characterization and optimization of l_ infty gains of linear switched systems in this paper we consider the l infty gain characterizations of linear switched systems lss and present various relevant results on their exact computation and optimization depending on the role of the switching sequence we study two broad cases first when the switching sequence attempts to maximize and second when it attempts to minimize the l infty gain the first named as worst case throughout the paper can be related to robustness of the system to uncontrolled switching the second relates to situations when the switching can be part to the overall decision making although in general the exact computation of l infty gains is difficult we provide specific classes the input output switching systems for which it is shown that linear programming can be used to obtain the worst case l infty gain this is a sufficiently rich class of systems as any stable lss can be approximated by one certain applications to robust control design are provided where we show that a switched compensation independently of the plant has no advantage over a linear time invariant lti compensation and further if the plant is strictly causal even a switched compensation which has a matched switching with the plant does not provide a better performance over an lti compensation also we present a new necessary and sufficient condition to check the stability of lss in form of a model matching problem on the other hand if one is interested in minimizing the l infty gain over the switching sequences we show that for finite impulse response fir switching systems the minimizing switching sequence can be chosen to be periodic for input only or output only switching an exact readily computable characterization of the minimal l infty gain is provided and it is shown that the minimizing switching sequence is constant which as also shown is not true for input output switching

fuzzy n cell numbers and the differential of fuzzy n cell number value mappings in this paper we give the definition of a special kind of n dimension fuzzy numbers fuzzy n cell numbers discuss their operations and representation theorems define a complete metric on the fuzzy n cell number space and prove that the metric is equivalent to the supremum metric derived by the hausdorff metric between the level sets of the n dimension fuzzy numbers and obtain an embedding theorem of the fuzzy n cell number space isometrically embeds it into a concrete banach space we also consider the differential of the fuzzy mappings from an interval into the fuzzy n cell number space by using the embedding theorem

attractors and asymptotic stability for fuzzy dynamical systems abstract in this work we study the asymptotic properties of maps on fuzzy spaces which are extensions of maps on the main results are in section 4 see theorem 21 and we give an illustrative example in the last section

a strong consistency result for fuzzy relative frequencies interpreted as estimator for the fuzzy valued probability the unavoidable imprecision of measurements of continuous physical quantities can be modelled by using the concept of fuzzy numbers and fuzzy vectors concerning a quantitative usage of such data the classical concept of relative frequencies for real data has to be extended to so called fuzzy relative frequencies for fuzzy data whereby the fuzzy relative frequency of a set is a fuzzy number analogous to a dempster s interval valued probabilities induced by multi valued mappings fuzzy valued probabilities induced by fuzzy random vectors are considered and analyzed it is proved that fuzzy relative frequencies can be interpreted as strongly consistent estimator for the corresponding fuzzy valued probability

time varying versus time invariant compensation for rejection of persistent bounded disturbances and robust stabilization it is shown that time varying compensation does not improve the optimal rejection of persistent bounded disturbances this result is obtained by exploiting a key observation that any time varying compensator which yields a given degree of disturbance rejection must do so uniformly over time thereby removing any advantage of time variation this key observation is exploited to show that time varying compensation does not improve the optimal rejection of disturbances regardless of the norm used to measure the disturbances thus absolutely summable finite energy or persistent bounded disturbances may be treated in the same manner it is shown that time varying compensation does not help in the bounded input bounded output robust stabilization of time invariant plants with unstructured uncertainty in doing so it is also shown that the small gain theorem is both necessary and sufficient for the bounded input bounded output stability of certain linear time varying plants subject to unstructured linear time varying perturbations

hamiltonian connectivity of the wk recursive network with faulty nodes a graph g is said to be hamiltonian connected if there is a hamiltonian path between every two distinct nodes of g let f denote the set of faulty nodes of g then g is f node hamiltonian connected if g f is hamiltonian connected we use k d t to denote a wk recursive network of level t each of whose basic modules is a d node complete graph compared with other networks it is rather difficult to construct a hamiltonian path between two arbitrary nodes in a faulty wk recursive network in this paper we show that k d t is d 4 node hamiltonian connected since the connectivity of k d t is d 1 the result is optimal in the worst case

