improving linguistic pairwise comparison consistency via linguistic discrete regions linguistic pairwise comparison matrices are widely used in decision making procedures however the matrices often give conflicting results when there are multiple criteria under consideration despite intensive research achieving consistency of such matrices remains a daunting task in this paper a novel approach based on linguistic discrete region is proposed to address the challenge unlike existing methods that require a single value for each comparison our approach allows a comparison to be expressed by a discrete region with multiple linguistic terms such front end gives users more freedom to express their opinions in the back end we propose an iterative searching algorithm that is able to achieve approximate optimal consistency for the comparison matrices with discrete region values the final results are single value matrices that not only guarantee approximate optimal consistency but comply with evaluators intentions a well as our approach does not modify any linguistic values like many existing methods we have conducted extensive evaluations and our empirical study confirms that the linguistic discrete region based approach significantly improves the consistency of linguistic pairwise comparison matrices

continuous dependence results for a general model of size dependent population dynamics we are concerned with a general model of size structured population dynamics with the growth rate depending on the individual s size and time in this paper we shall study the continuous dependence of the solution on all given data such as aging and birth functions growth rate functions and initial data

robust exact differentiation via sliding mode technique abstract the main problem in differentiator design is to combine differentiation exactness with robustness in respect to possible measurement errors and input noises the proposed differentiator provides for proportionality of the maximal differentiation error to the square root of the maximal deviation of the measured input signal from the base signal such an order of the differentiation error is shown to be the best possible one when the only information known on the base signal is an upper bound for lipschitz s constant of the derivative

behavioral analysis of a nonlinear three staged population model with age size structure we present and analyze a nonlinear egg juvenile adult model in which eggs and juveniles are structured by age while adults by size the model consists of three first order partial differential equations with initial and boundary conditions existence and uniqueness of nonnegative solutions to the state system are investigated by the method of characteristics and a comparison principle extinction or persistence conditions of the population are obtained via the upper lower solution technique our investigation extends some results in the literature

judgemental modelling based on geometric least square abstract the analytic hierarchy process developed by t l saaty has received widespread attention in the literature however this has not been without some criticisms including the problems of meaning of consistency and large data requirements this paper addresses the last two problems and presents a new method of calculating preference vectors to the user the procedure is essentially the same but the data requirements can be made less onerous and at the same time feedback is provided permitting a greater understanding of the data inputs preliminary results indicate the acceptability of the proposed methodology

stability analysis for equilibria in age specific population dynamics on considere une population de n especes dont les taux de vie dependent de l ge on etudie le comportement de stabilite a l equilibre pour les equations d evolution

parameter tuning of second order sliding mode controllers for linear plants with dynamic actuators tuning of second order sliding mode control 2 smc algorithms in linear systems with dynamic actuators is considered by means of a describing function df approach it is investigated how the parameters of a 2 smc algorithm the so called generalized sub optimal algorithm affect the frequency and the magnitude of the limit cycles that occur when the overall relative degree of the plant plus the actuator is three or more explicit formulas are given that allow for setting the parameters of the algorithm to obtain a periodic solution with the prescribed characteristics by means of simulation examples we show that the estimated chattering parameters are in good agreement with the actual ones we also show that the proposed design procedure can also be useful when the local linearization of a nonlinear dynamics is sufficiently accurate

on the net reproduction rate of continuous structured populations with distributed states at birth we consider a nonlinear structured population model with a distributed recruitment term the question of the existence of non trivial steady states can be treated at least in three different ways one approach is to study spectral properties of a parametrised family of unbounded operators the alternative approach which we develop here is based on the reformulation of the partial differential equation as an integral equation in this context we introduce a density dependent net reproduction rate and discuss its relationship to a biologically meaningful quantity finally we discuss a third approach which is based on a finite rank approximation of the recruitment operator

group decision making with a fuzzy linguistic majority abstract the determination of solutions in group decision making is considered the point of departure is a collection of individual fuzzy preference relations a solution is derived either directly from the individual fuzzy preference relations or by constructing first a social fuzzy preference relation as opposed to conventional approaches in which a crisp threshold type majority rule is used we employ a fuzzy majority rule specified by a fuzzy linguistic quantifier e g most much more than 50 etc a calculus of linguistically quantified propositions is applied using the fuzzy majority various solution concepts are derived mainly of the type of core minimax opposition set and consensus winner

a chi square method for obtaining a priority vector from multiplicative and fuzzy preference relations abstract decision makers dms preferences on decision alternatives are often characterized by multiplicative or fuzzy preference relations this paper proposes a chi square method csm for obtaining a priority vector from multiplicative and fuzzy preference relations the proposed csm can be used to obtain a priority vector from either a multiplicative preference relation i e a pairwise comparison matrix or a fuzzy preference relation or a group of multiplicative preference relations or a group of fuzzy preference relations or their mixtures theorems and algorithm about the csm are developed three numerical examples are examined to illustrate the applications of the csm and its advantages

