linear quadratic regulation becomes attractive also for systems with high sampling rates as on line quadratic programming solvers are no more required for the implementation

distributed global output feedback control for a class of euler lagrange systems this paper investigates the distributed tracking control problem for a class of euler lagrange multiagent systems when the agents can only measure the positions in this case the lack of the separation principle and the strong nonlinearity in unmeasurable states pose severe technical challenges to global output feedback control design to overcome these difficulties a global nonsingular coordinate transformation matrix in the upper triangular form is first proposed such that the nonlinear dynamic model can be partially linearized with respect to the unmeasurable states and a new type of velocity observers is designed to estimate the unmeasurable velocities for each system then based on the outputs of the velocity observers we propose distributed control laws that enable the coordinated tracking control system to achieve uniform global exponential stability both theoretical analysis and numerical simulations are presented to validate the effectiveness of the proposed control scheme

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

extensions of fuzzy aggregation abstract we discuss the equivalence between aggregation of fuzzy sets and integration with respect to a special class of non additive set functions both fuzzy integral and choquet integral are considered first we study aggregation of a finite family of fuzzy sets and then we extend our results to aggregation of an infinite family the concepts of comonotonic maxitivity and additivity play a central role we argue that for the purpose of aggregating fuzzy sets comonotonic maxitivity is a more desirable requirement than comonotonic additivity in the absence of any such requirement we explore a wider class of aggregation procedures another important subject that we study is a comparison between two aggregation functions and we obtain a simple characterization in both the finite and infinite case our results are related to concepts that were studied in the three areas where non additive set functions and integrals were found particularly useful fuzzy sets theory mathematical economics and mathematical statistics

generalized bonferroni mean operators in multi criteria aggregation in this paper we provide a systematic investigation of a family of composed aggregation functions which generalize the bonferroni mean such extensions of the bonferroni mean are capable of modeling the concepts of hard and soft partial conjunction and disjunction as well as that of k tolerance and k intolerance there are several interesting special cases with quite an intuitive interpretation for application

leader follower swarm tracking for networked lagrange systems abstract in this paper swarm tracking problems with group dispersion and cohesion behaviors are discussed for a group of lagrange systems the agent group is separated into two subgroups one is called the leader group whose members are encapsulated with the desired generalized coordinates and generalized coordinate derivatives the other one referred to as the follower group is guided by the leader group the objective is to guarantee distributed tracking of generalized coordinate derivatives for the followers and to drive the generalized coordinates of the followers close to the convex hull formed by those of the leaders both the case of constant leaders generalized coordinate derivatives and the case of time varying leaders generalized coordinate derivatives are considered the proposed control algorithms are shown to achieve velocity matching connectivity maintenance and collision avoidance in addition the sum of the steady state distances between the followers and the convex hull formed by the leaders is shown to be bounded and the bound is explicitly given simulation results are presented to validate the effectiveness of theoretical conclusions

multivariate integration of functions depending explicitly on the minimum and the maximum of the variables abstract by using some basic calculus of multiple integration we provide an alternative expression of the integral a b n f x min x i max x i d x in which the minimum and the maximum are replaced with two single variables we demonstrate the usefulness of that expression in the computation of orness and andness average values of certain aggregation functions by generalizing our result to riemann stieltjes integrals we also provide a method for the calculation of certain expected values and distribution functions

hierarchical aggregation functions generated from belief structures we deal with the development of tools useful for the construction of multicriteria decision functions that allow for the modeling of the types of complexity that is the hallmark of human intelligence we first discuss the fuzzy measure describe its potential for characterizing relationships between multiple criteria and introduce the class of ordered aggregation functions that can be based on a fuzzy measure we then focus on the two fuzzy measures associated with the dempster shafer belief structure plausibility and belief and describe the types of ordered aggregation functions obtained using these measures this leads us to introduce a new class of aggregation functions obtained by allowing a decision maker to provide his decision imperative in terms of components concepts that contribute to his overall satisfaction each component consists of a value a subset of criteria and an agenda for combining the criteria in the component finally it is shown how these components can be combined to allow for the representation of hierarchical decision functions