the s differentiability of a fuzzy valued mapping several approaches to define the differential of fuzzy valued mappings can be found in the literature in this paper we introduce a new concept of differential of a fuzzy valued mapping which is based on the notion of differential of the support function associated with such a mapping properties of the new concept as well as the relation between it and previous approaches are also analyzed in detail

longest fault free paths in star graphs with vertex faults the star graph sn has been recognized as an attractive alternative to the hypercube since s1 s2 and s3 have trivial structures we focus our attention on sn with n 4 in this paper let fv denote the set of faulty vertices in sn we show that when fv n 5 sn with n 6 contains a fault free path of length n 2 fv 2 n 2 fv 1 between arbitrary two vertices of even odd distance since sn is bipartite with two partite sets of equal size the path is longest for the worst case scenario the situation of n 4 and fv n 5 is also discussed

radon nikodym theorem and vitali hahn saks theorem on fuzzy number measures in banach spacers abstract radon nikodym theorem is established on fuzzy number measures in banach spaces vitali hahn saks theorem is generalized to set valued measures and fuzzy number measures

estimation of a fuzzy regression model using fuzzy distances regression analysis is a powerful statistical tool that has many applications in different areas the problem of regression analysis under a fuzzy environment has been treated in the literature from different points of view and considering a variety of input output data crisp or fuzzy however we realize that in general most research papers have a conflict between the solution of the fuzzy regression problem using crisp distances minimizing a real error function and the interpretation of fuzzy data as possibility distributions the main aim of this paper is to develop a methodology to solve this problem introducing a fuzzy partial order and a family of fuzzy distance measures on the whole set of fuzzy numbers the new approach allows us to obtain linear and nonlinear models that reach the lowest fuzzy error the estimation process in general can be considered easier to apply in practice and it is not limited to triangular fuzzy numbers numerical examples are provided to illustrate the usefulness and applicability of these results and comparisons with existing methodologies show that the performance of the proposed solution is very satisfactory

hyper hamiltonian laceability on edge fault star graph the star graph possess many nice topological properties edge fault tolerance is an important issue for a network since the edges in the network may fail sometimes in this paper we show that the n dimensional star graph is n 3 edge fault tolerant hamiltonian laceable n 3 edge fault tolerant strongly hamiltonian laceable and n 4 edge fault tolerant hyper hamiltonian laceable all these results are optimal in a sense described in this paper

uncertain alternating renewal process and its application uncertain process is a sequence of uncertain variables indexed by time and space first this paper presents a kind of uncertain process known as the uncertain alternating renewal process whose alternating interarrival times are uncertain variables then it proves an uncertain alternating renewal theorem on the limit value of average working rate finally an application of the alternating renewal theorem is discussed

the 3 connected property of pyramid networks a k containerc u v of a graph g is a set of k disjoint paths joining u to v a k container c u v of g is a k container if it contains all the vertices of g a graph g is k connected if there exists a k container between any two distinct vertices in g let k g be the connectivity of g a graph g is superconnected if g is i connected for all email protected email protected email protected g the pyramid network is one of the important networks applied in parallel and distributed computer systems the connectivity of a pyramid network is three in this paper we prove that the pyramid network pm n is 3 connected and superconnected for n 1

fuzzy random renewal reward process and its applications this paper studies a renewal reward process with fuzzy random interarrival times and rewards under the independence associated with any continuous archimedean t norm the interarrival times and rewards of the renewal reward process are assumed to be positive fuzzy random variables whose fuzzy realizations are independent fuzzy variables under these conditions some limit theorems in mean chance measure are derived for fuzzy random renewal rewards in the sequel a fuzzy random renewal reward theorem is proved for the long run expected reward per unit time of the renewal reward process the renewal reward theorem obtained in this paper can degenerate to that of stochastic renewal theory finally some application examples are provided to illustrate the utility of the result

