abstract functional differential equations and reaction diffusion systems functional differential equations and reaction diffusion systems r h martin jr and h l smith abstract several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays suppose q is a bounded domain in rn with aq smooth and a is the laplacian operator on q also let m be a positive integer z a positive number and f fi m a continuous bounded function from 0 xc x q x c z 0 m into rm where c t 0 is the space of continuous functions from z 0 into r the purpose of this paper is to apply abstract results for semilinear functional differential equations in banach spaces to reactiondiffusion systems with time delays having the form a tu x t diau x t i t x ut x t a xeq i 1 m rdd ai x ui x t au i x t 81 x t t a x eaq u x a 0 x x 0 5 t 0 di 0 and ca q 0 o is c and i q x 0 oo r is c2 here an is the outward normal derivative on aq and if di 0 it is assumed that no boundary conditions are specified for this i also tu x t denotes the partial with respect to t whereas ut x denotes the member of c z 0 defined by 0 u x t 0 u x t 0 m our techniques provide basic existence criteria but the main point is that they can also be effectively applied to obtain estimates for solutions especially received by the editors october 7 1987 and in revised form october 7 1988 1980 mathematics subject classification 1985 revision primary 35r10 34k30

fuzzy number valued fuzzy measure and fuzzy number valued fuzzy integral on the fuzzy set abstract in this paper some new concepts the fuzzy number valued fuzzy measure autocontinuity and null additivity of fuzzy number valued fuzzy measures on the fuzzy algebra and the fuzzy number valued fuzzy integral on the fuzzy set are introduced some properties of fuzzy number valued fuzzy integrals and some convergence theorems for sequences of fuzzy number valued fuzzy integrals on a fuzzy set are discussed

fuzzy measures on metric spaces abstract the aim of the present paper is to study the regularity and tightness properties of fuzzy measures on metric spaces among other results we shall give lusin s theorem and egoroff s theorem we shall also prove the singleton characterization of atom of fuzzy measure and an algorithm to evaluate the fuzzy integrals of non negative measurable functions over an atom and a union of finite disjoint atoms

pseudo integral and generalized choquet integral abstract due to many applications the choquet integral as a powerful tool for modeling non deterministic problems needs to be further extended therefore the paper is devoted to a generalization of the choquet integral as a basis the pseudo integral for bounded integrand is extended to the case for nonnegative integrands at first and then the generalized choquet integral is defined as special cases pseudo choquet stieltjes integrals pseudo fuzzy stieltjes integrals g choquet integrals pseudo n fuzzy integrals and pseudo s fuzzy integrals are obtained and various kinds of properties and convergence theorems are shown meanwhile markov jensen minkowski and holder inequalities are proved in the end the generalized discrete choquet integral is discussed the obtained results for the generalized choquet integral cover some previous results on different types of nonadditive integrals

a possibility measure is not a fuzzy measure abstract in this note we show that a possibility measure is not a particular type of fuzzy measure except in trivial cases

weakly tight functions their jordan type decomposition and total variation in effect algebras in the present paper we have studied envelopes of a function m defined on a subfamily e containing 0 and 1 of an effect algebra l the notion of a weakly tight function is introduced and its relation to tight functions is investigated examples and counterexamples are constructed for illustration a jordan type decomposition theorem for a locally bounded real valued weakly tight function m defined on e is established the notions of total variation m on the subfamily e and m atoms on a sub effect algebra e along with a few examples of m atoms for null additive as well as non null additive functions are introduced and studied finally it is proved for a real valued additive function m on a sub effect algebra e that m is non atomic if and only if its total variation m is non atomic

on the null additivity and the uniform autocontinuity of a fuzzy measure abstract in this paper we prove that if the space x is countable and the fuzzy measure is finite then the null additivity is equivalent to the uniform autocontinuity as a special case the answer for the open problem 2 in wang zhenyuan on the null additivity and the autocontinuity of a fuzzy measure fuzzy sets and systems 45 1992 223 226 is affirmative

on the weak convergence of sequences of fuzzy measures and metric of fuzzy measures in this paper on the sugeno s fuzzy measures space we first put forward the concepts of the weak convergence and the metric of fuzzy measures and then an equivalent condition on the weak convergence of sequences of fuzzy measure are given finally in the sense of this metric we obtain that the family of fuzzy measures constitute a separable metric space

