spectral shift functions and dirichlet to neumann maps the spectral shift function of a pair of self adjoint operators is expressed via an abstract operator valued titchmarsh weyl m function this general result is applied to different self adjoint realizations of second order elliptic partial differential operators on smooth domains with compact boundaries and schrodinger operators with compactly supported potentials in these applications the spectral shift function is determined in an explicit form with the help of energy parameter dependent dirichlet to neumann maps

multiplicity one theorems the archimedean case let g be one of the classical lie groups gln 1 r gln 1 c u p q 1 o p q 1 on 1 c so p q 1 son 1 c and let g 0 be respectively the subgroup gln r gln c u p q o p q on c so p q son c embedded in g in the standard way we show that every irreducible casselman wallach representation of g 0 occurs with multiplicity at most one in every irreducible casselman wallach representation of g similar results are proved for the jacobi groups gln r nh2n 1 r gln c n h2n 1 c u p q nh2p 2q 1 r sp2n r nh2n 1 r sp2n c nh2n 1 c with their respective subgroups gln r gln c u p q sp2n r and sp2n c

random fuzzy dependent chance programming and its hybrid intelligent algorithm abstract a fuzzy random variable is a measurable function from a probability space to a collection of fuzzy sets while a random fuzzy variable is a function from a collection of random variables to 0 1 this paper provides a spectrum of random fuzzy dependent chance programming in which the underlying philosophy is based on selecting the decision with maximal chance to meet the event in order to speed up the solution process we train a neural network to approximate chance functions based on the training data generated by the random fuzzy simulation finally we integrate random fuzzy simulation neural network and genetic algorithm to produce a more powerful and effective hybrid intelligent algorithm for solving random fuzzy dependent chance programming models and illustrate its effectiveness by some numerical examples

on fuzzy random linear programming abstract the fuzzy random linear programming having fuzzy random variable coefficients and the decision vector of fuzzy pseudorandom variables is studied the first results show the fact that a fuzzy pseudorandom resp fuzzy random optimization solution of a fuzzy random linear programmings the subsequent conclusions present methods random optimization solutions of relative random linear programmings the subsequent conclusions present methods that a fuzzy pseudorandom resp fuzzy random optimization solution of a fuzzy random linear programming is structured by a class of pseudorandom resp random optimization solutions of relative random linear programmings finally some theorems are proved which solve the problems finding the fuzzy probability distribution function and fuzzy mathematical expectation of optimization value for a fuzzy random linear programming these results reveal properties of a fuzzy random linear programming and give the solution for a fuzzy random linear programming

fuzzy random programming with equilibrium chance constraints to model fuzzy random decision systems this paper first defines three kinds of equilibrium chances via fuzzy integrals in the sense of sugeno then a new class of fuzzy random programming problems is presented based on equilibrium chances also some convex theorems about fuzzy random linear programming problems are proved the results provide us methods to convert primal fuzzy random programming problems to their equivalent stochastic convex programming ones so that both the primal problems and their equivalent problems have the same optimal solutions and the techniques developed for stochastic convex programming can apply after that a solution approach which integrates simulations neural network and genetic algorithm is suggested to solve general fuzzy random programming problems at the end of this paper three numerical examples are provided since the equivalent stochastic programming problems of the three examples are very complex and nonconvex the techniques of stochastic programming cannot apply in this paper we solve them by the proposed hybrid intelligent algorithm the results show that the algorithm is feasible and effectiveness

the theory of fuzzy stochastic processes abstract in this paper we deal with the general theory of fuzzy stochastic processes we give the suitable definitions of fuzzy random function fuzzy stochastic process and their fall shadow distribution functions the concepts of separability and measurability of a fuzzy random function are introduced and some properties of these new concepts are derived we investigate the continuity of fuzzy sample function of a fuzzy stochastic process

fuzzy decision making for fuzzy random multiobjective linear programming problems with variance covariance matrices we focus on fuzzy random multiobjective linear programming problems with variance covariance matrices and propose a fuzzy decision making method to obtain a satisfactory solution in the proposed method it is assumed that the decision maker has fuzzy goals for both permissible levels and the corresponding objective functions for a probability maximization model or a fractile optimization model and that such fuzzy goals are quantified by eliciting the corresponding membership functions the satisfactory solution based on the fuzzy decision is obtained using the bisection method and the convex programming technique

interactive multiobjective fuzzy random programming through the level set based probability model this paper considers a multiobjective linear programming problem involving fuzzy random variable coefficients a new fuzzy random programming model is proposed by extending the ideas of level set based optimality and a stochastic programming model the original problem involving fuzzy random variables is transformed into a deterministic equivalent problem through the proposed model an interactive algorithm is provided to obtain a satisficing solution for a decision maker from among a set of newly defined pareto optimal solutions it is shown that an optimal solution of the problem to be solved iteratively in the interactive algorithm is analytically obtained by a combination of the bisection method and the simplex method