properties of a hierarchical network based on the star graph this paper introduces a new class of interconnection networks named star pyramid an n level star pyramid is formed by piling up star graphs of dimensions 1 to n in a hierarchy connecting any node in each i dimensional star 1

performance optimization over positive l cones abstract in this paper we study linear systems with positivity type of constraints first we consider the case where the input to a system is restricted to be in the positive cone of l denoted by l and seek to characterize the system s induced norm from l to l we obtain an exact characterization of this norm which is particularly easy to calculate in the case of lti systems furthermore we consider and solve the model matching problem and show that time varying linear or nonlinear control filtering does not improve the performance with respect to this norm for lti systems in the second part of the paper we consider the case when the output is forced to be in the positive l cone when the input is in this cone we show if internal positivity is sought a dynamic optimal controller offers no advantage over a static one also if the measurement matrix satisfies certain conditions synthesizing an optimal static output feedback controller reduces to a linear program

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

proof that pyramid networks are 1 hamiltonian connected with high probability wu revealed in 2001 that pyramid networks are hamiltonian connected this investigation demonstrates that a pyramid network with one faulty node or one faulty edge is hamiltonian connected excluding some special faulty cases by building a hamiltonian path between any two distinct nodes in it although a pyramid network with one fault is not hamiltonian connected this study indicates that a pyramid network is 1 hamiltonian connected with a very high probability

existence and uniqueness for solutions to fuzzy stochastic differential equations driven by local martingales under the non lipschitzian condition abstract this paper makes a research into a class of fuzzy stochastic differential equations fsdes driven by a continuous local martingale under the non lipschitzian condition such equations can be useful in modelling of hybrid systems where the phenomena are subjected to two kinds of uncertainties randomness and fuzziness simultaneously the solutions of fsdes are the fuzzy stochastic processes and their uniqueness is considered to be in a strong sense thus the existence and uniqueness of solutions to fsdes under the non lipschitzian condition is first proven and the continuity of solutions to fsdes with respect to the initial data or the coefficients of the equations is investigated

analysis of time varying control strategies for optimal disturbance rejection and robustness analysis of linear time invariant systems that are controlled by time varying controllers is given the problems of disturbance rejection and robustness are formulated and analyzed using functional analytic methods which reveal the properties that are common to these problems the theoretical development presented uses the theory and techniques of nuclear operators and their relation with the duality theory of tensor products of banach spaces the authors show how time varying compensation offers no advantage over time invariant compensation for the problem of disturbance rejection over general signal spaces in both continuous and discrete time and for the problem of l sub infinity robust stabilization of time invariant plants in addition another application of the theory for the problem of norm minimization subject to a norm constraint is presented

the l average value and the fuzzy expectation of a fuzzy random variable abstract the concepts of fuzzy random variable and the associated fuzzy expected value have been introduced by puri and ralescu as an extension of measurable set valued functions random sets and of the aumann integral of these functions respectively on the other hand the average function has been suggested by campos and gonzalez as an appropriate function to rank fuzzy numbers in this paper we are going to analyze some useful properties concerning the average value of the expectation of a fuzzy random variable and some practical implications of these properties are also commented on

output feedback control of markov jump linear systems in continuous time this paper addresses the dynamic output feedback control problem of continuous time markovian jump linear systems the fundamental point in the analysis is an lmi characterization comprising all dynamical compensators that stabilize the closed loop system in the mean square sense the h sub 2 and h sub spl infin norm control problems are studied and the h sub 2 and h sub spl infin filtering problems are solved as a by product

notes on fuzzy complex analysis several fuzzy complex analysis problems are discussed pointing out some errors in literature and some weaknesses of introduced concepts a modified approach to fuzzy complex analysis is proposed and its impact is discussed