global attractivity in monotone and subhomogeneous almost periodic systems abstract a global attractivity theorem is first proved for a class of skew product semiflows then this result is applied to monotone and subhomogeneous almost periodic reaction diffusion equations ordinary differential systems and delay differential equations for their global dynamics

minimal wave speed in a diffusive epidemic model with temporal delay abstract taking incubation period into account we modify capasso et al s epidemic model and consider a reaction diffusion system with time delay by the method of upper and lower solutions to a related second order ordinary differential equation with infinite time delay we establish the existence of the minimal wave speed for the modified epidemic model and show that incubation period reduces the minimal wave speed of epidemic model indeed

fundamental convergence of sequences of measurable functions on fuzzy measure space abstract the concepts of fundamental almost everywhere and fundamental pseudo almost everywhere on fuzzy measure space are introduced the relations among convergence of sequences of measurable functions are further discussed the corresponding results on classical measure space are generalized and some of these results are improved in essence

autocontinuity and convergence theorems for the choquet integral we provide convergence theorems for the choquet integral for various notions of convergence monotone almost uniform convergence from above below is associated to monotone autocontinuity from above below the dominated almost uniform convergence is associated to monotone autocontinuity autocontinuity can be associated to the dominated convergence in measure in mean or in strict measure

a unified approach to the monotone convergence theorem for nonlinear integrals abstract we present a unified approach to the monotone convergence theorem for nonlinear integrals such as the choquet the sipos the sugeno and the shilkret integral a nonlinear integral may be viewed as a nonlinear functional defined on a set of pairs of a nonadditive measure and a measurable function we thus formulate our general type of monotone convergence theorem for such a functional the key tool is a perturbation of functional that manages not only the monotonicity of the functional but also the small change of the functional value arising as a result of adding small amounts to a measure and a function in the domain of the functional our approach is also applicable to the lebesgue integral when a nonadditive measure is additive

on fuzzy measures defined by seminormed fuzzy integrals and semiconormed fuzzy integrals abstract in this paper we show that for the continuous t seminorms and continuous t semiconorms the properties of null addivity pseudo null addivity autocontinuity and pseudo autocontinuity of fuzzy measures g can be preserved by the fuzzy measures g h and g h defined by seminormed fuzzy integrals and semiconormed fuzzy integrals respectively at most under the conditions that x y 0 x y 0 and x y x y g can be preserved by the fuzzy measures g h under the condition that x y 0 x y 0

the range of null additive fuzzy and non fuzzy measures abstract in this paper a wide class of non additive set functions is investigated for finite null additive fuzzy and non fuzzy measures saks decomposition type theorem theorem on darboux property and lyapunov s type theorems are proved

convergence to periodic solutions in periodic quasimonotone reaction diffusion systems abstract the author studies the periodic time dependent quasimonotone reaction diffusion systems u i t d i u i f i t x u 1 u n t 0 x u i n i u i 0 t 0 x u i x 0 u 0 i x x formula i 1 2 n in a proper banach space satisfying i fi uj 0 for all 1 i j n ii f t x u is periodic in t of period 0 and iii fi t x u fi t x u for all 0 1 and i 1 2 n it is proved that every solution of such a system converges to a periodic solution the same result also holds if we replace iii by iii f t x u is analytic and every periodic solution is liapounov stable

duality and ordinality in fuzzy measure theory this paper reformulates the duality in fuzzy measure theory discussed by liu as the cardinal duality principle this principle guarantees that if a proposition concerning a finite fuzzy measure holds then its dual also holds it is however not applicable to propositions concerning infinite fuzzy measures by introducing the concept of ordinality the author converts the principle into the ordinal duality principle which is applicable to all ordinal propositions concerning general finite or infinite fuzzy measures

stochastic convergence uniform integrability and convergence in mean on fuzzy measure spaces the paper deals with the convergence of sequences of measurable functions on fuzzy measure spaces a classical result that relates the uniform integrability plus stochastic convergence with convergence in mean is extended to this case where the additivity property of measures is not required we also investigate the sufficient and necessary conditions that fuzzy measures must satisfy in the dominated convergence theorem

