tensor operators and projection techniques in infinite dimensional representations of semi simple lie algebras polynomial identities satisfied by the infinitesimal generators of a semi simple lie group are employed to construct projection operators which project a tensor product representation v lambda x v v lambda finite dimensional and irreducible v an infinite dimensional representation admitting an infinitesimal character onto a primary subrepresentation such projection operators project out the generalised shift components of a tensor operator acting on an infinite dimensional representation v in direct analogy with the finite dimensional analysis of bracken and green 1971 applications of these methods to evaluating the matrix elements of the generators of the locally compact groups u p q and o p q in unitary discrete irreducible representations are discussed

some quantities represented by the choquet integral this paper shows that the choquet integral can represent some useful quantities such as supremum infimum essential supremum essential infimum mean median quantile 100 percentile and l estimators including trimmed mean

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

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

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

representations of the lie algebra of derivations for quantum torus abstract let der c q be the derivation lie algebra of the quantum torus c q we construct a functor from gld modules to der c q modules which generalizes the constructions obtained by shen scientia sinica a 29 1986 570 larsson internat j modern phys a 7 1992 6493 and rao j algebra 182 1996 401 we also give a complete description of the structure of the der c q modules when all the entries of the quantum torus matrix q qij d d are roots of unity

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

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

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

monotone set functions defined by choquet integral abstract given a nonnegative monotone set function and a nonnegative measurable function on a measurable space the choquet integral determines a new nonnegative monotone set function that is absolutely continuous with respect to the original one in a generalized sense for monotone set functions this new set function preserves almost all desirable structural characteristics of the original monotone set function such as continuity subadditivity superadditivity null additivity converse null additivity autocontinuity converse autocontinuity uniform autocontinuity uniform converse autocontinuity and fuzzy multiplicativity such a construction is a useful method to define sound fuzzy measures in various applications

fuzzy integrals for set valued mappings in this paper we introduce the concept of fuzzy integrals for set valued mappings which is an extension of fuzzy integrals for single valued functions defined by sugeno we give some properties including convergence theorems on fuzzy integrals for set valued mappings

extensions of inhomogeneous polynomial representations for sl m 1 n we extend an inhomogeneous polynomial representation of special linear lie superalgebras sl m 1 n to an inhomogeneous representation on the tensor space of any irreducible tensor representation of the general linear lie superalgebras gl m n with this polynomial space via shen s mixed product we find a sufficient and necessary condition for irreducibility of these inhomogeneous representations and get the jordan holder series of those which are not irreducible furthermore we point out that all these irreducible modules are lowest weight modules their lowest weights and character formulas are obtained

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

some properties and convergence theorems of set valued choquet integrals the paper aims at discussing the set valued choquet integral which is the integral of set valued random variables with respect to capacities we mainly present representation theorems of the set valued random variable by using a sequence of choquet integrable selections and then we investigate some properties of set valued choquet integrals especially subadditive property and inequality of the metric of set valued choquet integrals we also prove fatou s lemmas lebesgue dominated convergence theorem and monotone convergence theorem of set valued choquet integrals under the weaker conditions than that in previous works

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

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

l additive measures on measure spaces abstract in his thesis sugeno has introduced a class of non additive set functions g which have been called additive measures he has printed out that g can be represented by a density function if it is defined on the power set of a finite set in this article this concept is generalized for arbitrary measure spaces moreover it is shown that any density function on a measure space determines a unique parameter 1 as in the finite case additive measures are belief functions iff 0 and plausibility functions iff 0 the proof of this statement is achieved by a generally applicable reduction of the problem to finite algebras

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

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

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

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

some properties of choquet integrals of set valued functions abstract in this paper we will define choquet integrals of set valued functions then we show some properties of choquet integrals of set valued functions

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

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

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

continuity properties and alexandroff theorem in vietoris topology in several previous papers we introduced and studied various continuity properties in the set valued case precisely we established results concerning increasing decreasing convergence exhaustivity order continuity and regularity in hausdorff topology for closed set valued monotone set multifunctions on a real normed space in this paper taking as starting point of a previous work we introduce and study from another point of view corresponding continuity properties in vietoris topology for more general monotone set multifunctions on a hausdorff linear topological space thus we obtain generalizations of some previous results which in turn generalize to the set valued case well known results from classical fuzzy i e monotone measure theory an alexandroff theorem in vietoris topology and its converse are also established

computing vertex surjective homomorphisms to partially reflexive trees a homomorphism from a graph g to a graph h is a vertex mapping f v g v h such that f u and f v form an edge in h whenever u and v form an edge in g the h coloring problem is that of testing whether a graph g allows a homomorphism to a given graph h a well known result of hell and nesetril determines the computational complexity of this problem for any fixed graph h we study a natural variant of this problem namely the surjectiveh coloring problem which is that of testing whether a graph g allows a homomorphism to a graph h that is vertex surjective we classify the computational complexity of this problem for when h is any fixed partially reflexive tree thus we identify the first class of target graphs h for which the computational complexity of surjectiveh coloring can be determined for the polynomial time solvable cases we show a number of parameterized complexity results including in particular ones on graph classes with locally bounded expansion