root mean square gains of switched linear systems in this note we compute the root mean square rms gain of a switched linear system when the interval between consecutive switchings is large the algorithm proposed is based on the fact that a given constant spl gamma provides an upper bound on the rms gain whenever there is a separation between the stabilizing and the antistabilizing solutions to a set of spl gamma dependent algebraic riccati equations the motivation for this problem is the application of robust stability tools to the analysis of hybrid systems

the theoretical fundamentals of learning theory based on fuzzy complex random samples statistical learning theory based on real valued random samples has been regarded as one of the influential developments for small samples statistical estimation and learning the key theorem of learning theory and the bounds on the rate of convergence of learning process are the most important theoretical fundamentals of the statistical learning theory in this paper we discuss a statistical learning theory based on fuzzy complex random samples firstly the definition of fuzzy complex numbers is introduced and the fuzzy complex random variables along with their numeric characteristic are investigated secondly we carry out further research focused on a special type of fuzzy complex number namely rectangular fuzzy complex number and establish some properties and develop important theorems we also prove the strong law of large numbers based on fuzzy complex random variables thirdly the definitions of the fuzzy complex expected risk functional the fuzzy complex empirical risk functional the fuzzy complex empirical risk minimization principle and the consistency are provided and discussed finally the key theorem of learning theory and the bounds on the rate of convergence of learning process based on fuzzy complex random samples are discussed

set valued choquet integrals revisited this paper performs a further investigation on the set valued choquet integral given by jang and kwon fuzzy sets and systems 112 2000 233 some incorrect properties are revised it is pointed out that the definition for convergence of sequence of sets or set valued functions is unreasonable by using the usual kuratowski s convergence some new convergence theorems for the set valued choquet integral are shown meanwhile some other properties are obtained

optimal path cover problem on block graphs abstract let g v e be a block graph first we show that an algorithm for finding the path partition number p g by j h yan and g j chang gives wrong answers to some block graphs then we present an efficient algorithm for finding a minimum path partition of g not just the path partition number p g the complexity of this algorithm is o m where m e

on embedding cycles into faulty twisted cubes the twisted cube tq n is an alternative to the popular hypercube network recently some interesting properties of tq n were investigated in this paper we study the pancycle problem on faulty twisted cubes let f e and f v be the numbers of faulty edges and faulty vertices in tq n respectively we show that with f e f v 3

necessary and sufficient conditions for asymptotic model matching of switching linear systems this paper investigates the problem of designing a feedback controller to force the response of a given plant to match asymptotically that of a prescribed model in case both the plant and the model are switching linear systems matching has to be achieved with stability of the feedback loop for any initial conditions of the plant the model and the controller in case it is dynamic and for any choice of the switching law solvability of the problem is characterized in terms of necessary and sufficient conditions that in part refer to the geometric structure of the difference system which compares the output of the model and of the plant stability is considered both for slow switching and for arbitrary switching proofs of the solvability conditions provide viable procedures for synthesizing the static or dynamic controllers that achieve the matching respectively when the state of the model is measurable and when it is not weaker sufficient conditions that can be practically checked by simple algorithmic procedures are provided both in the general situation and under slightly restrictive hypotheses

on the restudy of fuzzy complex analysis part 1 the sequence and series of fuzzy complex numbers and their convergences this paper studies the convergence of the sequence and series of fuzzy complex numbers we define the metric convergence and levelwise convergence of sequences on the metric space of fuzzy complex numbers and discuss the relationship between two convergences all this may be a foundation for researching fuzzy complex analysis

fuzzy complex analysis ii integration abstract this paper continues the author s research in fuzzy complex analysis where we now define and study the basic properties of a fuzzy contour integral for fuzzy mappings which map a rectifiable curve in the complex plane into fuzzy complex numbers