persistence of periodic orbits with sliding or sewing by singular perturbation abstract in this paper we deal with piecewise smooth singularly perturbed systems we study the effect of singular perturbation when the phase portrait of the reduced problem has periodic orbits with sliding or sewing points counter examples are used to show that in general only one parameter is not sufficient to ensure the persistence of periodic orbits with an additional parameter derived from the sotomayor teixeira regularization we get conditions which guarantee the persistence

chattering avoidance by second order sliding mode control relying on the possibility of generating a second order sliding motion by using as control the first derivative of the control signal instead of the actual control a new solution to the problem of chattering elimination in variable structure control vsc is presented such a solution inspired by the classical bang bang optimal control strategy is first depicted and expressed in terms of a control algorithm by introducing a suitable auxiliary problem involving a second order uncertain system with unavailable velocity then the applicability of the algorithm is extended via suitable modifications to the case of nonlinear systems with uncertainties of more general types the proposed algorithm does not require the use of observers and differential inequalities and can be applied in practice by exploiting such commercial components as peak detectors or other approximated methods to evaluate the change of the sign of the derivative of the quantity accounting for the distance to the sliding manifold

brief paper oscillations and transfer properties of relay feedback systems with time delay linear plants oscillations and transfer properties of relay feedback systems with linear plants having a dead time time delay are considered poincare maps are found explicitly in terms of the system parameters the oscillatory and transfer properties are presented in the format of the locus of a perturbed relay system lprs which represents the continuum of all possible periodic solutions and transfer properties of the system with a given linear plant conditions of local orbital asymptotic stability are found in terms of the system parameters the proposed approach is illustrated by examples

brief paper dynamic sliding mode control design using attracting ellipsoid method a methodology for the design of sliding mode controllers for linear systems subjected to matched and unmatched perturbations is proposed it is considered that the control signal is applied through a first order low pass filter the technique is based on the existence of an attracting invariant ellipsoid such that the convergence to a quasi minimal region of the origin using the suboptimal control signal is guaranteed the design procedure is given in terms of the solution of a set of matrix inequalities a benchmark example illustrating the design is given

generalized analytic network process the analytic network process anp is a methodology for multi criteria decision making used to derive priorities of the compared elements in a network hierarchy where the dependences and feedback within and between the elements can be considered however the anp is limited to the input preferences as crisp judgments which is often unfavorable in practical applications as an extension of the anp a generalized analytic network process g anp is developed to allow multiple forms of preferences such as crisp fuzzy judgments interval interval fuzzy judgments hesitant hesitant fuzzy judgments and stochastic stochastic fuzzy judgments in the g anp a concept of complex comparison matrices ccms is developed to collect decision makers preferences in the multiple forms from a stochastic point of view we develop an eigenvector method based stochastic preference method evm spm to derive priorities from ccms the main steps of the g anp are summarized and the implementation of the g anp in matlab and excel environments are given in detail which is also a prototype for a decision support system a real life example of the piracy risk assessment to the energy channels of china is proposed to demonstrate the g anp

jie ke versus alphago a ranking approach using decision making method for large scale data with incomplete information abstract ranking historical players in sports is challenging since some players have never played against each other it is even more complex in go because of alphago a project based on artificial intelligence who became the world s number 1 after it defeated the 528th and the 4th human go players alphago is ranked high in the current go ranking system because it is undefeated the objective of this paper is to propose a new ranking method for large scale go players by means of incomplete fuzzy pair wise comparison matrix whose priority vector is derived using a cosine similarity measure using match results provided by go4go net experiments are designed to rank top go players in the past 45 years and examine the change in ranking after alphago faced off against jie ke furthermore the proposed method was applied to rank all 1544 go players available at go4go net to illustrate its efficiency in handling large scale data

stability conditions for the non linear mckendrick equations non linear mckendrick equation with age dependent mortality and fertility is considered the author appl math comput 131 1 2002 107 deduced the characteristic equation whose roots determine the stability we are able to give sufficient conditions for the stability of the stationary solutions of the system in some cases

expansion of solution of an inverted pendulum system with time delay in this paper the solution expansion for an inverted pendulum system with time delay is studied the linearized model of this nonlinear system near its equilibrium is derived on the assumption that a unique equilibrium exists in it then the asymptotic expressions of its eigenvalues and the eigenvalues corresponding eigenvectors are obtained moreover although the set of these eigenvectors does not form a schauder basis for the state space the solution of this model still can be expressed by these eigenvectors in the form of infinite series under certain conditions finally a simulation is provided to support these results