a numerically robust state space approach to stable predictive control strategies recent work with predictive control strategies has shown that the stable gpc sgpc approach has significant computational and numerical advantages however sgpc is cast in the transfer function framework which limits its application here we develop a means of extending the results to state space models and show that improved numerical conditioning can be obtained for many stable predictive control strategies

domain semantics of possibility computations the purpose of this paper is to introduce a kind of computational model called possibility computation to deal with non determinism both its denotational and logical semantics in the framework of domain theory are established and their equivalence is verified in this approach the denotational semantics will be set up by assigning to programs possibility state transformers i e scott continuous functions from the domain of input states to the possibility powerdomain of the codomain of final states this possibility powerdomain of a dcpo will consist of all possibility valuations ordered pointwise of this dcpo the logical semantics will be given by fuzzy predicate transformers introduced by the first author and jung following dijkstra s predicate transformers two semantics equivalence will be verified in terms of the integration of fuzzy predicates with respect to possibility valuations the categorical monad of the possibility powerdomain will be investigated

linear systems with state and control constraints the theory and application of maximal output admissible sets the initial state of an unforced linear system is output admissible with respect to a constraint set y if the resulting output function satisfies the pointwise in time condition y t in y t or 0 the set of all possible such initial conditions is the maximal output admissible set o sub infinity the properties of o sub infinity and its characterization are investigated in the discrete time case it is generally possible to represent o sub infinity or a close approximation of it by a finite number of functional inequalities practical algorithms for generating the functions are described in the continuous time case simple representations of the maximal output admissible set are not available however it is shown that the discrete time results may be used to obtain approximate representations

on the relationship between the crescent method and suowa operators different families of functions have been proposed in the literature with the purpose of simultaneously generalizing weighted means and ordered weighted averaging owa operators see for instance weighted owa and semiuninorm based owa suowa operators recently jin et al have introduced in the literature a new procedure called the crescent method to melt additive capacities with those of owa operators the main aim of this article is to establish a relationship between the crescent method and suowa operators from this relationship we give closed form expressions for some well known indices such as the shapley values the veto and favor indices and the k conjunctiveness and k disjunctiveness indices

equivalent representations of set functions this paper introduces four alternative representations of a set function the ma bius transformation the co ma bius transformation and the interactions between elements of any subset of a given set as extensions of shapley and banzhaf values the links between the five equivalent representations of a set function are emphasized in this presentation

consensus of networked mechanical systems with communication delays a unified framework this technical note addresses the consensus problem of networked uncertain mechanical systems which interact on directed graphs containing a spanning tree and are subjected to nonuniform communication delays the challenge lies in the unclear input output property of a linear networked system containing communication delays and the unclear convergent property of this system under an external input we establish a new input output property of this linear networked system and moreover its convergent property under an external input upon which we establish a unified framework to resolve the consensus problem of multiple mechanical systems the proposed consensus framework unifies extends the existing results and in addition yields a fully cascaded closed loop system with lyapunov like analysis and frequency domain input output analysis we show that the proposed unified consensus control scheme ensures consensus without the integral action of the sliding vector and scaled weighted average consensus with the integral action of the sliding vector simulation results are provided to demonstrate the performance of the proposed consensus schemes

generalized medians distance aggregation operators are introduced in the case of singleton based distance a well known class of k medians is recovered for interval based distance characterization of p r distance aggregation operators is given in general as well as for idempotent operators based on the triangle of median factors medians are introduced owa operators are shown to be a linear convex combination of special j medians

flocking of networked uncertain euler lagrange systems on directed graphs this paper investigates the flocking problem of networked nonlinear euler lagrange systems with parametric uncertainties and they are assumed to interact on directed graphs with a directed spanning tree we propose an adaptive controller to achieve the flocking objective and the resultant closed loop networked system bears the cascade structure using a new similarity decomposition approach a critical characteristic root based approach and the input output stability analysis we demonstrate the convergence of the position velocity synchronization errors among the uncertain nonlinear euler lagrange agents we also show that the velocities of the euler lagrange systems converge to the weighted average velocity value simulation results are provided to demonstrate the performance of the proposed controller

graded dominance and related graded properties of fuzzy connectives graded properties of binary and unary fuzzy connectives valued in mtl algebras are studied including graded monotony a generalized lipschitz property commutativity associativity unit and null elements and the dominance relation between fuzzy connectives the apparatus of fuzzy class theory or higher order fuzzy logic is employed as a tool for easy derivation of graded theorems on the connectives