generalized fuzzy integrals part i fundamental concepts abstract in this paper we introduce a definition of fuzzy integral which is a generalization of both s fuzzy integral defined by m sugeno and n fuzzy integral due to zhao ruhuaiand discuss the fundamen tal properties of this kind of fuzzy integral

fuzzy numbers and fuzzification of the choquet integral to deal with linguistic attributes in databases the integrand of the choquet integral should be allowed to assume fuzzy numbers this paper provides a detailed discussion on one fuzzification of choquet integral in which the integrand as well as the integration result is fuzzy numbers based on the extension principle it is a generalized choquet integral for fuzzy valued integrand interval valued integrand as well as the crisp valued integrand two numerical methods are provided to calculate the membership function of the integration value of this generalized choquet integral with respect to the fuzzy measure and the signed fuzzy measure respectively the presented generalized choquet integral with respect to signed fuzzy measure can act as an aggregation tool which is especially useful in many information fusing and data mining problems such as regression and classification where not only crisp data but also heterogeneous fuzzy data are involved

lebesgue and saks decompositions of σ finite fuzzy measures two kinds of absolute continuity of fuzzy measures are distinguished and relations between them are established the scope of fuzzy measures under our consideration is limited in a family of those that are finite and absolute continuous with respect to a finite autocontinuous fuzzy measure under this restriction lebesgue decomposition and saks decomposition are proved

identifications of parameters in ill posed linear parabolic equations abstract in this paper we study the identification of conductivities q in linear parabolic equation y t q y f in 0 t with boundary condition y x t 0 on 0 t and without initial data where the observations are taken in an open subset of we obtain the existence and introduce an approximation process for the identification problem

on the null additivity of the fuzzy measure abstract in this paper egoroff s theorem and other several results on fuzzy measure space of papers 1 and 4 are improved the importance of the concept of null additivity which was first introduced by wang in 1 is further shown

the convergence for a sequence of fuzzy integrals of fuzzy number valued functions on the fuzzy set abstract in this paper a new concept of fuzzy number valued fuzzy integral of fuzzy number valued function with respect to fuzzy number valued fuzzy measure on the fuzzy set is introduced and some equivalent definitions of the above mentioned concept are given and its elementary properties are discussed and a series of the convergent theorems of fuzzy number valued fuzzy integrals on the fuzzy set are obtained

the relationship between structural characteristics of fuzzy measure abstract in this paper some new concepts property s 1 property ps property ps 1 are introduced the converse problems of convergence theorems such as egoroff s theorem and riesz s theorem are discussed some new results about the relationship between structural characteristics of fuzzy measure and convergences of sequences of measurable functions are obtained

the autocontinuity of set function and the fuzzy integral abstract the autocontinuity and some other concepts of a set function are introduced and sugeno s fuzzy measure with some annexed conditions is studied on a fuzzy measure space egoroffs theorem is proved it is also proved that f mean convergence is equivalent to convergence in measure for a sequence of measurable functions finally some convergence theorems of sequence of fuzzy integrals are proved especially using the concept of autocontinuity a necessary and sufficient condition for the convergence in measure theorem is given

global asymptotics in some quasimonotone reaction diffusion systems with delays abstract both dichotomy and trichotomy on the global asymptotics of some quasimonotone reaction diffusion systems with delays are established in terms of the principal eigenvalue of linear weakly coupled elliptic systems applications to a class of delayed reaction diffusion models of single species growth and to a reaction diffusion system with delay modelling the spread of bacterial infections are provided

sugeno integral based on absolutely monotone real set functions the class of all absolutely monotone and sign stable set functions with m a 0 denoted by amss is introduced necessary and sufficient conditions are obtained for a set function m m a 0 to be a member of amss a sugeno type integral of an a measurable real valued function is defined with respect to an absolutely monotone and sign stable set function and some of its properties are shown a representation of a comonotone cosigned additive functional by sugeno integral based on m amss is obtained

relationship among continuity conditions and null additivity conditions in non additive measure theory the paper shows all the implication relationship among six continuity conditions and two null additivity conditions with respect to non additive measures the six continuity conditions are continuity from above order continuity strong order continuity exhaustivity continuity from below and null continuity and the two null additivity conditions are null additivity and weak null additivity the implication relationship is summarized in a diagram

