on some regularity of periodic solutions of the wave equation with a nonlinear or degenerate dissipative term on considere une equation d onde avec un terme dissipatif non lineaire u tt u xx u t f x t sur a b r avec la condition limite u a t u b t 0 t r ou s est une fonction du genre s k 0 s r s r 0 k 0 0 et f est une fonction periodique sur a b r

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

regular non additive measure and choquet integral the regular non additive measure is defined it is shown that the choquet integral of a choquet integrable function can be approximated by the integral of a continuous function with compact support

boundedness and symmetry of comonotonically additive functionals the relations between a comonotonically additive and monotone functional i and the induced fuzzy measures i and i are discussed we present a necessary and sufficient condition of the functional i for i x i x and i x i x

lusin s theorem on fuzzy measure spaces in this paper we show that weakly null additive fuzzy measures on metric spaces possess regularity lusin s theorem which is well known in classical measure theory is generalized to fuzzy measure space by using the regularity and weakly null additivity a version of egoroff s theorem for the fuzzy measure defined on metric spaces is given an application of lusin s theorem to approximation in the mean of measurable function on fuzzy measure spaces is presented

regularity aspects of non additive set multifunctions abstract in this paper continuity properties of set multifunctions such as regularity and continuity from above and below as well as others are introduced by way of a wijsman topology some of the relationships between them are established different examples counterexamples and applications are provided

the alexandroff theorem for riesz space valued non additive measures the alexandroff theorem for a compact non additive measure with values in a riesz space is still valid for the following two cases one is the case that the measure is autocontinuous and the riesz space has the weak asymptotic egoroff property and the other is the case that the measure is uniformly autocontinuous and the riesz space is weakly distributive a close connection between regularity and continuity of non additive measures is also given

on lusin s theorem for non additive measures that take values in an ordered topological vector space abstract lusin s theorem was established for real valued monotone measures under an equivalent condition to egoroff s theorem recently in this paper we show that the same result remains valid for non additive measures that take values in an ordered topological vector space we apply our result to several ordered topological vector spaces

a remark on holder continuity of periodic solutions to some nonlinear wave equations on considere l equation d onde semilineaire a une dimension u tt u xx u t f t x sur r 0 avec les conditions aux limites homogenes u t 0 u t 0 t r ou est une fonction c 1 non decroissante qui se comporte comme s k s r s r 0 on etudie la regularite des solutions 2 periodiques

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

on a sufficient condition of lusin s theorem for non additive measures that take values in an ordered topological vector space classical lusin s theorem is extended for real valued fuzzy measures under the weak null additivity condition recently in this paper we show similar results for non additive measures that take values in an ordered topological vector space firstly we prove lusin type theorem for weakly null additive borel measures that are continuous from above and possess an additional continuity property suggested by sun in 1994 secondly we state another one for weakly null additive fuzzy borel measures our results are applicable to several ordered topological vector spaces

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

extension and representation of comonotonically additive functionals the domain of comonotonically additive and monotone functionals on the class of continuous functions with compact support is extended in a natural way a necessary and sufficient condition for which the extended functional is comonotonically additive and monotone is presented it is shown that the extended functional can be represented by a choquet integral when the extended functional is comonotonically additive and monotone

regular fuzzy measure and representation of comonotonically additive functional this paper discusses the functional i defined on the class of continuous functions which is comonotonically additive and monotone the notion of regular fuzzy measure is proposed and the uniqueness theorem of regular fuzzy measure is shown it is also shown that i can be represented by the difference of two choquet integrals with respect to regular fuzzy measures when the universal set x is a locally compact hausdorff space and that i can be represented by one choquet integral with respect to a regular fuzzy measure when x is a compact hausdorff space

convergence theorems for monotone measures in classical measure theory there are a number of convergence theorems such as the egorov the riesz and the lusin theorem among others we consider monotone measures i e monotone set functions vanishing in the empty set and defined on a measurable space and discuss how and to which extent classical convergence theorems can be carried over to this more general case