constraint softening in model predictive control with off line optimized admissible sets for systems with additive and multiplicative disturbances abstract an approach to the softening of constraints is explored for a class of mpc algorithms that employ off line computed constraint admissible sets for simplified on line computations the proposed approach relies on the use of exact penalty functions to ensure that the solution coincides with the actual optimal solution if the original mpc problem is feasible and that there are constraint violations at minimum possible levels if the original problem is infeasible the approach is implemented for a class of linear systems with additive and multiplicative disturbances using a dynamic policy based mpc algorithm results specific to the cases of non stochastic and stochastic disturbances are explored and assessed with simulation examples

a sensitivity analysis approach to introducing weight factors into decision functions in fuzzy multicriteria decision making in fuzzy multicriteria decision making the evaluations for criteria are aggregated using a suitable decision function many of the aggregation operators from fuzzy set theory that can be used as decision functions assume that the criteria have equal importance this paper considers the extension of these functions when the criteria are not equally weighted the criteria weights are interpreted as factors influencing the sensitivity of the decision function to the corresponding criteria a set of conditions is specified which a weighted decision function should satisfy this leads to a systematic way of introducing the weight factors into the decision functions the proposed analysis is applied to a class of operators in which the parameter may be interpreted as the decision maker s characteristic optimism index in this context it is shown that the well known method of multiplication of weight factors with membership values is suitable for optimistic decision makers while yager s power raising method is suitable for pessimistic decision makers only a geometric interpretation of the decision making process is also given

constrained robust feedback model predictive control for uncertain systems with polytopic description for the constrained uncertain systems with polytopic description a new design method of robust feedback model predictive control is proposed by using a sequence of feedback control laws and designing the parameter dependent lyapunov function for each model the design method provides more degrees of freedom and then can improve the control performance and enlarge the feasible region based on the characteristic property of the design method an offline design algorithm is developed to reduce the mpc controller s online computation burden the numerical examples verify the effectiveness of the results presented in this article

parametric characterization of aggregation functions the aim of this contribution is to find a common framework for parametric characterization of aggregation functions exploiting the notions of unipolar and bipolar parametric characterization and also unify the ideas of global and local parametric characterization we revise the known approaches to classification of aggregation functions in special classes in this framework and also propose some new parameters in classes of averaging conjunctive and disjunctive aggregation functions

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

an axiomatic approach of the discrete choquet integral as a tool to aggregate interacting criteria the most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean however in many problems the criteria considered interact and a substitute to the weighted arithmetic mean has to be adopted we show that under rather natural conditions the discrete choquet integral is an adequate aggregation operator that extends the weighted arithmetic mean by taking into consideration of the interaction among criteria the axiomatic that supports the choquet integral is presented and an intuitive approach is proposed as well

aggregating membership values by a choquet fuzzy integral based operator a new type of aggregator the choquet fuzzy integral based operator is introduced and applied in aggregation of membership values in this paper we generalized the definition of the fuzzy integral as a tool for membership aggregation the generalization involves replacing the max or min operator in information integration with a choquet fuzzy integral based aggregator resulting in increased flexibility the characteristics of the choquet fuzzy integral are studied and a two phase aggregating process is proposed also we demonstrate a good classification result using the proposed aggregator to integrate the memberships of several clusters in a complex unconstrained handwritten digit recognition domain

penalty based aggregation of multidimensional data abstract research in aggregation theory is nowadays still mostly focused on algorithms to summarize tuples consisting of observations in some real interval or of diverse general ordered structures of course in practice of information processing many other data types between these two extreme cases are worth inspecting this contribution deals with the aggregation of lists of data points in r d for arbitrary d 1 even though particular functions aiming to summarize multidimensional data have been discussed by researchers in data analysis computational statistics and geometry there is clearly a need to provide a comprehensive and unified model in which their properties like equivariances to geometric transformations internality and monotonicity may be studied at an appropriate level of generality the proposed penalty based approach serves as a common framework for all idempotent information aggregation methods including componentwise functions pairwise distance minimizers and data depth based medians it also allows for deriving many new practically useful tools