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

choquet like integrals abstract integrals based on a pseudo addition and a pseudo multiplication with properties similar to those of the choquet and the sugeno integral respectively are introduced the structure of convenient pseudo arithmetical operations leading to a choquet like integral is studied

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

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

a theory of fuzzy measures representations the choquet integral and null sets abstract some theorems of t murofushi and m sugeno fuzzy sets and systems 29 1989 201 227 concerning representation of fuzzy measures and the choquet integral are generalized it is shown that if there is a certain relation between two measurable functions then the choquet integral is additive for these two functions in addition this article discusses null sets with respect to fuzzy measures and also fuzzy measures defined on a class which is not a algebra

irreducible representations of nongraded witt type lie algebras abstract from his classification of quadratic conformal algebras corresponding to certain hamiltonian pairs in integrable systems xu gave an explicit construction of seven types of nongraded infinite dimensional simple lie algebra related to a finite set of locally finite derivations on certain commutative associative algebras in this paper we construct a family of irreducible generalized weight modules for the nongraded witt type lie algebras based on finite dimensional irreducible modules of general linear lie algebras our results are nongraded generalizations of rao s work on irreducible representations of the derivation lie algebra of the algebra of laurent polynomials in several variables

new generalized simple lie algebras of cartan type over a field with characteristic 0 abstract we construct four new series of generalized simple lie algebras of cartan type using the mixtures of grading operators and down grading operators our results in this paper are further generalizations of those in osborn s work j algebra 185 1996 820 835

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

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

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

a fuzzy gould type integral in this paper we introduce and study a set valued gould type integral of a real function with respect to a fuzzy multimeasure taking values in the family of all nonempty closed subsets of a banach space x some classical properties of the integral are obtained only using the hypothesis of monotonicity for the set valued fuzzy measure

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

integrals of set valued functions for decomposable measures abstract in this paper based on weber s 1984 integrals for archimedean t conorms decomposable measures integrals of set valued functions for archimedean t conorms decomposable measures are established some results similar to aumann s set valued integrals are given these include convexity closedness convergence theorems etc all these are the generalization of aumann s results

stochastic differential equations with fuzzy drift and diffusion a new framework for the fuzzification of stochastic differential equations is presented it allows for a detailed description of the model uncertainty and the non predictable stochastic law of natural systems e g in ecosystems even the probability law of the random dynamic changes due to unobservable influences like anthropogenic disturbances or climate variation the fuzziness of the stochastic system is modelled by a fuzzy set of stochastic differential equations which is identified with a fuzzy set of initial conditions time dependent drift and diffusion functions using appropriate function spaces the extension principle leads to a consistent theory providing fuzzy solutions in terms of fuzzy sets of processes fuzzy states fuzzy moments and fuzzy probabilities

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

on the representation of choquet integrals of set valued functions and null sets in this paper we consider the definition of set valued choquet integrals we obtain some properties and the representation of set valued choquet integrals and also we discuss some fundamental relations between null sets and set valued choquet integrals

a note on the interval valued generalized fuzzy integral by means of an interval representable pseudo multiplication and their convergence properties in this paper we consider the generalized fuzzy integral which is a fuzzy integral based on the idempotent pseudo addition supremum and a pseudo multiplication studied by xie and fang in 2006 the purpose of this study is to define the interval valued generalized fuzzy integral with respect to a fuzzy measure by means of an interval representable pseudo multiplication of measurable interval valued functions and to investigate some characterizations and convergence properties of them

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

locally constrained homomorphisms on graphs of bounded treewidth and bounded degree a homomorphism from a graph g to a graph h is locally bijective surjective or injective if its restriction to the neighborhood of every vertex of g is bijective surjective or injective respectively we prove that the problems of testing whether a given graph g allows a homomorphism to a given graph h that is locally bijective surjective or injective respectively are np complete even when g has pathwidth at most 5 4 or 2 respectively or when both g and h have maximum degree 3 we complement these hardness results by showing that the three problems are polynomial time solvable if g has bounded treewidth and in addition g or h has bounded maximum degree