algebraic properties and topological properties of the quotient space of fuzzy numbers based on mares equivalence relation abstract in this paper we obtain some algebraic properties and topological properties of the quotient space of fuzzy numbers with respect to the equivalence relation defined by mares every fuzzy number has only one mares core and equivalent fuzzy numbers have the same mares core in addition equivalence classes of fuzzy numbers can be only expressed as the sum of its mares core and the set of symmetric fuzzy numbers which shows the notable difference between the equivalence classes of fuzzy numbers and the cosets of the normal subgroup in a group based on these results we introduce a new concept of convergence under which the quotient space is complete as an application of the main results it is shown that if we identify every fuzzy number with the corresponding equivalence class there would be more differentiable fuzzy functions than what is found in the literature

almost periodic solutions of fuzzy systems we prove the existence of almost periodic solutions and asymptotically almost periodic solutions for the fuzzy functional differential equations moreover we consider uniform stable and uniformly asymptotically stable of almost periodic solutions for the fuzzy system

on the restudy of fuzzy complex analysis part ii the continuity and differentiation of fuzzy complex functions we consider functions mapping complex numbers into fuzzy complex numbers or mapping fuzzy complex numbers into complex numbers we study the continuity and differentiation of such functions

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

on the k path partition of graphs the k path partition problem is to partition a graph into the minimum number of paths so that none of them has length more than k for a given positive integer k the problem is a generalization of the hamiltonian path problem and the problem of partitioning a graph into the minimum number of paths the k path partition problem remains np complete on the class of chordal bipartite graphs if k is part of the input and we show that it is np complete on the class of comparability graphs even for k 3 on the positive side we present a polynomial time solution for the problem with any k on bipartite permutation graphs which form a subclass of chordal bipartite graphs

longest fault free paths in star graphs with edge faults in this paper we aim to embed longest fault free paths in an n dimensional star graph with edge faults when n spl ges 6 and there are n 3 edge faults a longest fault free path can be embedded between two arbitrary distinct vertices exclusive of two exceptions in which at most two vertices are excluded since the star graph is regular of degree n 1 n 3 edge faults is maximal in the worst case when n spl ges 6 and there are n 4 edge faults a longest fault free path can be embedded between two arbitrary distinct vertices the situation of n 6 is also discussed

strong law of large numbers for t normed arithmetics we prove a strong law of large numbers for sequences of pairwise i i d fuzzy random variables addition is given by the extension principle associated with a general continuous triangular norm our result includes the slln for levelwise sums obtained when the chosen triangular norm is the minimum

on the convergence of fuzzy sets three kind of convergences are defined on a space of fuzzy sets relationships between these convergences are studied some comments on the fixed point property are represented

some new topological properties of the triangular pyramid networks abstract the triangular pyramid proposed by razavi and sarbazi azad the triangular pyramid routing and topological properties information sciences 180 2010 2328 2339 is a hierarchical structure based on triangular meshes in this paper we show that the triangular pyramid shares some nice symmetry properties of the pyramid we also determine the connectivity of the triangular pyramid and prove that it is 1 fault tolerant vertex pancyclic

uniform stabilization of discrete time switched and markovian jump linear systems the uniform stability of discrete time switched linear systems possibly with a strongly connected switching path constraint and the existence of finite path dependent dynamic output feedback controllers uniformly stabilizing such a system are both shown to be characterized by the existence of a finite dimensional feasible system of linear matrix inequalities this characterization is based on the observation that a linear time varying system is uniformly stable only if there exists a finite path dependent quadratic lyapunov function the synthesis of a uniformly stabilizing controller is done without conservatism by solving any feasible system of linear matrix inequalities among an increasing family of systems of linear matrix inequalities the result carries over to the almost sure uniform stabilization of markovian jump linear systems

optimal disturbance attenuation for discrete time switched and markovian jump linear systems an exact condition for uniform stabilization and disturbance attenuation for switched linear systems is given in the discrete time domain via the union of an increasing family of linear matrix inequality conditions associated with each markovian jump linear system is a switched linear system so we obtain a necessary and sufficient condition for almost sure uniform stabilization and disturbance attenuation for markovian jump linear systems as well the results lead to semidefinite programming based controller synthesis techniques from which optimal finite path dependent linear dynamic output feedback controllers arise naturally in particular under the notion of path by path optimal disturbance attenuation finite path dependent controllers can outperform the usual mode dependent ones