an algorithm for reducing complexity in parametric predictive control multi parametric quadratic programming solutions to predictive control can require large numbers of regions which would make practical implementation difficult this paper demonstrates how an underexplored prediction class can be combined with parametric programming to give far simpler solutions and at little cost to optimality the key proposal is to explore how one can give more flexibility in the shape of the predictions without increasing the required numbers of degrees of freedom this flexibility allows terminal regions to be enlarged

distributed coordinated tracking with a dynamic leader for multiple euler lagrange systems in this note we study a distributed coordinated tracking problem for multiple networked euler lagrange systems the objective is for a team of followers modeled by full actuated euler lagrange equations to track a dynamic leader whose vector of generalized coordinates is time varying under the constraints that the leader is a neighbor of only a subset of the followers and the followers have only local interaction we consider two cases i the leader has a constant vector of generalized coordinate derivatives and ii the leader has a varying vector of generalized coordinate derivatives in the first case we propose a distributed continuous estimator and an adaptive control law to account for parametric uncertainties in the second case we propose a model independent sliding mode control algorithm simulation results on multiple networked two link revolute joint arms are provided to show the effectiveness of the proposed control algorithms

extending yager s orness concept for the owa aggregators to other mean operators abstract in this paper we address the problem of defining the orness closeness to the maximum and andness closeness to the minimum of fuzzy aggregation operators in particular we center our study in fuzzy mean aggregators as defined by dubois prade and yager for this purpose we propose the introduction of the orness distribution function orness average value orness extension measure and orness sequence which we believe are valid concepts to characterize this type of aggregation operators we study their application to several well known mean operators and prove as well that in the case of yager s owa operators the orness average value that we propose coincides with yager s original orness definition we also introduce a method for the construction of mean operators from a predefined orness distribution function and make some considerations about the extension of these concepts to the cases of weighted aggregations or aggregations based on fuzzy measures

generalized means as model of compensative connectives abstract empirical investigations have shown that instead of strong logical and and or connectives there is often some degree of compensation in between in this paper the generalized means are proposed as connective operators for fuzzy set theory which easily allow for modelling the degree of compensation in a natural manner including the arithmetic and geometric means as well as the maximum and minimum operators as special cases numerical examples with empirical data form an illustration of this concept some aspects of applications to decision making are discussed

min max feedback mpc using a time varying terminal constraint set and comments on efficient robust constrained model predictive control with a time varying terminal constraint set abstract in this paper a robust mpc scheme using a time varying terminal constraint set for input constrained systems with a polytopic uncertainty description is proposed the new scheme is a refinement of the algorithm published in efficient robust constrained model predictive control with a time varying terminal constraint set z wan m v kothare systems control lett 48 2003 375 383 the original result contains an error in the stability proof which is solved in this paper by introducing within horizon feedback p o m scokaert d q mayne ieee trans automat control 43 8 1998 1136 1142 in the on line algorithm the new scheme is proven to be robustly asymptotically stabilizing but at the cost of an increased computational complexity

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

graded properties of unary and binary fuzzy connectives the paper studies basic graded properties of unary and binary fuzzy connectives i e unary and binary operations on the set of truth degrees of a background fuzzy logic extending the logic mtl of left continuous t norms the properties studied in this paper are graded generalizations of monotony lipschitz continuity null and unit elements idempotence commutativity and associativity the paper elaborates the initial study presented in previous papers and focuses mainly on parameterization of graded properties by conjunction multiplicities of subformulae in the defining formulae preservation of graded properties under compositions and slight variations of fuzzy connectives the values of graded properties for basic connectives of the ground logic and the dependence of the values on the ground logic the results are proved in the formal framework of higher order fuzzy logic mtl also known as fuzzy class theory fct general theorems provable in fct are illustrated on several semantic examples

generalized ordered modular averaging operator and its application to group decision making in this paper we propose a new class of operators called the ordered quasi modular averaging oqma operators based on the ordered modular averaging oma operators it is shown that the oqma operators are monotonic bounded idempotent commutative and quasi comonotone modular moreover we introduce the generalized ordered modular averaging goma operator which is a special case of the oqma operator some special cases of the goma operator are discussed an orness measure to reflect the or like degree of the goma operator is proposed we further extend the goma operator to the generalized ordered hybrid modular gohm operator which focuses not only on the degree of importance with respect to input arguments but also their serial positions finally a new method based on the gohm operator for multi attribute group decision making is presented and a numerical example shows that the developed approach is feasible