abstract linear partial differential equations related to size structured population models with diffusion abstract we study abstract linear partial differential equations in banach spaces and or banach lattices related to size structured population models with spatial diffusion and their dual problems we introduce mild solutions through semigroup theory and characteristic method and investigate differentiability of mild solutions existence of a unique mild solution is shown also a comparison result is obtained as well as the boundedness of mild solutions is investigated in the banach lattice setting furthermore we consider the dual problems and then we introduce weak solutions and establish their uniqueness

solving multi period project selection problems with fuzzy goal programming based on topsis and a fuzzy preference relation project portfolio managers are multi objective decision makers dms who are expected to select the best mix of projects by maximizing profits and minimizing risks over a multi period planning horizon however project portfolio decisions are complex multi objective problems with a high number of projects from which a subset has to be chosen subject to various constraints and a multitude of priorities and preferences we propose a goal programming gp approach for project portfolio selection that embraces conflicting fuzzy goals with imprecise priorities a fuzzy goal with an aspiration level and a predefined membership function is defined for each objective the impreciseness in the priorities of the membership values of the fuzzy goals is modeled with fuzzy relations this leads to type ii fuzzy sets since fuzzy relations are organized between the membership values of the fuzzy goals which are themselves fuzzy sets the proposed model is based on the technique for order preference by similarity to ideal solution topsis and fuzzy preference relations topsis is used to reduce the multi objective problem into a bi objective problem the resulting bi objective problem is solved with fuzzy gp fgp the fuzzy preference relations are used to help dms express their preferences with respect to the membership values of the fuzzy goals the proposed approach is used to solve a real life problem characterized as a fuzzy multi objective project selection with multi period planning horizon mops mpph the performance of the proposed approach is compared with a competing method in the literature we show that our approach generates high quality solutions with minimal computational efforts

analysis of closed loop performance and frequency domain design of compensating filters for sliding mode control systems for a sliding mode sm system containing parasitic dynamics a model of chattering and a model of the averaged motions of the order equal to the original order of the system are obtained via the use of the locus of a perturbed relay system lprs method the latter model proves that the averaged motions in an sm system differ from those in the reduced order model in particular such phenomena as the nonideal disturbance rejection and the nonideal input tracking are observed it is shown that the non reduced order model transforms into the reduced one when the parasitic dynamics are removed yet the chattering and the averaged motion being the two components of the motion in the sm system belong to two different frequency ranges spectra as a result a frequency characteristic shaping aimed at achieving the desired frequency of chattering and enhancing the closed loop performance becomes possible this opportunity is explored in this paper examples that illustrate the proposed approach are provided

logarithmic least squares prioritization and completion methods for interval fuzzy preference relations based on geometric transitivity abstract this article introduces the notion of geometric transitivity which may be used to define consistent interval fuzzy preference relations some useful properties are presented for consistent interval fuzzy preference relations a close investigation reveals that existing methods for determining the analogous property of consistency are not robust to permutations of the pairwise judgments and not able to reflect the hesitancy in the decision maker s preference a parametric transformation formula is put forward to convert a normalized interval weight vector into a consistent interval fuzzy preference relation by minimizing the squared difference between the logarithm of the ratio of the original judgment and the logarithm of the ratio of the converted consistent one a logarithmic least squares model is developed to derive interval weights from any interval fuzzy preference relation based on geometric transitivity a logarithmic least squares model is established to rectify inconsistency for complete and inconsistent interval fuzzy preference relations and a logarithmic least squares completion approach is further developed to estimate missing values for incomplete interval fuzzy preference relations numerical examples are furnished to show the validity of the proposed models and compare with other existing methods

multiple attribute decision making based on fuzzy preference information on alternatives ranking and weighting this paper investigates the multiple attribute decision making madm problem with fuzzy preference information on alternatives and proposes an eigenvector method to rank them three optimization models are introduced to assess the relative importance weights of attributes in a madm problem which integrate subjective fuzzy preference relations and objective information in different ways since the decisions these models lead to are based on both subjective and objective information they are more balanced and credible than those that consider only one type of information an example is provided to illustrate the application of the proposed models

robust estimation of priorities in the ahp abstract a pairwise comparison matrix of the analytic hierarchy process ahp is considered as a contingency table that helps to identify unusual or false data elicited from a judge special techniques are suggested for robust estimation of priority vectors they include transformation of a saaty matrix to matrix of shares of preferences and solving an eigenproblem designed for the transformed matrices we also introduce an optimizing objective that produces robust priority estimation numerical results are compared using the ahp with these differing approaches the comparison demonstrates that robust estimations yield priority vectors not prone to influence of possible errors among the elements of a pairwise comparison matrix