cooperative systems of differential equations with concave nonlinearities on considere le systeme dynamique discret engendre par une application monotone concave t r n r n on etudie ensuite des systemes d equations differentielles cooperatifs periodiques x f t x a non linearites concaves

identification of nonlinearity in k approximate periodic parabolic equations abstract this work is concerned with the identification of nonlinearities in k approximate periodic parabolic equations with observations on a subdomain of the physical domain some approximation processes for the identification problems are given

transformation theorems for fuzzy integrals on fuzzy sets abstract in this paper sugeno s fuzzy integrals studied in 5 8 9 are generalized some equivalent definitions of fuzzy integrals on fuzzy sets are given and several transformation theorems of such type of fuzzy integrals are proved these results reveal the relations between the fuzzy integrals on fuzzy sets and on classical sets

the completion of a fuzzy measure and its applications this paper discusses first the completion of a fuzzy measure which is defined on a ring then as an application of the complete fuzzy measure both convergence almost everywhere and convergence in fuzzy measure egoroff s theorems are provided

existence uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal this paper is concerned with a nonlocal evolution equation which is used to model the spatial dispersal of organisms we study the existence uniqueness and stability of the positive steady solution for this nonlocal evolution equation under general conditions the global dynamics are also investigated and a trichotomy of the global asymptotics is established

fuzzy measures defined by fuzzy integral and their absolute continuity abstract given a measurable space x f a fuzzy measure on x f and a nonnegative functionfonxthat is measurable with respect to f we can define a new set function on x f by the fuzzy integral it is known that is a lower semicontinuous fuzzy measure on x f and moreover if is finite then is a finite fuzzy measure as well in this paper we generalize in several different ways the concept of absolute continuity of set functions as defined in classical measure theory in addition we investigate the relationship among these generalizations by using the structural characteristics of set functions such as null additivity and autocontinuity and determine which types of absolute continuity of fuzzy measures are possessed by the fuzzy measure or the lower semicontinuous fuzzy measure obtained by the fuzzy integral

identification of discontinuous parameters in flow equations a problem of identifying possibly discontinuous diffusion coefficients in parabolic equations is considered general theorems on existence and convergence of galerkin approximations are proved in l 1 setting classes of functions of bounded variation are discussed and the variation estimates are obtained a double discretization method with the variations constraints is used in two and three dimensional problems and the numerical experiments are presented

autocontinuity convergence in measure and convergence in distribution abstract it is shown that the autocontinuity is equivalent to the property that the convergence in measure implies the convergence in distribution this result is applied to denneberg s dominated convergence theorem for the choquet integral

reaction diffusion systems with time delays monotonicity invariance comparison and convergence in a recent paper we have obtained differential inequality results developed comparison theorems and established invariance criteria for mild solutions of abstract functional differential equations in a banach space the primary application for these results is to reaction diffusion systems in which the reaction nonlinearity contains time delays in the present paper we apply these results to reaction diffusion systems with time delays of the form u t d u f x u t x x u u n 0 x where is a bounded open set in r n with smooth boundary u r n d diag d 1 d n with d i 0

an algorithm for identification of fuzzy measure in the paper the connection between fuzzy measures and lebesgue measure is discussed special attention is focused on fuzzy measures which satisfy the so called l rule a relation between such measures and probability measures is given basing on this relation a simple and fast algorithm for identification of a sugeno fuzzy measure is presented

the convergence of dg fuzzy integrals abstract the definition of another kind of generalized fuzzy integrals is introduced by means of the so called generalized triangular conorm it is said to be dual generalized fuzzy integrals and is denoted by dg fuzzy integrals in this paper several equivalent forms of dg fuzzy integrals are given particularly the convergence theorem in fuzzy measure and the monotone convergence theorems are obtained

on the null additivity and the autocontinuity of a fuzzy measure abstract in this paper further research on the null additivity and autocontinuity of fuzzy measures is made we prove that autocontinuity from below and autocontinuity from above of a fuzzy measure are equivalent when this fuzzy measure is finite furthermore if the space x is countable then the null additivity is equivalent to the autocontinuity