regularity and lusin s theorem for riesz space valued fuzzy measures a smoothness condition the multiple egoroff property is introduced and imposed on a riesz space to show that every weakly null additive riesz space valued fuzzy borel measure on any metric space is regular it is also proved that lusin s theorem remains valid for such riesz space valued non additive measures

oscillatory phenomena associated to semilinear wave equations in one spatial dimension let g be a nonincreasing odd c function and i 0 we establish that for any solution u s c r hq 0 of the equation utt uxx g u 0 and any io 0 l the function t u t xo satisfies the following alternative either u t x0 0 vt g r or vo r there exist t and t2 in a a 21 such that u ti xo 0 and u t2 xo 0 we study the structure of the set of points satisf ing the first possibility we give analogous results for ux and for some other homogeneous boundary conditions

regularity and autocontinuity of set multifunctions in this paper we study different types of regularity for monotone uniformly autocontinuous set multifunctions defined on a ring of subsets of a locally compact hausdorff space t and taking values in the family of closed nonvoid sets of a real normed space x

convergence of sequence of measurable functions on fuzzy measure spaces abstract the purpose of this paper is to investigate the convergence of sequence of measurable functions on fuzzy measure spaces several classical results on the convergence of measurable functions such as egoroff s theorem lebesgue s theorem and riesz s theorem are extended to fuzzy measure spaces by using the pseudometric generating property and order continuity of fuzzy measures

lusin s theorem on monotone measure spaces in this paper a kind of regularity of monotone measures is shown by using the pseudometric generating property of set function for short p g p and an equivalence condition for egoroff s theorem lusin s theorem which is well known in classical measure theory is generalized to monotone measure spaces the continuity from above and below of set functions is not required in the discussions therefore the previous results obtained by jiang et al are generalized an approximation of measurable functions by continuous functions on monotone measure spaces is presented

choquet integral and fuzzy measures on locally compact space the concept of outer regular fuzzy measures is proposed and it is shown that a functional of certain type on the cone of positive continuous functions with compact supports is represented as a choquet integral with respect to a outer regular fuzzy measure it is also shown that the choquet integral of positive continuous functions with compact supports is represented as a lebesgue integral with the same integrands this representation is a generalization of certain previous results of others which are useful for computation of the upper and lower expected value

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

a lusin type theorem for regular monotone uniformly autocontinuous set multifunctions in this paper we continue our study concerning monotone uniformly autocontinuous regular set multifunctions as an application a lusin type theorem under a suitable type of measurability is obtained and several applications for finitely purely atomic multisubmeasures are proved

boltzmann cellular automata studies of the spinodal decomposition abstract a nonlinear galilean invariant 2 color boltzmann cellular automaton is used to study spinodal decomposition in 2 dimensional systems the initial conditions for the process correspond to a well mixed state of two fluids present in equal proportions we specify two types of such initial conditions corresponding to a correlated quench and to a deep quench in the former case a specific color is assigned randomly to each site in the latter individual states on each site are populated by the two colors about evenly with small fluctuations in the correlated quench situation the domain growth exponent is initially equal to 0 33 0 06 and for the late time stage it is equal to 0 66 0 06 in the deep quench situation on the other hand the effective exponent from initial value of 0 33 takes on the value of 0 82 0 05 for intermediate time scales and only at later times it crosses over to the exponent corresponding to the correlated quench spinodal decomposition taking place in a porous medium is slower and the effective exponents are nonuniversal inadequacies in the existing models of the surface tension in cellular automata are pointed out

finite difference lattice boltzmann methods for binary fluids we investigate two fluid bhatnagar gross krook bgk kinetic methods for binary fluids the developed theory works for asymmetric as well as symmetric systems for symmetric systems it recovers sirovich s theory and is summarized in models a and b for asymmetric systems it contributes models c d and e which are especially useful when the total masses and or local temperatures of the two components are greatly different the kinetic models are discretized based on an octagonal discrete velocity model the discrete velocity kinetic models and the continuous ones are required to describe the same hydrodynamic equations the combination of a discrete velocity kinetic model and an appropriate finite difference scheme composes a finite difference lattice boltzmann method the validity of the formulated methods is verified by investigating i uniform relaxation processes ii isothermal couette flow and iii diffusion behavior

lusin s theorem for monotone set valued measures on topological spaces abstract on a topological space the inner regularity outer regularity and regularity of a monotone set valued measure are considered their properties are discussed based on these the versions of egoroff s theorem and lusin s theorem for monotone set valued measures on a topological space are shown respectively