analysis of chattering in systems with second order sliding modes a systematic approach to the chattering analysis in systems with second order sliding modes is developed the neglected actuator dynamics is considered to be the main cause of chattering in real systems the magnitude of oscillations in nonlinear systems with unmodeled fast nonlinear actuators driven by second order sliding mode control generalized suboptimal 2 smc g so algorithms is evaluated sufficient conditions for the existence of orbitally stable periodic motions are found in terms of the properties of corresponding poincare maps for linear systems driven by 2 smc g so algorithms analysis tools based on the frequency domain methods are developed the first of these techniques is based on the describing function method and provides for a simple approximate approach to evaluate the frequency and the amplitude of possible periodic motions the second technique represents a modified tsypkin s method and provides for a relatively simple theoretically exact approach to evaluate the periodic motion parameters examples of analysis and simulation results are given throughout this paper

a least deviation method to obtain a priority vector of a fuzzy preference relation based on the transfer relationship between fuzzy preference relation and multiplicative preference relation this paper proposes a least deviation method to obtain a priority vector of a fuzzy preference relation and studies its desirable properties a simple convergent iterative algorithm is given and its practicality is shown by two numerical examples

oscillations and transfer properties of relay servo systems with integrating plants asymmetric limit cycles and input output properties of relay feedback systems with integrating plants are studied in the technical note it is noted that an integrating plant introduces significantly different dynamics so that a different than traditional system representation is needed to obtain a fixed point of poincare map conditions of orbital asymptotic stability are obtained the infinite set of possible periodic solutions and transfer characteristics is presented in the form of the locus of a perturbed relay system lprs a formula of lprs is derived an example of analysis of oscillations and transfer properties is given

linguistic multiperson decision making based on the use of multiple preference relations in multiperson decision making situations it is quite natural that different decision makers who may have different background and knowledge will provide their preferences by different kinds of preference relations this paper proposes a linguistic multiperson decision making model lmdmm based on linguistic preference relations integrating fuzzy preference relations different types of multiplicative preference relations and multigranular linguistic preference relations in the lmdmm several transformation functions are first obtained to relate fuzzy preference relations and different types of multiplicative preference relations with multigranular linguistic preference relations then we design the selection process of the lmdmm based on the use of the fuzzy majority and the extended ordered weighted averaging operator or the 2 tuple ordered weighted averaging operator and discuss conditions under which the proposed selection process satisfies the social choice axioms at last we analyze the internal consistency of the proposed transformation functions the results in this paper are helpful to complete chiclana et al s fuzzy decision model integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations fuzzy sets and systems 97 1998 33 48

stability and regularity results for a size structured population model in the present paper a nonlinear size structured population dynamical model with size and density dependent vital rate functions is considered the linearization about stationary solutions is analyzed by semigroup and spectral methods in particular the spectrally determined growth property of the linearized semigroup is derived from its long term regularity these analytical results make it possible to derive linear stability and instability results under biologically meaningful conditions on the vital rates the principal stability criteria are given in terms of a modified net reproduction rate

structured populations the stabilizing effect of the inflow of newborns from an external source and the net growth rate we investigate the effect of a positive population inflow of individuals from an external source on the dynamical behaviour of certain physiologically structured population models we treat a size structured model with constant inflow and nonlinear birth rate and an age structured model with nonlinear density dependent inflow and linear birth rate analogously to the inherent net reproduction rate we introduce a net growth rate and discuss how this net growth rate can be related to our stability instability conditions

sliding regimes in general non linear systems a relative degree approach in this paper we treat the problem of inducing local sliding regimes on non linear smooth surfaces defined in the state space of general non linear controlled systems a suitable notion of relative degree is found to be of crucial importance in establishing the most salient properties of non linear systems undergoing sliding motion the relevance of sliding modes in several control problems as complementary outer loop feedback is examined

on counter examples to aizerman and kalman conjectures counter examples to aizerman s and kalman s conjectures are considered investigation of the behaviour in the vicinity of the origin and at a distance from the origin is done the simultaneous exis

higher order sliding mode controllers with optimal reaching higher order sliding mode hosm control design is considered for systems with a known permanent relative degree in this paper we introduce the robust fuller s problem that is a robust generalization of the fuller s problem a standard optimal control problem for a chain of integrators with bounded control by solving the robust fuller s problem it is possible to obtain feedback laws that are hosm algorithms of generic order and in addition provide optimal finite time reaching of the sliding manifold a common difficulty in the use of existing hosm algorithms is the tuning of design parameters our methodology proves useful for the tuning of hosm controller parameters in order to assure desired performances and prevent instabilities the convergence and stability properties of the proposed family of controllers are theoretically analyzed simulation evidence demonstrates their effectiveness