periodic boundary value problems for impulsive fuzzy differential equations the peculiarity of the hukuhara derivative makes it impossible to find periodic solutions for fuzzy differential equations with the exception of very restrictive situations in this work we consider a boundary value problem associated with an impulsive fuzzy differential equation and approximate the extremal solutions in a fuzzy functional interval using the monotone method fuzzy comparison results are useful in our procedure and the expression of the solution for some impulsive periodic linear differential problems is also provided

the intersection operation in light of joint observables and bell inequalities in operational probability theory operational probability theory appears as a smooth extension of classical probability theory that fulfills quantum physics needs in this paper we first explain the need to extend the concept of the intersection operation in the light of the concept of joint observables then we tried to determine the basic features that characterize any possible definition of the intersection operation furthermore we tried to know if there is a relation between the definitions of the intersection operation of both fuzzy and operational probability theories these relations are used first to find a suitable suggestion to define the intersection operation second they are used besides the studies made on bell inequalities in fuzzy probability theory to find the conditions that should be satisfied by the intersection operation to ensure the possibility of the violation of bell inequalities in operational probability theory

fuzzy complex numbers abstract this paper first defines fuzzy complex numbers and shows closure under the basic arithmetic operations it is shown that arithmetic of fuzzy complex numbers may be performed in terms of cuts next two special types of fuzzy complex numbers based on the forms z x iy and z re i for regular complex numbers are investigated introducing a metric on the space of fuzzy complex numbers then allows us to discuss continuity and differentiability of fuzzy complex functions

b fuzzy probabilities abstract we treat b fuzzy probabilities in nonstandard frameworks by the methods based on boolean valued models and especially boolean powers these formal methods apart from the difficulties associated with the formal model itself give a simple and powerful theory for fuzzy probability spaces and fuzzy random variables essentially everything is reduced to a transfer principle however one can also work using classical methods of proofs we first give the necessary background on nonstandard frameworks within these frameworks we develop boolean fuzzy probabilities and fuzzy random variables

performance optimization of switched systems a model matching approach in this paper we consider a prototypical model matching problem where the various mappings involved are systems that switch arbitrarily among n stable linear time invariant lti systems the interest is placed on optimizing the worst case performance of this model matching system over all possible switchings with either l infin induced norm or h 2 norm as the performance criterion this optimization is performed over all youla kucera parameters that switch causally in time among n stable lti systems for the particular setup at hand it is shown that the optimal youla kucera parameter need not depend on the switching trajectory in the cases of partially matched switching and unmatched switching and that it can be obtained as an lti solution to an associated standard l 1 or h 2 optimization in the case of matched switching two convergent sequences to the optimal solution from above and below are formulated in terms of linear programs and quadratic programs respectively for the l infin induced and h 2 norm optimizations an approximate solution with any given precision is possible by finite truncation applications of these results to sensitivity minimization linear switched parameter systems and cooperative control are provided

fuzziness and randomness in an optimization framework abstract a semi infinite approach for linear programming in the presence of fuzzy random variable coefficients is described as a byproduct a way for dealing with optimization problems including both fuzzy and random data is obtained numerical examples are provided for the sake of illustration

the spanning laceability on the faulty bipartite hypercube like networks a w container c u v of a graph g is a set of w disjoint paths joining u to v a w container of g is a w container if it contains all the nodes of v g a bipartite graph g is w laceable if there exists a w container between any two nodes from different parts of g let n and k be any two positive integers with n 2 and k