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

fuzzy regular measures on topological spaces in this paper the concepts of the inner regularity outer regularity and regularity of a fuzzy measure are introduced on a topological space their properties are studied in detail egoroff theorem and lusin theorem are proved finally the conditions for a fuzzy measure to be tight and perfect are given respectively

atoms of weakly null additive monotone measures and integrals in this paper we prove some properties of atoms of weakly null additive monotone measures by using the regularity and weak null additivity a sin gleton characterization of atoms of monotone measures on a metric space is shown it is a generalization of previous results obtained by pap the calculation of the sugeno integral and the choquet integral over an atom is also presented respectively similar results for recently introduced universal integral are also given following these results it is shown that the sugeno integral and the choquet integral over an atom of monotone measure is maxitive linear and standard linear respectively convergence theorems for the sugeno integral and the choquet integral over an atom of a monotone measure are also shown

conditions for choquet integral representation of the comonotonically additive and monotone functional if the universal set x is not compact but locally compact a comonotonically additive and monotone functional for short c m on the class of continuous functions with compact support is not represented by one choquet integral but represented by the difference of two choquet integrals the conditions for which a c m functional can be represented by one choquet integral are discussed

a further investigation for fuzzy measures on metric spaces the pseudometric generating property of non additive set functions also plays an important role as the autocontinuity in fuzzy measure theory jiang ph d thesis chiba university 1996 wang and klir fuzzy measure theory plenum press new york 1992 a further research on this property has been presented in jiang et al fuzzy sets and systems 1998 the aim of this paper is to prove the egoroff s theorem and lusin s theorem for measurable functions on metric spaces hold for those fuzzy measures with the exhaustivity and pseudometric generating property

on the regularities of fuzzy set multifunctions with applications in variation extensions and fuzzy set valued integrability problems in this paper we continue our studies 6 7 concerning regularity in this sense we obtain extension results by preserving regularity and we establish basic properties and continuity properties for the variation of fuzzy set multifunctions this enables us to get relationships among different types of regularity and also to point out regularity properties of the fuzzy set valued integral 20

atoms of fuzzy measures and fuzzy integrals abstract some analytical properties of sugeno s fuzzy measures especially of atoms of fuzzy measures are investigated a fuzzy integral of riemann type is defined through atoms and it is proved that a continuous function is fuzzy integrable in the sense of riemann and has the same integral as that of sugeno

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

a set valued egoroff type theorem in this paper an egoroff type theorem for a fuzzy multimeasure defined on a s algebra of subsets of an abstract space and taking values in the family of all nonvoid closed subsets of a real normed space is established some necessary and or sufficient conditions under which egoroff s theorem is valid are also presented

inner and outer representation by choquet integral the representations of comonotonically additive and monotone functionals are investigated an i regular non additive measure is defined as a non additive measure whose values can be calculated from its values on the inner compact sets and the values on compact sets can be calculated from its values on the outer open sets the basic properties of an i regular non additive measure are shown the inner representation of the functional is proposed and is compared with the outer representation

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

modeling attitude to risk in human decision processes an application of fuzzy measures abstract several models of the human decision process have been proposed classical examples of which are utility theory and prospect theory in recent times the theory of fuzzy measures and integrals has emerged as an alternative meriting further investigation specifically one is interested in the degrees of disjunction and conjunction and the veto and favor indices that represent the tolerance measure of the decision maker though several theoretical expositions have appeared in contemporary literature empirical studies applying these concepts to the real world are scarce this paper reports two studies based on a model of strategic telecommunication investment decisions from a research work involving a survey of executives the first study involves building fuzzy models corresponding to each individual decision maker with the results grouped based on the decision makers propensity to risk as determined by their degrees of disjunction the shapley indices and the interaction effects are determined for each pooled dataset corresponding to each group to contrast this approach with those of conventional nomothetic comparisons of decision policies the decision makers are grouped based on a clustering analysis of the individual linear regression models the data for each cluster are pooled and the fuzzy measures learned from the dataset are analyzed for comparison purposes the results not only serve as a demonstration of fuzzy measure analysis as a viable approach to studying qualitative decision making but also provide useful methodological insights into applying fuzzy measures to strategic investment decisions under risk