k intolerant capacities and choquet integrals we define an aggregation function to be at most k intolerant if it is bounded from above by its kth lowest input value applying this definition to the discrete choquet integral and its underlying capacity we introduce the concept of k intolerant capacities which when varying k from 1 to n cover all the possible capacities on n objects just as the concepts of k additive capacities and p symmetric capacities have been previously introduced essentially to overcome the problem of computational complexity of capacities k intolerant capacities are proposed here for the same purpose but also for dealing with intolerant or tolerant behaviors of aggregation we also introduce axiomatically indices to appraise the extent to which a given capacity is k intolerant and we apply them on a particular recruiting problem

fuzzy measure and probability distributions distorted probabilities this work studies fuzzy measures and their application to data modeling we focus on the particular case when fuzzy measures are distorted probabilities we analyze their properties and introduce a new family of measures m dimensional distorted probabilities the work finishes with the application of two dimensional distorted probabilities to a modeling problem results of the application of such fuzzy measure to data modeling using choquet integral are discussed

new classes of threshold aggregation functions based upon the tsallis q exponential with applications to perceptual computing we introduce two new classes of single parameter aggregation functions based upon the tsallis q exponential qe function of nonextensive statistical mechanics these aggregation functions denoted qe aggregation facilitate simple modeling of the common human reasoning trait of threshold inference where either 1 at least one input must exceed a threshold in order to achieve a nonzero aggregation output or 2 if any one of the inputs exceeds a different threshold the aggregation output takes its maximum value we illustrate the thresholding behavior of these functions on interval type 2 fuzzy inputs using an example known in the literature as the investment judgment advisor we believe that the new qe class of aggregation operators will prove useful in extending the range of options available for the design of perceptual computing systems

indicators for the characterization of discrete choquet integrals ordered weighted averaging owa operators and their extensions are powerful tools used in numerous decision making problems this class of operator belongs to a more general family of aggregation operators where each operator of this family is understood as a discrete choquet integral aggregation operators are usually characterized by indicators in this article four indicators usually associated with the owa operator are extended to the discrete choquet integral namely the degree of balance the divergence the variance indicator and renyi entropies all of these indicators are considered from a local and a global perspective linearity of indicators for linear combinations of capacities is investigated and to illustrate the usefulness of results indicators of the probabilistic ordered weighted averaging powa operator are derived finally a numerical example is provided to discuss the results in a specific context

an orness measure for quasi arithmetic means in this paper an orness measure to reflect the or like degree of the quasi arithmetic mean operator is proposed with the generating function representation method some properties of a quasi arithmetic mean associated with its orness measure are analyzed then the paper focuses on two kinds of parameterized quasi arithmetic means with exponential function and power function generators respectively some properties of them are examined and compared as the aggregation value for any set always monotonically increases with the orness level the orness level can be used as a control parameter to represent the decision maker s preference a generic method to get the quasi arithmetic mean operator which makes the aggregation result consistent with its orness level is also examined finally the properties of the quasi arithmetic mean and that of the exponential and power function generators are extended to the weighted quasi arithmetic mean by considering the importance of the aggregated elements

pictorial representations of fuzzy connectives part i cases of t norms t conorms and averaging operators part i of this paper shows a number of examples of existing t norms and t conorms which are known as good models of fuzzy set theoretic intersection and union and then the pictorial representations of t norms and t conorms are made with the aid of a computer several new examples of t norms and t conorms are also given averaging operators between min and max are summarized and their pictorial representations are also made

synchronization of networks of nonidentical euler lagrange systems with uncertain parameters and communication delays this paper addresses the problem of synchronizing networks of nonidentical nonlinear dynamical systems described by euler lagrange equations which are assumed fully actuated with their states available for measurement but with unknown parameters the only assumption made on the communication graph is that it is connected moreover the communication is subject to constant time delays which are also unknown the main result of the paper is the construction of an adaptive controller that achieves global full state synchronization i e the difference between the agents positions and velocities asymptotically converges to zero if a desired trajectory for all systems is given a slight modification to the proposed scheme achieves also full state synchronization simulations using a ten robot manipulator network are used to illustrate the performance of the proposed schemes