fuzzy complex numbers representations operations and its analysis abstract as a key theoretical basis of fuzzy complex analysis a new representation of fuzzy complex numbers is proposed in this paper which unifies the exponential form trigonometric form and algebraic form of fuzzy complex numbers and some arithmetic operations are investigated the concepts of strong sum and strong difference are defined in order to simplify the addition and subtraction operations of complex fuzzy numbers and establish the calculus theory of fuzzy complex valued functions the metric between two fuzzy complex numbers the derivative differentiability and analyticity of fuzzy complex valued functions are defined and characterized the necessary and sufficient conditions of the analyticity of fuzzy complex valued functions are investigated furthermore the integral of fuzzy complex valued functions and cauchy integral theorem are given and discussed

linear programming with fuzzy random variable coefficients abstract linear programming with fuzzy random variable coefficients is introduced by discussing a practical engineering problem in order to study the solution of the linear programming with fuzzy random variable coefficients we discuss the simplex algorithm for linear programming with random variable coefficients furthermore the solution and distribution problem of this new fuzzy random programming are studied

a note on two point boundary value problems associated with non linear fuzzy differential equations in recent papers lakshmikantham et al and o regan et al assert that two point boundary value problem for a fuzzy differential equation is equivalent to an integral equation and the proofs of the main results in the above cited papers use this equivalence we prove by a counterexample that by using h differentiability or hukuhara differentiability this assertion does not hold moreover it is proved that a large class of two point boundary value problems have no solutions at all under h differentiability or hukuhara differentiability

notes on on the restudy of fuzzy complex analysis part i and part ii in this note we show by counterexamples that some results of qiu and colleagues on the restudy of fuzzy complex analysis part i the sequence and series of fuzzy complex numbers and their convergences fuzzy sets and systems 115 2000 445 450 on the restudy of fuzzy complex analysis part ii the continuity and differentiation of fuzzy complex functions fuzzy sets and systems 120 2001 517 521 concerning the convergence of the series of fuzzy complex numbers and the differentiation of fuzzy complex functions are incorrect and offer some of their modified versions we also show that the derivative introduced by them is inappropriate for the functions mapping complex numbers into fuzzy complex numbers

compatibility between fuzzy set operations and level set operations applications to fuzzy difference abstract three types of binary operation between any two fuzzy sets are proposed in this paper the concept of 0 level set of fuzzy set plays an important role for defining the binary operations between two fuzzy sets according to the decomposition theorem of fuzzy sets the consistency between the membership functions and level sets should be rigorously verified when the binary operation between two fuzzy sets is defined by using their level sets the consistency is investigated thoroughly in this paper for the purpose of guaranteeing the existence of such binary operations moreover we also propose the so called hausdorff difference between any two fuzzy sets to define the difference of any two fuzzy numbers

a fuzzy statistical test of fuzzy hypotheses abstract a fuzzy hypothesis is introduced and a testing method of a fuzzy hypothesis is proposed for random data the proposed test produces a conclusion which is also fuzzy some applications of the fuzzy statistical test are demonstrated particularly the test of the difference of two population means is considered in detail and the fuzzy hypothesis that two population means are nearly equal is tested by the proposed procedure

jensen and chebyshev inequalities for pseudo integrals of set valued functions set valued functions are an important mathematical notion and play a crucial role in several practical areas at the same time pseudo analysis as a background allows extension of some classical mathematical notions to the forms that are highly applicable in some nonstandard situations this paper focuses on pseudo integration of set valued functions which is generalization of aumann s research and corresponding extensions of the jensen and chebyshev integral inequalities to the set valued case since the integral inequalities in question are widely used in various aspects of mathematics the main motivation for the presented research lies in the possibility of expanding the applicability of these inequalities by combining the properties of set valued functions with pseudo analysis