the vitali convergence in measure theorem of nonlinear integrals abstract the vitali convergence in measure theorem for the abstract lebesgue integral is fundamental in lebesgue integration theory and yields the bounded convergence theorem and the dominated convergence theorem as its applications in this paper in a unified way using the perturbation method the vitali convergence in measure theorem is established for nonlinear integrals such as the choquet sipos sugeno and shilkret integrals and their symmetric and asymmetric extensions it is derived from the fatou and the reverse fatou type lemmas for perturbative nonlinear integral functionals

on the fundamental convergence in the c mean in problems of information fusion abstract the choquet integral can be regarded as one of aggregation operators being used in information fusion in this study we offer an interpretation of sequences of measurable functions and the choquet integral in the framework of information fusion based on an efficiency measure space we also define a new concept of a fundamental convergence in the c mean of sequences of measurable functions and discuss its theoretical underpinnings along with related interpretation issues as well as deliver some new results furthermore an application of this concept is discussed in the context of information fusion more specifically based on the theoretical investigations this idea is applied to the determination of a measurable function being used in the choquet integral

the bounded convergence in measure theorem for nonlinear integral functionals in this paper we introduce a new notion of the perturbation of nonlinear functionals to formulate a functional form of the convergence theorems for nonlinear integrals in nonadditive measure theory as its direct consequences we obtain the bounded convergence in measure theorems for typical nonlinear integrals which show that the autocontinuity of a nonadditive measure is equivalent to the validity of the bounded convergence in measure theorems for the choquet the sugeno and the shilkret integrals as well as their symmetric and asymmetric extensions

global attractivity in concave or sublinear monotone infinite delay differential equations abstract we study the dynamical behavior of the trajectories defined by a recurrent family of monotone functional differential equations with infinite delay and concave or sublinear nonlinearities we analyze different sceneries which require the existence of a lower solution and of a bounded trajectory ordered in an appropriate way for which we prove the existence of a globally asymptotically stable minimal set given by a 1 cover of the base flow we apply these results to the description of the long term dynamics of a nonautonomous model representing a stage structured population growth without irreducibility assumptions on the coefficient matrices

spreading speeds of a partially degenerate reaction diffusion system in a periodic habitat abstract this paper is devoted to the study of the spreading speeds of a partially degenerate reaction diffusion system with monostable nonlinearity in a periodic habitat we first obtain sufficient conditions for the existence of principal eigenvalues in the case where solution maps of the associated linear systems lack compactness and prove a threshold type result on the global dynamics for the periodic initial value problem then we establish the existence and computational formulae of spreading speeds for the general initial value problem it turns out that the spreading speed is linearly determinate

asymptotic structural characteristics of fuzzy measure and their applications abstract in fuzzy measure theory as sugeno s fuzzy measures lose additivity in general the concept almost which is well known in classical measure theory splits into two different concepts almost and pseudo almost in order to replace the additivity it is quite necessary to investigate some asymptotic behaviors of a fuzzy measure at sequences of sets which are called waxing and waning and to introduce some new concepts such as autocontinuity converse autocontinuity and pseudo autocontinuity these concepts describe some asymptotic structural characteristics of a fuzzy measure in this paper by means of the asymptotic structural characteristics of fuzzy measure we also give four forms of generalization for both egoroff s theorem riesz s theorem and lebesgue s theorem respectively and prove the almost everywhere pseudo almost everywhere convergence theorem the convergence in measure pseudo in measure theorem of the sequence of fuzzy integrals in the last two theorems the employed conditions are not only sufficient but also necessary

exponential stability of traveling waves in a nonlocal dispersal epidemic model with delay abstract in this paper we are concerned with the stability of traveling waves of a nonlocal dispersal epidemic model with delay in the quasi monotone case we prove the exponential stability of traveling wavefronts by the weighted energy method and the comparison principle when the initial perturbation around the traveling wavefront decays exponentially as x but can be arbitrarily large in other locations in the non quasi monotone case we investigate the exponential stability of traveling waves when the initial perturbation around the traveling wave is properly small in a weighted norm

on the level continuity of fuzzy integrals in this paper we define the level convergence of measurable functions on a fuzzy measure space by using the closure operator in the moore sense we study some of the properties of this convergence and give conditions for the continuity of the fuzzy integral in relation to the level convergence

persistence and extinction in two species reaction diffusion systems with delays abstract both uniform persistence and global extinction are established for two species predator prey and competition reaction diffusion systems with delays in terms of the principal eigenvalues of the scalar elliptic eigenvalue problems by appealing to the theories of abstract persistence asymptotically autonomous semiflows and monotone dynamical systems

