a convergence theorem for arrays of l r fuzzy numbers the purpose of this paper is to provide a general law of large numbers for arrays of l r fuzzy numbers

t norm based addition of fuzzy intervals abstract the aim of this paper is to provide new results regarding the effective practical computation of t norm based additions of lr fuzzy intervals

shape preserving additions of fuzzy intervals abstract triangular norm based additions preserving the lr shape of lr fuzzy intervals are studied the connection between t norm based additions preserving the linearity of fuzzy intervals and additions preserving lr shape for invertible shapes l and r is given a possibility of controlling the growth of the spread during the calculations with lr fuzzy intervals is shown

a space time fractional phase field model with tunable sharpness and decay behavior and its efficient numerical simulation abstract we present a space time fractional allen cahn phase field model that describes the transport of the fluid mixture of two immiscible fluid phases the space and time fractional order parameters control the sharpness and the decay behavior of the interface via a seamless transition of the parameters although they are shown to provide more accurate description of anomalous diffusion processes and sharper interfaces than traditional integer order phase field models do fractional models yield numerical methods with dense stiffness matrices consequently the resulting numerical schemes have significantly increased computational work and memory requirement we develop a lossless fast numerical method for the accurate and efficient numerical simulation of the space time fractional phase field model numerical experiments shows the utility of the fractional phase field model and the corresponding fast numerical method

on the compositional rule of inference under triangular norms abstract the aim of this paper is to provide a close upper bound of the membership function for the compositional rule of inference under archimedean t norm where both the observation and the relation parts are given by hellendoorn s function 1980 in particular if the left and right spreads of the observation part is the same as those of the relation part then this upper bound is the exact membership function which generalizes the earlier result by fuller and zimmermann 1982 in that assumption of twice differentiability is deleted

on product sum of triangular fuzzy numbers abstract we study the problem if a i i n are fuzzy numbers of triangular form then what is the membership function of the infinite or finite sum a 1 a 2 defined via the sup product norm convolution

a new method for stability analysis of nonlinear discrete time systems we address the problem of global lyapunov stability of discrete time systems with known coefficients we develop a method for reduction of dissipativity domain effectively testing if the system has a convex lyapunov function our implementation is immediately applicable to differentiable systems with bounded nonlinearities but the method proposed is more general and applicable to nondifferentiable systems with bounded right hand sides our main application emphasis is on stability analysis of recurrent neural networks we illustrate how to use our approach with examples

on the convergence of t sum of l r fuzzy numbers abstract this paper presents the membership function of infinite or finite sum defined by the sup t norm convolution of l r fuzzy numbers under the conditions of the convexity of additive generators and the concavity of l r as an application we shall calculate the membership function of the limit distribution of the hamacher sum hr sum for 0 r 2 which generalizes fuller s results fuzzy sets and systems 41 1991 83 87 42 1991 205 212 in the case r 0 1 2

a t sum bound of lr fuzzy numbers abstract in this paper we provide an upper bound and a lower bound of t sum of lr fuzzy numbers with different spreads where t is archimedean t norm and also show in three examples how close they are to actual membership functions furthermore we study when the membership function of t sum achieves the upper bound

on computation of the compositional rule of inference under triangular norms abstract this paper is devoted to the derivation of exact calculation formulas for the compositional rule of inference under archimedean t norms when both the observation and the relation parts are given by hellendoorn s function 6

sufficient conditions for stabilization of sampled data nonlinear systems via discrete time approximations given a parameterized by sampling period t family of approximate discrete time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all t sufficiently small we present conditions which guarantee that the same family of controllers semi globally practically stabilizes the exact discrete time model of the plant for sufficiently small sampling periods when the family of controllers is locally bounded uniformly in the sampling period the inter sample behavior can also be uniformly bounded so that the time varying sampled data model of the plant is uniformly semi globally practically stabilized the result justifies controller design for sampled data nonlinear systems based on the approximate discrete time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied our analysis is applicable to a wide range of time discretization schemes and general plant models

lyapunov functions stability and input to state stability subtleties for discrete time discontinuous systems in this note we consider stability analysis of discrete time discontinuous systems using lyapunov functions we demonstrate via simple examples that the classical second method of lyapunov is precarious for discrete time discontinuous dynamics also we indicate that a particular type of lyapunov condition slightly stronger than the classical one is required to establish stability of discrete time discontinuous systems furthermore we examine the robustness of the stability property when it was attained via a discontinuous lyapunov function which is often the case for discrete time hybrid systems in contrast to existing results based on smooth lyapunov functions we develop several input to state stability tests that explicitly employ an available discontinuous lyapunov function

on the convergence of product sum series of l r fuzzy numbers we study series a1 a2 an of l r fuzzy numbers where addition is defined via the sup product norm convulation and obtain some convergence theorems which generalize earlier results by fuller cf 2

a note to the t sum of l r fuzzy numbers abstract we generalize the results of hong and hwang 1994 for the membership function of finite infinite sum of l r fuzzy numbers where the sum is based on some continuous archimedean t norm t

characterisation of archimedian t norms and a law of large numbers abstract we study a law of large numbers for mutually t related fuzzy numbers where t is an archimedian t norm and extend earlier results of fuller in this area in particular we show that the class of archimedian t norms can be characterised by the validity of a very general law of large numbers for sequences of l r fuzzy numbers

a note on product sum of l r fuzzy numbers abstract triesch 1993 provided a partial answer to fuller s 1991 question about the membership function of the finite sum defined via the sup product norm convolution of l r fuzzy numbers in this short note we prove the other half

smooth lyapunov functions and robustness of stability for difference inclusions we demonstrate the equivalence of robust global asymptotic stability gas of the origin and the existence of a smooth lyapunov function for difference inclusions defined by upper semicontinuous set valued maps sufficient conditions for robust gas are given as an application of these results we give conditions for robust gas of difference equations defined by discontinuous right hand sides

forward and converse lyapunov theorems for discrete dynamical systems this technical note addresses the stability analysis of nonlinear dynamic systems three main contributions are made first we show that the standard assumption of a continuous lyapunov function can be and in some cases must be relaxed we introduce the concept of the weak lyapunov function which requires that an annulus condition be satisfied we believe that this annulus condition is a more natural construct because it is precisely what is needed to make the forward lyapunov theorem true second we provide an example of a nonlinear system with stable equilibrium point that cannot be shown to be stable with a continuous lyapunov function finally we demonstrate a simpler and less restrictive proof of the converse lyapunov theorem

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

a law of large numbers for fuzzy numbers in a banach space abstract we study a law of large numbers for mutually t related fuzzy number in a banach space where t is an archimedean t norm and extend earlier results of fuller and triesch in this area