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

the application of fuzzy integrals in multicriteria decision making abstract this paper presents a synthesis on the application of fuzzy integrals as an innovative tool for criteria aggregation in decision problems the main point is that fuzzy integrals are able to model interaction between criteria in a flexible way the methodology has been elaborated mainly in japan and has been applied there successfully in various fields such as design reliability evaluation of goods etc it seems however that this technique is still very little known in europe it is one of the aims of this review to disseminate this emerging technology in many industrial fields

additive fuzzy measures and integrals iii abstract a point of view concerning fuzzy measures is explained to this end a new concept of disjointness for fuzzy is introduced and studied also a concept of an additive class of fuzzy sets is defined to be a class of fuzzy sets closed under some additive operations the fuzzy measures are defined to be sum preserving real functions over such additive classes some basic properties of the fuzzy measures are derived in contrast with other homonymous concepts studied in literature our fuzzy measures lead to an additive fuzzy integral see the part ii of the paper

parameterized defuzzification with continuous weighted quasi arithmetic means an extension parameterized aggregation becomes an attractive idea in many applications by applying the quasi arithmetic mean based defuzzification method and its orness measure we extend the properties of discrete quasi arithmetic mean with an orness measure to the case of continuous weighted quasi arithmetic means and apply them to the parameterized estimation of fuzzy or random variables when facing the uncertainty of these variables the decision maker can obtain the crisp value estimation which is always consistent with his her preference information two families of continuous weighted quasi arithmetic means with exponential and power function generators are discussed combining these conclusions with that of the discrete case we can understand better the properties of quasi arithmetic means and extend their possible applications

learning k maxitive fuzzy measures from data by mixed integer programming abstract fuzzy measures model interactions between the inputs in aggregation problems their complexity grows exponentially with the dimensionality of the problem and elicitation of fuzzy measure coefficients either from domain experts or from empirical data poses a significant challenge the notions of k additivity and k maxitivity simplify the fuzzy measures by limiting interactions to subsets of up to k elements learning fuzzy measures from data is an important elicitation technique which relies on solving an optimisation problem a heuristic learning algorithm to identify k maxitive fuzzy measures from the data on the basis of hlms heuristic least mean squares was recently presented in murillo et al 2017 11 we present an alternative formulation of the fitting problem which delivers a globally optimal solution through the solution of a mixed integer programming mip problem to deal with high computational cost of mip in moderate to large dimensions we also propose a simple mip relaxation technique which involves solving two related linear programming problems we also provide a linear programming formulation for fitting k tolerant fuzzy measures we discuss implementations of the fitting methods and present the results of numerical experiments

fuzzy integral in multicriteria decision making abstract this paper presents a synthesis on the use of fuzzy integral as an aggregation operator in multicriteria decision making definitions essential properties are given and compared to those of usual aggregation operators a quick survey on applications is given

determining the fuzzy measures in multiple criteria decision aiding from the tolerance perspective abstract we consider multiple criteria decision aiding mcda in the case of interactions between criteria in dealing with interactions between criteria fuzzy measures and integrals have demonstrated great advantages nevertheless the determination of fuzzy measures has proven difficult because the capacities of not only single criterion but also all subsets of criteria need to be identified due to the value judgment essence of mcda the attitudes of the decision maker dm are typically modeled to identify fuzzy measures in this paper the tolerance attitudes of the dm which implies a direct requirement instead of partial preference are modeled with regard to the determination of fuzzy measures for the first time with two scales developed in this paper the dm can directly express the tolerance attitudes to certain criteria other than providing partial preference through pairwise comparison as a result it requires less prior knowledge and is more efficient to some extent further the inherent interacting mechanism of criteria under different tolerance attitudes is explored at last the tolerance attitudes are applied to the process of multiple criteria analysis using a choquet integral a classic student evaluation problem is given as an example the evaluation results are compared with additive models this paper not only provides a new inspiration to the determination of fuzzy measures but also improves the descriptive capacity of fuzzy measures to the real world