analysis of second order sliding mode algorithms in the frequency domain a frequency domain analysis of the second order sliding mode algorithms particularly of the twisting algorithm is carried out in the frequency domain with the use of the describing function method and tsypkin s approach it is shown that in the presence of an actuator the transient process may converge to a periodic motion parameters of this periodic motion are analyzed a comparison of the periodic solutions in the systems with higher order sliding mode controllers and the oscillations that occur in classical sliding mode systems with actuators is done

eigenvector and logarithmic least squares abstract the eigenvector method deals with two questions simultaneously closeness and order together they belong to the field topology of order the metric idea of closeness is inadequate to judge what is a good approximation to data involving order relations there is usually a condition which relates order in the derived scale to order in the data this is precisely the kind of condition captured by the eigenvector but not by the logarithmic least squares estimate

singularly perturbed analysis of chattering in relay control systems for sliding mode control systems with fast actuators sufficient conditions for the exponential decreasing of the amplitude of chattering and unlimited growth of frequency are found the connection between the stability of actuators and the stability of the plant on the one hand and the stability of the sliding mode system as the whole on the other hand is investigated the algorithm for correction of sliding mode equations is suggested for taking into account the presence of fast actuators

variable structure control of synchronous generator singularly perturbed analysis synchronous generators have a natural different time scale dynamics that is why for modelling and control design in such systems the methods of singular perturbations are widely used in this paper the possibilities of sliding mode control design for synchronous generators are analysed with this aim the concept of singular perturbation is revised in order to use it for relay control systems the obtained results are used for sliding mode control of synchronous generator

a method based on multiobjective optimization for deriving a ranking from a fuzzy preference relation abstract methods for deriving final ranking from a fuzzy preference relation do not perform well in presence of irrelevant alternatives or in case of complex graphs with numerous circuits a new method for improving the quality of their prescriptions is proposed here it rests on the idea of reducing differences between a global model of preferences and a final ranking via multiobjective optimization this proposal is also more robust than others in relation to irrelevant alternatives it can be seen as an intent of reconciling two schools of thought related to decision aid one approach accepts the fuzziness of preferences the other is based on a system of axioms that model a normative rationality

applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy ahp the lack of consistency in decision making can lead to inconsistent conclusions in fuzzy analytic hierarchy process fuzzy ahp method it is difficult to ensure a consistent pairwise comparison furthermore establishing a pairwise comparison matrix requires nx n 1 2 judgments for a level with n criteria alternatives the number of comparisons increases as the number of criteria increases therefore the decision makers judgments will most likely be inconsistent to alleviate inconsistencies this study applies fuzzy linguistic preference relations fuzzy linprera to construct a pairwise comparison matrix with additive reciprocal property and consistency in this study the fuzzy ahp method is reviewed and then the fuzzy linprera method is proposed finally the presented method is applied to the example addressed by kahraman et al c kahraman d ruan i dogan fuzzy group decision making for facility location selection information sciences 157 2003 135 153 this study reveals that the proposed method yields consistent decision rankings from only n 1 pairwise comparisons which is the same result as in kahraman et al research the presented fuzzy linguistic preference relations method is an easy and practical way to provide a mechanism for improving consistency in fuzzy ahp method

performance analysis of second order sliding mode control systems with fast actuators the robustness of the second order sliding mode control 2 smc algorithm known as the generalized sub optimal algorithm is analyzed with respect to the cascade introduction of a linear fast actuator it is shown that if the actuator dynamics are sufficiently fast then the system trajectories converge to an invariant set that includes the second order sliding domain s s 0 it is also shown that the size of the invariant set has quadratic dependence with respect to the actuator small parameter mu for the sliding variable s and linear dependence for its derivative s this means that in the steady state the system trajectories converge to an invariant domain described by the following conditions s les o mu2 and s les o mu a simulation example is given to confirm the proposed

accuracy of homogeneous sliding modes in the presence of fast actuators it is shown that the higher the order r of the homogeneous sliding mode is the less sensitive it is to the presence of unaccounted for fast stable actuators with being an infinitesimal actuator time constant the sliding variable magnitude is proved to be proportional to r the system chattering is shown to be not amplified in the presence of actuators

a variable time step method for an age dependent population model with nonlinear diffusion we propose a method for solving a model of age dependent population diffusion with random dispersal this method unlike previous methods allows for variable time steps and independent age and time discretizations we use a moving age discretization that transforms the problem to a coupled system of parabolic equations the system is then solved by backward differences in time and a galerkin approximation in space the equations that need to be solved at each step treat each age group separately a priori l2 error estimates are obtained by an energy analysis these estimates are superconvergent in the age variable we present a postprocessing technique which capitalizes on the superconvergence