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

a periodic reaction advection diffusion model for a stream population abstract this paper is devoted to the study of spatial dynamics of a periodic reaction advection diffusion model for a stream population in the case of an unbounded domain we establish the existence of the leftward and rightward spreading speeds and their coincidence with the minimal wave speeds for monotone periodic traveling waves respectively in the case of a bounded domain we obtain a threshold result on the global stability of either zero or the positive periodic solution

further discussion on the hahn decomposition theorem for signed fuzzy measure abstract this paper gives a counterexample that the union of two negative sets is not a negative set for signed fuzzy measure showing that the proof of theorem 2 in liu 1993 is not valid furthermore we provide a proof for the hahn decomposition theorem when the space x is countable or the signed fuzzy measure possess the property d

global asymptotic behaviour in some functional parabolic equations the global asymptotic behavior in some functional parabolic equations was presented the sufficient condition for the global convergence to a spatially uniform equilibrium in the system of functional partial differential equations was provided results were observed to be valid for all non negative spatio temporal kernels which also satisfied a uniform normailzation condition

convergence in measure theorems of nonlinear integrals of functions integrable to the pth power abstract one can find a subadditive measure and a sequence f n n n of nonnegative measurable functions converging in measure to such a function f with the property that for any p 1 f n p no longer converges in measure to f p therefore in nonadditive measure theory an additional and intrinsic discussion is needed to prove integral convergence theorems for functions integrable to the pth power the purpose of the paper is to propose a method for automatically deriving pth power versions of convergence in measure theorems of nonlinear integrals from already established ones the proposed method is based on the robustness of some properties of integral functional under the operation f f p raising a nonnegative function f to the pth power

lebesgue decomposition theorem for σ finite signed fuzzy measures further research on signed fuzzy measures is made lebesgue decomposition theorems for finite signed fuzzy measures and fuzzy measures are proved under the null null additive condition thus the relative result in classical measure theory is generalized

fuzzy integrals of fuzzy valued functions abstract this paper based on the fuzzy measures and integrals given by sugeno first defines fuzzy integrals of set valued functions and then the fuzzy integral of fuzzy valued functions is obtained and discussed next it defines the fuzzy integrals of fuzzy mappings then pays much effort to the fuzzy integral of interval valued functions the properties and convergence theorems are obtained all these are generalizations of earlier results

on the regularity of the fuzzy measure on metric fuzzy measure spaces abstract in this paper the concept of the regular fuzzy measure on metric spaces is introduced some of its properties are discussed and lusin s theorem is shown in addition a condition for which a uniformly autocontinuous set function is a fuzzy measure is given

fuzzy integrals of set valued mappings and fuzzy mappings abstract the paper based on sugeno 1974 first defines the concept of fuzzy integrals of set valued mappings by the similar way of aumann 1965 then it is discussed some results similar to aumann integral are obtained these include convexity closedness fatou s lemmas and the lebesgue convergence theorem etc at last the fuzzy integral of fuzzy mappings is defined the extended results corresponding with fuzzy integrals of set valued mappings are showed

on the pseudo autocontinuity of fuzzy measures abstract the property ps of fuzzy measures is introduced a set of characterizations of the pseudo autocontinuity of fuzzy measures are given the equivalence of pseudo autocontinuity from above and pseudo autocontinuity from below is established the convergence pseudo in measure is investigated

on fuzzy measures defined by fuzzy integrals on definit une mesure floue comme une fonction ensemble sur 7b f qui est une algebre de sous ensembles de l ensemble x