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

aggregating membership values by a choquet fuzzy integral based operator a new type of aggregator the choquet fuzzy integral based operator is introduced and applied in aggregation of membership values in this paper we generalized the definition of the fuzzy integral as a tool for membership aggregation the generalization involves replacing the max or min operator in information integration with a choquet fuzzy integral based aggregator resulting in increased flexibility the characteristics of the choquet fuzzy integral are studied and a two phase aggregating process is proposed also we demonstrate a good classification result using the proposed aggregator to integrate the memberships of several clusters in a complex unconstrained handwritten digit recognition domain

an interpretation of fuzzy measures and the choquet integral as an integral with respect to a fuzzy measure abstract in this paper the non additivity of sugeno s fuzzy measures is interpreted in terms of addition and the rationality of the choquet integral is discussed it is pointed out that a fuzzy measure on a set x expresses the interaction between the subsets of x and can be represented by an additive measure it is shown through concrete examples that the choquet integral is reasonable as an integral with respect to a fuzzy measure it is also found that the choquet integral is closely related with the representation of a fuzzy measure

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

a complete complexity classification of the role assignment problem in social network theory a society is often represented by a simple graph g where vertices stand for individuals and edges represent relationships between those individuals the description of the social network is tried to be simplified by assigning roles to the individuals such that the neighborhood relation is preserved formally for a fixed graph r we ask for a vertex mapping r vg vr such that r ng u nr r u for all u vg if such a mapping exists the graph g is called r role assignable and the corresponding decision problem is called the r role assignment problem kristiansen and telle conjectured that the r role assignment problem is an np complete problem for any simple connected graph r on at least three vertices in this paper we prove their conjecture in addition we determine the computational complexity of the role assignment problem for nonsimple and disconnected role graphs as these are considered in social network theory as well

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

a note on convergence properties of interval valued capacity functionals and choquet integrals based on the classical theory of random sets feng and nguyen 2007 5 studied the convergence of capacity functionals of random sets in terms of choquet integrals in this paper we consider an interval valued capacity functional which is motivated by the goal to generalize a capacity functional and the choquet integral with respect to an interval valued capacity in particular we discuss some convergence theorems for interval valued capacity functionals and interval valued probability measures in the hausdorff metric and choquet weak sense

non monotonic fuzzy measures and the choquet integral abstract this paper discusses non monotonic fuzzy measures which are set functions without monotonicity and the choquet integral with respect to non monotonic fuzzy measures a concrete example shows that the choquet integral is meaningful in the case of non monotonic fuzzy measures as well as in the case of ordinary fuzzy measures every comonotonically additive positively homogeneous functional of bounded variation can be represented as a choquet integral with respect to a non monotonic fuzzy measure of bounded variation the space of such functionals is a real banach space isometrically isomorphic to the space of non monotonic fuzzy measures of bounded variation

computing role assignments of chordal graphs in social network theory a simple graph g is called k role assignable if there is a surjective mapping that assigns a number from 1 k called a role to each vertex of g such that any two vertices with the same role have the same sets of roles assigned to their neighbors the decision problem whether such a mapping exists is called the k role assignment problem this problem is known to be np complete for any fixed k 2 in this paper we classify the computational complexity of the k role assignment problem for the class of chordal graphs we show that for this class the problem can be solved in linear time for k 2 but remains np complete for any k 3 this generalizes earlier results by sheng and answers her open problem

extensions of the conformal representations for orthogonal lie algebras abstract the conformal transformations with respect to the metric defining o n c give rise to an inhomogeneous polynomial representation of o n 2 c using shen s technique of mixed product we generalize the above representation to an inhomogeneous representation of o n 2 c on the tensor space of any finite dimensional irreducible o n c module with the polynomial space where a hidden central transformation is involved moreover we find a condition on the constant value taken by the central transformation such that the generalized representation is irreducible in our approach pieri s formulas invariant operators and the idea of kostant s characteristic identities play key roles the result could be useful in understanding higher dimensional conformal field theory with the constant value taken by the central transformation as the central charge our representations virtually provide natural extensions of the conformal transformations on a riemannian manifold to its vector bundles

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

generalized projective representations for sl n 1 it is well known that n dimensional projective group gives rise to a non homogeneous representation of the lie algebra sl n 1 on the polynomial functions of the projective space using shen s mixed product for witt algebras also known as larsson functor we generalize the above representation of sl n 1 to a non homogeneous representation on the tensor space of any finite dimensional irreducible gl n module with the polynomial space moreover the structure of such a representation is completely determined by employing projection operator techniques and well known kostant s characteristic identities for certain matrices with entries in the universal enveloping algebra in particular we obtain a new one parameter family of infinite dimensional irreducible sl n 1 modules which are in general not highest weight type for any given finite dimensional irreducible sl n module the results could also be used to study the quantum field theory with the projective group as the symmetry

the general pettis sugeno integral of vector multifunctions relative to a vector fuzzy multimeasure abstract in this paper we define and study the general pettis sugeno integral of a vector multifunction relative to a vector fuzzy multimeasure both taking values in a locally convex space x ordered by a closed convex pointed cone x with nonempty interior several classic properties of this integral and some estimation and comparative results with the pettis lebesgue integral are established