asynchronous exponential growth of semigroups of nonlinear operators the property of asynchronous exponential growth is analyzed for the abstract nonlinear differential equation z t az t f z t t 0 z 0 x x where a is the infinitesimal generator of a semigroup of linear operators in the banach space x and f is a nonlinear operator in x asynchronous exponential growth means that the nonlinear semigroup s t t 0 associated with this problem has the property that there exists 0 and a nonlinear operator q in x such that the range of q lies in a one dimensional subspace of x and limt e ts t x qx for all x x it is proved that if the linear semigroup generated by a has asynchronous exponential growth and f satisfies f x f x x where f r r and f r r dr then the nonlinear semigroup s t t 0 has asynchronous exponential growth the method of proof is a linearization about infinity examples from structured population dynamics are given to illustrate the results

a goal programming approach to group decision making based on multiplicative preference relations and fuzzy preference relations abstract this paper proposes a goal programming approach to solve group decision making gdm problems where the preference information on alternatives provided by decision makers is represented in two different formats i e multiplicative preference relations and fuzzy preference relations in order to narrow the gap between the collective opinion and each decision maker s opinion a linear goal programming model is constructed to integrate the two different formats of preference relations and to compute the collective ranking values of the alternatives thus the ranking of alternatives or selection of the most desirable alternative s is obtained directly from the computed collective ranking values a numerical example is also used to illustrate the applicability of the proposed approach

integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations abstract the purpose of this paper is to study a fuzzy multipurpose decision making problem where the information about the alternatives provided by the experts can be of a diverse nature the information can be represented by means of preference orderings utility functions and fuzzy preference relations and our objective is to establish a general model which cover all possible representations firstly we must make the information uniform using fuzzy preference relations as uniform preference context secondly we present some selection processes for multiple preference relations based on the concept of fuzzy majority fuzzy majority is represented by a fuzzy quantifier and applied in the aggregation by means of an owa operator whose weights are calculated by the fuzzy quantifier we use two quantifier guided choice degrees of alternatives a dominance degree used to quantify the dominance that one alternative has over all the others in a fuzzy majority sense and a non dominance degree that generalises orlovski s non dominated alternative concept the application of the two above choice degrees can be carried out according to two different selection processes a sequential selection process and a conjunction selection process

interval priorities in ahp by interval regression analysis abstract this paper proposes an interval approach for obtaining interval weights of priorities in the analytic hierarchy process ahp reflecting inconsistency of pairwise comparison ratios given by a decision maker even if pairwise comparison values with respect to preference are given as crisp values the priority weights should be estimated as intervals because of a decision maker s uncertainty of judgments we deal with two types of comparison matrices represented as crisp and interval elements this allows some uncertainty of estimations made by a decision maker the proposed approach can obtain the estimated interval priorities since interval regression analysis is based on the concept of possibility the interval weights obtained by the proposed method can be interpreted as the possible ranges estimated from the given data the sum of widths of the obtained intervals can be regarded as the degree of inconsistency included in the given data it is emphasized that interval data of preference can obtain the lower and upper models for the estimated weight intervals

α and β curves sister sister and mother daughter correlations in cell population dynamics abstract the and curves and sister sister and mother daughter cycle length correlations are analyzed for a general model of age and size structured cell population dynamics some basic facts concerning these concepts are established a criterion is given for log a and log a to have asymptotically equal slopes the significance of size dependence upon sister sister and mother daughter correlations is demonstrated some numerical examples are given to illustrate the concepts

remarks on semilinear partial functional differential equations with infinite delay abstract in this paper we will be concerned with the abstract semilinear equation x t ax t f t xt t x where a represents the infinitesimal generator of a linear c0 semigroup in a banach space and x denotes the segment of the solution x due to the initial function taken from up to t conditions for existence continuous dependence and regularity of solutions are given which are independent of the topology of the phase space as well as conditions which guarantee the compactness of bounded orbits even if exp at is not compact for t 0

analysis of chattering in continuous sliding mode controllers an analysis of two most popular continuous sliding mode algorithms the power fractional sliding mode algorithm and a second order sliding mode algorithm known as the super twisting is carried out in the frequency domain with the use of the describing function method it is shown that in the presence of an actuator the transient process converges to a periodic motion parameters of this periodic motion are analyzed a few examples are considered to illustrate the obtained results

finite time control of robotic manipulators this work offers the solution at the control feed back level of the accurate trajectory tracking subject to finite time convergence dynamic equations of a rigid robotic manipulator are assumed to be uncertain moreover globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory based on the suitably defined non singular terminal sliding vector variable and the lyapunov stability theory we propose a class of absolutely continuous robust controllers which seem to be effective in counteracting both uncertain dynamics and unbounded disturbances the numerical simulation results carried out for a robotic manipulator consisting of two revolute kinematic pairs operating in a two dimensional joint space illustrate performance of the proposed controllers