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

some notes on the regularity of fuzzy measures on metric spaces abstract the purpose of this paper is to correct and modify some conclusions shown in a paper by wu congxin and ha minghu fuzzy sets and systems 66 1994 373 379 and to give some further results

the emergence of fifty fifty probability judgments through bayesian updating under ambiguity this paper explains the empirical phenomenon of persistent fifty fifty probability judgments through a model of bayesian updating under ambiguity to this purpose i characterize an announced probability judgment as a bayesian estimate given as the solution to a choquet expected utility maximization problem with respect to a neo additive capacity that has been updated in accordance with the generalized bayesian update rule only for the non generic case in which this capacity degenerates to an additive probability measure the agent will learn the event s true probability if the number of i i d data observations gets large in contrast for the generic case in which the capacity is not additive the agent s announced probability judgment becomes a persistent fifty fifty probability judgment after finitely many observations

non atomicity and the darboux property for fuzzy and non fuzzy borel baire multivalued set functions in this paper we establish results concerning non atomicity and the darboux property for multisubmeasures fuzzy multivalued set functions defined on the baire respectively borel d ring b 0 respectively b of a locally compact hausdorff space

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

set valued lusin type theorem for null null additive set multifunctions in a previous paper we presented a set valued egoroff type theorem for monotone set multifunctions in this paper a new version of this set valued egoroff type theorem is obtained it enables a set valued lusin type theorem for null null additive monotone continuous set multifunctions to be established several applications of this lusin type theorem are given pointing out some relationships among m measurability a measurability and totally measurability of real functions we also compare our new lusin type theorem with lusin s theorem previously obtained by the second author

cellular automaton fluids 1 basic theory continuum equations are derived for the large scale behavior of a class of cellular automaton models for fluids the cellular automata are discrete analogues of molecular dynamics in which particles with discrete velocities populate the links of a fixed array of sites kinetic equations for microscopic particle distributions are constructed hydrodynamic equations are then derived using the chapman enskog expansion slightly modified navier stokes equations are obtained in two and three dimensions with certain lattices viscosities and other transport coefficients are calculated using the boltzmann transport equation approximation some corrections to the equations of motion for cellular automaton fluids beyond the navier stokes order are given

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

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

pseudo atoms of fuzzy and non fuzzy measures in this paper we introduce the concept of pseudo atoms of set functions and establish some fundamental conclusions about pseudo atoms on the assumption of null null additivity we give the necessary and sufficient conditions which insure that the set of non null measure contains no pseudo atoms further we obtain several decomposition theorems about pseudo atoms and atoms of set functions

lattice boltzmann study of spinodal decomposition in two dimensions a lattice boltzmann model using the shan chen prescription for a binary immiscible fluid is described and the macroscopic equations obeyed by the model are derived the model is used to quantitatively examine spinodal decomposition of a two dimensional binary fluid this model allows examination of the early time period corresponding to interface formation and shows agreement with analytical solutions of the linearized cahn hilliard equation despite the fact that the model contains no explicit free energy functional this regime has not to the knowledge of the authors been previously observed using any lattice boltzmann method in agreement with other models a scaling law with the exponent 2 3 is observed for late time domain growth breakdown of scaling is also observed for certain sets of simulation parameters

regularities of riesz space valued non additive measures with applications to convergence theorems for choquet integrals a deeper investigation of radonness and t smoothness properties of riesz space valued borel non additive measures is carried out to this end due to a lack of e argument in a riesz space the multiple egoroff property is introduced and enforced on the involved riesz space the established regularity properties of borel non additive measures are instrumental when formulating certain types of monotone convergence theorems for choquet integrals