on set valued fuzzy measures so far there have been many discussions on sugeno s fuzzy measures and fuzzy integrals but most of them are concentrated on single valued functions motivated by aumann s set valued integral j math anal appl 12 1965 1 we have introduced the fuzzy integral of set valued functions fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341 ph d dissertation harbin institute of technology 1998 it is a well behaved extension of fuzzy integrals of single valued functions it is well known that arstein s set valued measure trans am math soc 165 1972 103 is an important branch in set valued analysis set valued analysis birkhauser berlin 1990 or theory of correspondences theory of correspondences wiley new york 1984 compared to it the present paper will try to establish the basic idea of set valued fuzzy measures which are monotone set valued set functions it is also a natural generalization of single valued fuzzy measures as well as an extension of set valued measures in the case of one dimension these works include the concept of set valued fuzzy measures set valued fuzzy measures defined by set valued fuzzy integrals and set valued pseudo additive measures it can be viewed as a continuation of previous work fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341

fuzzy valued fuzzy measures and generalized fuzzy integrals in this paper the concept of fuzzy valued fuzzy measures is introduced at first and then based on the generalized fuzzy integral given by wu et al fuzzy sets and systems 57 1993 219 the generalized fuzzy integral of fuzzy valued functions with respect to fuzzy valued fuzzy measures is defined and the properties and convergence theorems are given all these are extensions of the sugeno theory of fuzzy integrals and its applications ph d thesis tokyo institute of technology 1974 and wu et al 1993 theory

on set valued fuzzy integrals abstract in the paper we extend fuzzy integrals of point valued functions which were defined by ralescu and adams to set valued functions some properties similar to auman integrals are shown and these include convexity monotonicity fatou s lemma lebesgue convergence theorem etc

generalized fuzzy integrals of set valued functions in this paper based on wu s generalized fuzzy integrals of point valued function c wu et al fuzzy sets and systems 70 1995 75 a theory of generalized fuzzy integrals of fuzzy valued functions will be investigated it includes definitions properties and various kinds of convergence theorems these are extensions of results in c wu et al fuzzy sets and systems 70 1995 75 d zhang and z wang fuzzy sets and systems 54 1993 63

the dynamical systems approach to differential equations bulletin new series of the american mathematical society volume 11 number 1 july 1984 the dynamical systems approach to differential equations by morris w hirsch 1 this harmony that human intelligence believes it discovers in nature does it exist apart from that intelligence no without doubt a reality completely independent of the spirit which conceives it sees it or feels it is an impossibility a world so exterior as that even if it existed would be forever inaccessible to us but what we call objective reality is in the last analysis that which is common to several thinking beings and could be common to all this common part we will see can be nothing but the harmony expressed by mathematical laws h poincare la valeur de la science p 9 ignorance of the roots of the subject has its price no one denies that modern formulations are clear elegant and precise it s just that it s impossible to comprehend how any one ever thought of them m spivak a comprehensive introduction to differential geometry introduction the mathematical subject we call dynamical systems was fathered by poin care developed sturdily under birkhoff and has enjoyed a vigorous new growth for the last twenty years as i try to show in chapter i it is interesting to look at this mathematical development as the natural outcome of a much broader theme which is as old as science itself the universe is a sytem which changes in time every mathematician has a particular way of thinking about mathematics but rarely makes it explicit yet such perspectives in any particular field can be of great value to nonexperts who must apply the results of the field or who want to learn them in some fields the points of view of its practitioners cluster around several comparatively clearly defined concepts and insights dynamical systems theory is one of them the basic concepts go back to poincare the main thrust of chapters i and ii is to explain rather discursively some of received by the editors december 14 1983 1980 mathematics subject classification primary 00a25 00a99 01a45 01a55 01a60 34a40 34c35 34d10 34d30 35b05 35b35 35b40 35b50 35b30 35k55 54h20 58f25 58f40 58f12 58f10 58d25 58d07 46a40 46e10 47h07 47h20 92a15 92a17 secondary 06f30 35b65 58f13 35j60 46e05 92 03 90 03 90a16 supported in part by national science foundation and institute for advanced study 1984 american mathematical society 0273 0979 84 1 00 25 per page