integrating multiplicative preference relations in a multipurpose decision making model based on fuzzy preference relations the aim of this paper is to study the integration of multiplicative preference relation as a preference representation structure in fuzzy multipurpose decision makingproblems assumingfuzzy multipurpose decision makingproblems under di4erent preference representation structures ordering utilities and fuzzy preference relations and using the fuzzy preference relations as uniform representation elements the multiplicative preference relations are incorporated in the decision problem by means of a transformation function between multiplicative and fuzzy preference relations a consistency study of this transformation function which demonstrates that it does not change the informative content of multiplicative preference relation is shown as a consequence a selection process based on fuzzy majority for multipurpose decision makingproblems under multiplicative preference relations is presented to design it an aggregation operator of information called ordered weighted geometric operator is introduced and two choice degrees the quanti7er guided dominance degree and the quanti7er guided non dominance degree are de7ned for multiplicative preference relations c 2001 elsevier science b v all rights reserved

a nonlinear model of population dynamics containing an arbitrary number of continuous structure variables a nonlinear model is presented for the dynamics of a population in which each individual is characterized by its chronological age and by an arbitrary finite number of additional structure variables the nonlinearities are introduced by assuming that the birth and loss processes as well as the maturation rates of individuals are controlled by a functional of the population density the model is a generalization of the classical sharpe lotka mckendrick model of age structured population growth the nonlinear age structured model of gurtin and maccamy and the age size structured cell population model of bell and anderson based on a reformulation of the model in terms of a coupled system of equations the existence for all positive time of unique solutions to the model is proved using a contraction mapping argument the existence of equilibrium solutions is discussed and sufficient conditions are proved for the local asymptotic stability of equilibria using results from the theory of strongly continuous

euler s discretization of single input sliding mode control systems in this note the dynamical behaviors of euler s discretization of the equivalent control based sliding mode control smc systems are studied we show that if the discretized smc system is asymptotically stable then every trajectory converges to a period 2 cycle bounds for the steady states are derived which allow one to estimate the maximum chattering amplitude for a given value of the time step the analysis and results are verified with several computer simulations

improving minimax disparity model to determine the owa operator weights determining the ordered weighted averaging owa operator weights is important in decision making applications several approaches have been proposed in the literature to obtain the associated weights this paper provides an alternative disparity model to identify the owa operator weights the proposed mathematical model extends the existing disparity approaches by minimizing the sum of the deviation between two distinct owa weights the proposed disparity model can be used for a preference ranking aggregation a numerical example in preference ranking and an application in search engines prove the usefulness of the generated owa weights

stability results for a size structured population model with resources dependence and inflow it is undoubted that the survival of individuals of populations is dependent on resources e g foods we formulate a system of integro differential equations to model the dynamics of a size structured and resources dependent population a kind of inflow of newborn individuals from external environment is considered the resource dependence is incorporated through the size growth mortality fertility and feeding rates of the target population the existence of the stationary size distributions are discussed and the linear stability is investigated by means of the semigroup theory and the characteristic equation technique some sufficient conditions for stability instability of stationary states are obtained and two examples and the corresponding simulations are presented

analysis of delayed sliding mode control systems under zero order holder discretization zero order holder discretization effects in sliding mode control systems with an input delay are studied stability conditions are formulated conditions for the existence of periodic solutions are derived and the existence of periodic steady states is investigated the influence of the discretization step and the delay on the period and the amplitude of steady state oscillations is discussed structure of basins of attraction of periodic orbits with different switching patterns is studied simulation results are presented to illustrate various behaviors

on the qualitative behaviour of populations with age specific interactions abstract a mathematical model describing the age dependent dynamics of a population is studied under very general assumptions existence of nonzero equilibrium solutions is proven for some special kind of rate law it is shown that this model can asymptotically be described by means of a simpler system of ordinary differential equations an example is given where the model admits nonconstant time periodic solutions

pde model of cell cycle dynamics and clustering in yeast abstract autonomous oscillation and cell cycle clustering in yeast cultures has attracted great interest recently and responsive signaling feedback models have been proposed to explain this phenomenon here we apply a nonlinear physiologically structured partial differential equation model of the cell population to describe clustering in yeast cultures the existence and uniqueness of the solutions and the linear stability of the stationary state are discussed some results regarding clustering are proven where the solutions of the partial differential equation converge to traveling delta measures

an averaging approach to chattering the singularly perturbed relay control systems sprcs as mathematical models of chattering in the small neighborhood of the switching surface in sliding mode systems are examined sufficient conditions for existence and stability of fast periodic solutions to the sprcs are found it is shown that the slow motions in such sprcs are approximately described by equations derived from equations for the slow variables of sprcs by averaging along fast periodic motions it is shown that in the general case when the equations of a plant contain relay control nonlinearly the averaged equations do not coincide with the equivalent control equations or with the filippov s definition 1988 for the sliding motions in the reduced system however in the linear case they coincide