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

computing role assignments of split graphs a k role assignment of a simple graph g is a surjective function r v g 1 k where r u u n u r v v n v for every pair u v v g with r u r v this concept appears in the context of social networks it is known that the problem of finding a 2 role assignment of chordal graphs can be solved in linear time and that deciding whether a graph of this class admits a k role assignment for any fixed k 3 is np complete in this work we investigate this problem on split graphs a subclass of chordal graphs we characterize the split graphs admitting a 3 role assignment such result leads to a linear time algorithm for this case furthermore we prove that deciding whether a split graph has a k role assignment is np complete for any fixed k 4

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

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

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

space of fuzzy measures and convergence the convergences of the net generalized sequence of fuzzy measures are discussed it is shown that three types of convergence are not equivalent in general case however they are equivalent if the universal set is finite

characterization and comparison of sugeno and choquet integrals abstract starting from the concept of equiordered functions we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure sugeno and choquet integrals the characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals pointing out their formal similarities and their conceptual differences

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

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

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

irreducible representations of the lie algebra of the diffeomorphisms of ad dimensional torus in this paper we investigate the irreducibility of certain modules for the lie algebra of diffeomorphisms of torus t the lie algebra of diffeomorw 1 1 x phisms can be described as the derivations of a s c t t see 1 d w x w x rss we denote this lie algebra by der a larsson l1 constructed a functor from gl modules to der a modules in this paper we prove that d the image of a finite dimensional irreducible gl module is most often d irreducible the only exceptions are fundamental modules and the onedimensional modules in these cases we describe the sub modules and the quotients surprisingly the same class of modules image of finite dimen w x sional gl module are also constructed in e without any reference to d gl modules they are motivated by the vertex operator constructions in d w x em more details near the end of this introduction we will now describe our results in more detail let gl be the d lie algebras of d d matrices over complex numbers c let gl s sl d d c id where sl is the finite dimensional simple lie algebra of trace zero d matrices and id the identity matrix which is central it is well known that finite dimensional irreducible modules and dominant integral weights are in one one correspondence for a finite dimensional simple lie algebra so let v c be finite dimensional irreducible sl module corresponding to a d dominant integral weight c let id the central element act by a complex number b and denote the corresponding gl module by v c b d a d d larsson defined see 1 6 a functor f for a belonging to c rz from w x gl modules to der a modules in l1 these modules are weight modules d

fuzzy t conorm integral with respect to fuzzy measures generalization of sugeno integral and choquet integral abstract this article discusses integrals with respect to sugeno s fuzzy measures sugeno integrals and choquet integrals with respect to general fuzzy measures are generalized in the setting of a t conorm algebraic system first t conorm integrals with respect to decomposable measures based on t conorm algebraic system are defined they are a modification of the weber integral secondly they are extended to fuzzy t conorm integrals with respect to general fuzzy measures the extension is made in the same way as the extension of the lebesgue integral to the choquet integral the class of fuzzy t conorm integrals includes choquet integrals and sugeno integrals properties of the integrals especially their representation are discussed

fuzzy measures and measures of fuzziness abstract in this paper the fuzzy integral defined by z x wang fuzzy math wuhan china in press which is different from that defined by m sugeno theory of fuzzy integrals and its applications ph d tokyo inst of technology 1974 is further considered and it is shown that the fuzzy measures of ordinary sets and fuzzy sets can be determined by each other summing up the results on the measure of fuzziness by a deluca and s a termini inform and control 20 1972 301 312 z x wang op cit and r r yager internat j gen systems 5 1979 221 229 inform and control 44 1980 236 260 the axioms for measures of fuzziness are given furthermore as an application of the furry integrals a measure of fuzziness is defined inversely it is proven that a measure of fuzziness satisfying some conditions can surely be expressed as a fuzzy integral with respect to some fuzzy measure

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

non atomicity for fuzzy and non fuzzy multivalued set functions in this paper we extend the concept of set valued fuzzy measures introduced and studied by guo and zhang 2004 on set valued fuzzy measures information sciences 160 2004 13 25 to the class of multivalued set functions taking values in the family of non empty closed subsets of a real normed space also we introduce the notions of atom and non atomicity of a multivalued set function and present some of their properties we also establish an extension result by preserving non atomicity for a fuzzy multisubmeasure multimeasure

strong integral of multifunctions relative to a fuzzy measure abstract in this paper we define and study an integral for measurable multifunctions taking values in the family of all nonvoid subsets of 0 with respect to a fuzzy measure unlike various ways of defining such an integral e g aumann way using different selections dunford way riemann way we use the sugeno method directly applied to multifunctions the originality of our definition is that the value of the integral is a real scalar and not usually a set some classical integral properties a convergence theorem and relationships with other integrals are presented