indeterminate integrals with respect to nonadditive measures recently nonadditive set functions have been used in information fusion and data mining to describe the interaction among the predictive attributes in this case replacing the traditional weighted average or more generally the linear mapping from a higher dimensional space to a one dimensional space relevant nonlinear integrals should be used as the aggregation tool to express how the objective attribute depends on predictive attributes several different types of nonlinear integral such as the choquet integral and the wang integral have been discussed in literature in these models the objective attribute is the integral while the predictive attributes are the integrand in this paper a new concept of indeterminate integral is introduced when the universe of discourse is finite it is a family of integrals including nonlinear integrals mentioned above and therefore possesses a large adaptability as a new aggregation tool each specified type of indeterminate integral can be obtained from the family of indeterminate integrals by specifying a decomposition of the integrand such a new aggregation tool can be used in information fusion and data mining as well as in expert systems

minimal sets in monotone and sublinear skew product semiflows i the general case abstract the dynamics of a general monotone and sublinear skew product semiflow is analyzed paying special attention to the long term behavior of the strongly positive semiorbits and to the minimal sets four possibilities arise depending on the existence or absence of strongly positive minimal sets and bounded semiorbits as well as on the coexistence or not of bounded and unbounded strongly positive semiorbits previous results are unified and extended and scenarios which are impossible in the autonomous or periodic cases are described

monotone semiflows generated by functional differential equations abstract this obtains sufficient condition for an autonomous functional differential equation to generate a strongly monotone semiflow on a suitable state space this allows the application to functional differential equations of very powerful recent results on strongly monotone semiflows due to hirsch and matano in addition a very striking relationship is established between such functional differential equations and corresponding ordinary differential equations an example involving a biochemical feedback loop is considered keywords stability steady states

a reaction advection diffusion system modeling the competition for two complementary resources with seasonality in a flowing habitat abstract in this current paper we investigate a periodic bio reactor model where microorganisms compete for two essential nutrient resource s needed for growth for the single population growth model we show that when the trivial solution is locally asymptotically stable then the single population will be washed out when the trivial solution is unstable there is a unique periodic positive solution which attracts all solutions with nonzero initial data for the two species model we prove that the existence of a periodic coexistence state is possible if each species can invade the semi trivial periodic state established by the other species more precisely if the semi trivial periodic solutions are both unstable there exists at least one periodic coexistence solution numerical work indicates conditions for persistence depend on the flow characteristics advection and diffusivity from our numerical simulations competitive exclusion bistability and coexistence are all observed

autocontinuity of set valued fuzzy measures and applications the main object of this paper is to further the study of set valued fuzzy measures introduced by gavrilut in 2009 some asymptotic structural characteristics of set valued fuzzy measures such as null additivity and autocontinuity are investigated in terms of applications convergence theorems for sequences of measurable functions are established

pseudometric generating property and autocontinuity of fuzzy measures several necessary and sufficient conditions for the pseudometric generating property of non additive set functions are given the relation among the pseudometric generating property and autocontinuity of fuzzy measures is depicted by using the absolute continuity and exhaustivity moreover any uniformly autocontinuous finite fuzzy measure is equivalent to a subadditive finite fuzzy measure a further research on purely atomic fuzzy measures is also made

fuzzy number fuzzy measures and fuzzy integrals i fuzzy integrals of functions with respect to fuzzy number fuzzy measures this paper based on the fuzzy measures and fuzzy integrals given by sugeno first defines interval number fuzzy measures inf measures and fuzzy number fuzzy measures fnf measures and the fuzzy integral of function with respect to inf measures are given then it defines the fuzzy integral of functions with respect to fnf measures and the properties and convergence theorems are obtained all these are generalizations of sugeno s works

monotonicity and stability for some reaction diffusion systems with delay and dirichlet boundary conditions abstract in this work we are concerned with the monotonicity and the stability study for quasi monotone reaction diffusion systems with delay and subject to dirichlet boundary conditions we first establish some invariance and comparison results for abstract retarded functional differential equations with nondense domain operators this allows us to show the monotonicity of the semiflow in a suitable phase space we also discuss a stability criterion independently of delay

on fuzzy number valued fuzzy measures defined by fuzzy number valued fuzzy integrals ii abstract in this paper we discuss some properties of a fuzzy number valued fuzzy set function defined by a fuzzy number valued fuzzy integral on the fuzzy set and give sufficient conditions that it is a fuzzy number valued fuzzy measure