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

reliable control using redundant controllers this paper presents a methodology for the design of reliable control systems by using multiple identical controllers to a given plant the resulting closed loop control system is reliable in the sense that it provides guaranteed internal stability and h sub spl infin performance in terms of disturbance attenuation not only when all controllers are operational but also when some controller outages sensor and or actuator occur a numerical example is given to illustrate the proposed design procedures

solving fuzzy complex system of linear equations abstract this paper proposes a new and simple method for solving general fuzzy complex system of linear equations in the original system the elements of unknown variable vector and right hand side vector are considered as complex fuzzy number initially the general system is solved by adding and subtracting the left and right bounds of the fuzzy complex unknown and right hand side fuzzy complex vector respectively subsequently above obtained solutions are used to get the final solution of the general fuzzy complex system of linear equations two theorems are stated and proved related to the proposed method a mathematical example and an application problem based on electrical circuit are solved using the present method results obtained are compared with the known results and are found to be in good agreement

convergence of set valued sub and supermartingales in the kuratowski mosco sense the purpose of this paper is to prove some convergence theorems of closed and convex set valued sub and supermartingales in the kuratowski mosco sense to get submartingale convergence theorems we give sufficient conditions for the kudo aumann integral and hiai umegaki conditional expectation to be closed both for compact convex set valued random variables and for closed convex set valued random variables we also give an example of a bounded closed convex set valued random variable whose kudo aumann integral is not closed

two node hamiltonicity of enhanced pyramid networks an enhanced pyramid network is an alternate hierarchical structure for a pyramid network this structure is created in a pyramid network by replacing each mesh with a torus at layers greater than one this work studies the fault tolerant hamiltonian problem on the enhanced pyramid network and demonstrates that an enhanced pyramid network with two faulty nodes is hamiltonian the result is optimal because edge connectivity and node connectivity of the enhanced pyramid network are both 4

hukuhara derivative of the fuzzy expected value in this paper we establish sufficient conditions to guarantee the exchange of the fuzzy expected value for a fuzzy random variable depending on certain parameter and its hukuhara derivative with respect to the parameter main results are obtained for two different sets of general conditions one of them requiring measurability conditions with respect to the product space the fuzzy random variable is defined from and the second one just requiring conditions over the projections of the fuzzy random variables

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

discrete time markovian jump linear quadratic optimal control this paper is concerned with the optimal control of discrete time linear systems that possess randomly jumping parameters described by finite state markov processes for problems having quadratic costs and perfect observations the optimal control laws and expected costs to go can be precomputed from a set of coupled riccati like matrix difference equations necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite with finite optimal expected cost

towards fuzzy differential calculus part 3 differentiation this paper deals successively with differentiation of ordinary functions at a fuzzy point and with differentiation of fuzzy valued functions at a nonfuzzy point in both cases the concept of differentiation is extended and the problem of the linearity is addressed in the second case practical methods of computation are presented in practical situations the available knowledge about mappings may be fuzzy it is the motivation of this work

numerical solutions of fuzzy differential and integral equations using the embedding method numerical procedures for solving fuzzy differential equations fdes and fuzzy integral equations fies with arbitrary kernels have been investigated sufficient conditions for convergence of the proposed algorithms are given and their applicability is illustrated with examples this work and its conclusions may narrow the gap between the theoretical research on fdes and fies and the practical applications already existing in the design of various fuzzy dynamical systems

fuzzy complex analysis i differentiation abstract we consider functions mapping real numbers into the set of generalized complex fuzzy numbers c we define two derivatives of such functions which are generalizations of the derivative of real fuzzy mappings presented by dubois and prade 4 5 sufficient conditions on the function are given so that derivative will be a function mapping real numbers into c if the functional value is always a rectangular complex fuzzy number made up to lr real fuzzy numbers then we show that the derivative is easily computed from the derivatives of the lr fuzzy numbers other properties of the derivatives are presented

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

a unified approach to asymptotic behaviors for the autoregressive model with fuzzy data we propose a unified estimator for the autoregressive model with fuzzy input output variables based on the least squares method the least squares estimation is investigated in presence of a unified r distance defined on the space of fuzzy numbers we investigate asymptotic properties of the unified estimator under some simple conditions as well as a generalization which reduces to the asymptotic properties under those distances when the distances are the special cases of r distance some simulation studies are included to compare the asymptotic properties of estimators formed under several distances being the special cases of r distance