stability of a nonlinear age dependent population model containing a control variable a very general nonlinear model of age dependent population growth which includes most of earlier presented extensions of the lotka von foerster model is considered a criterion for local asymptotic stability of equilibrium solutions of the model is given the conclusions of this paper are compared with analogous results for some important special cases considered by other authors

eigenvalue asymptotics in isothermal forced elongation in this paper we consider the formal linearization of the governing equations of forced elongation in the isothermal regime we give an asymptotic characterization of the spectrum of the associated strongly continuous semigroup to this end we develop rigorous asymptotic techniques to determine the asymptotic behavior of the eigenvalues by solving a characteristic integral equation in a generalized sector of the complex plane the spectral mapping theorem relating the spectrum of the semigroup to the spectrum of its generator proves essential numerical evidence will be given to demonstrate the accuracy of our asymptotic predictions

brief tracking in a class of nonminimum phase systems with nonlinear internal dynamics via sliding mode control using method of system center a method of asymptotic output tracking in a class of causal nonminimum phase uncertain nonlinear systems is considered local asymptotic stability of output tracking error dynamics are provided for the specified class of systems with the nonlinear hyperbolic at the origin internal dynamics forced by a reference output profile and external disturbances defined by a known linear exosystem the nonlinear vector field of the internal dynamics is expanded in a power series obtained at a selected operational point in the internal dynamics state space the presented technique employs some linear algebraic methods and sliding mode control approach the solution is a complete constructive algorithm

stability and instability of equilibria of an equation of size structured population dynamics in this paper we consider a quasilinear equation with a nonlinear boundary condition modelling the dynamics of a biological population structured by size we suppose vital rates depending on the total population this hypothesis introduces some nonlinearities on the equation and on the boundary condition we study the existence and uniqueness of solution of the initial value problem and the existence of stationary solutions after we calculate the spectrum of the linearization at an equilibrium and we study its local stability

deviation square priority method for distinct preference structures based on generalized multiplicative consistency preference structures such as fuzzy preference relations incomplete fuzzy preference relations utility values and preference orderings are very useful in depicting the decision makers preferences over the considered objects in group decision making they have been attracting great interest from both researchers and practitioners in recent decades an important issue on these preference structures is to investigate the techniques of deriving priority weights of the objects from them in this paper based on generalized multiplicative consistency we establish a general nonlinear optimization model with fuzzy preference relations incomplete fuzzy preference relations utility values and preference orderings by solving the model we get a system of nonlinear equations and prove the uniqueness of its solution then a convergent iterative algorithm is devised to derive the priority weights from this system of equations the model and the algorithm include a variety of special cases suitable for group decision making with one or several of the aforementioned preference structures a practical case illustration concerning a manufacturing company that is searching for the best compression ignition engine design is provided and the numerical results of the developed models and the algorithm and the existing ones are also compared and analyzed in order to demonstrate the advantages and practicality of our models and algorithm

small scale instabilities in dynamical systems with sliding we demonstrate with a minimal example that in filippov systems dynamical systems governed by discontinuous but piecewise smooth vector fields stable periodic motion with sliding is not robust with respect to stable singular perturbations we consider a simple dynamical system that we assume to be a quasi static approximation of a higher dimensional system containing a fast stable subsystem we tune a system parameter such that a stable periodic orbit of the simple system touches the discontinuity surface this is the so called grazing sliding bifurcation the periodic orbit remains stable and its local return map becomes piecewise linear however when we take into account the fast dynamics the local return map of the periodic orbit changes qualitatively giving rise to for example period adding cascades or small scale chaos

eigenvalue asymptotics in non isothermal elongational flow abstract we shall furnish an asymptotic description of the spectrum of a c0 semigroup generator arising in non isothermal elongational flow it will be shown that the spectrum coincides asymptotically with isolated eigenvalues lined up along a logarithmic curve the strategy for this result is based on delicate asymptotic estimates and ideas developed for the isothermal regime these estimates can be successfully employed only since the spectral mapping theorem is valid for the semigroup

fast switches in relay feedback systems relays are common in automatic control systems even linear systems with relay feedback are however far from fully understood new results are given about the behavior of these systems via a state space approach it is proved that there exist multiple fast switches if and only if the sign of the first nonvanishing markov parameter of the linear system is positive fast switches are shown to occur as part of stable limit cycles an analysis is developed for these limit cycles that illustrates how they can be predicted

on the stability of stationary age distributions age structured nonlinear single species and predator prey population models are treated and a straightforward relatively simple method is shown to arrive at a condition of stability of stationary solutions