building confidence interval based fuzzy random regression models in real world regression analysis statistical data may be linguistically imprecise or vague given the co existence of stochastic and fuzzy uncertainty real data cannot be characterized by using only the formalism of random variables in order to address regression problems in the presence of such hybrid uncertain data fuzzy random variables are introduced in this study to serve as an integral component of regression models a new class of fuzzy regression models that is based on fuzzy random data is built and is called the confidence interval based fuzzy random regression model ci frrm first a general fuzzy regression model for fuzzy random data is introduced then using expectations and variances of fuzzy random variables sigma confidence intervals are constructed for fuzzy random input output data the ci frrm is established based on the sigma confidence intervals the proposed regression model gives rise to a nonlinear programming problem that consists of fuzzy numbers or interval numbers since sign changes in the fuzzy coefficients modify the entire programming structure of the solution process the inherent dynamic nonlinearity of this optimization makes it difficult to exploit the techniques of linear programming or classical nonlinear programming therefore we resort to some heuristics finally an illustrative example is provided

trace formulas for additive and non additive perturbations abstract trace formulas for pairs of self adjoint maximal dissipative and accumulative as well as other types of resolvent comparable operators are obtained in particular the existence of a complex valued spectral shift function for a pair h h of maximal accumulative operators has been proved we investigate also the existence of a real valued spectral shift function moreover we treat in detail the case of additive trace class perturbations assuming that h and h h v are maximal accumulative and v is trace class we prove the existence of a summable complex valued spectral shift function we also obtain trace formulas for pairs h h assuming only that h and h are resolvent comparable in this case the determinant of the characteristic function of h is involved in trace formulas the results rely on the technique of boundary triplets for densely and non densely defined closed symmetric operators the approach allows to express the spectral shift function of a pair of extensions in terms of the abstract weyl function and the boundary operator we improve and generalize certain classical results of m g kre n for pairs of self adjoint and dissipative operators results of a v rybkin for such pairs as well as of v m adamjan b s pavlov and m g kre n for pairs h h with a maximal dissipative operator h

satisfying solutions for a possibilistic linear program abstract a branch and bound scheme is described for tackling a linear program under discrete possibilistic data we grapple also with the continuous case via recent results on inexact and semiinfinite programming it is shown that solutions yielded by these techniques are satisfying i e possibly and or necessarily feasible and optimal to a great extent finally approaches reported here and elsewhere are appraised in the light of their decision making philosophies and some directions for further developments indicated

on solutions and distribution problems of the linear programming with fuzzy random variable coefficients abstract this paper studies the solution method and distribution problems for two kinds of linear programming with fuzzy random variable coefficients some concepts of solutions for example the fuzzy pseudo random optimization solution are introduced for these new programming problems we prove some equivalent theorems that transform the fuzzy random programming problems into a series of random programming problems by using the simplex method of linear programming with random variable coefficients we give the solution method of linear programming with fuzzy random variable coefficients the formulas of probability distribution function projective distribution function and expectation on these new programmings are presented

on solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem in this paper a multiobjective quadratic programming problem fuzzy random coefficients matrix in the objectives and constraints and the decision vector are fuzzy variables is considered first we show that the efficient solutions fuzzy quadratic multiobjective programming problems series optimal solutions of relative scalar fuzzy quadratic programming some theorems are to find an optimal solution of the relative scalar quadratic multiobjective programming with fuzzy coefficients having decision vectors as fuzzy variables an application fuzzy portfolio optimization problem as a convex quadratic programming approach is discussed and an acceptable solution to such problem is given at the end numerical examples are illustrated in the support of the obtained results

on maass lifts and the central critical values of triple product l functions we express certain period integrals of maass lifts which appear in the gross prasad conjecture in terms of the central critical values of triple product l functions in the imbalanced case

fuzzy optimization an appraisal abstract this paper takes a general look at core ideas that make up the burgeoning body of fuzzy mathematical programming emphasizing the methodological view although fuzzy mathematical programming has enjoyed a rapidly increasing acceptance within the scientific community some technical hurdles exist to hinder a unanimity reasons for this as well as possible ways for improvement are also discussed

fuzzy random reliability of structures based on fuzzy random variables abstract using fuzzy random variables as basic variables the relationship between fuzzy random variables and fuzzy random events is established in this paper formulas of measures of a fuzzy random event and its cut set are presented the fuzzy random reliability of structures is defined on the basis of fuzzy measure and fuzzy integral further by using fuzzy random variables the fuzzy random failure function of structures is defined and the fuzziness between structural reliable state and failure state is also analyzed moreover the fuzzy random limit state equation of structures is built the probability calculation method of structural reliability under the reliable level is given finally the calculation procedures of structural fuzzy random reliability is proposed

fuzzy rule based models with randomized development mechanisms abstract fuzzy rule based models have attracted attention because of their modular architectures well developed design methodologies and practices as well as interpretability aspects methods exploiting factors of randomness offer significant efficiency and implementation simplicity that are essential in numerous application areas in this study we propose an original development of fuzzy rule based models established with the aid of concepts of randomization algorithms several design strategies involving different random prototypes generation and basis functions approximation are studied we investigate performance aspects of randomized rule base and look at the performance versus the key components of the models such as the number of rules and the use of the randomized algorithms in the development furthermore a comparative study is offered to quantify the efficiency of randomized algorithms experimental studies are reported for a series of publicly available data sets to illustrate the effectiveness of the proposed method and discuss its main features

spectral shift function of higher order this paper resolves affirmatively koplienko s sib mat zh 25 62 71 1984 conjecture on existence of higher order spectral shift measures moreover the paper establishes absolute continuity of these measures and thus existence of the higher order spectral shift functions a spectral shift function of order n is the function n n h v such that operatorname tr biggl f h v sum k 0 n 1 frac 1 k frac d k dt k bigl f h tv bigr bigg t 0 biggr int mathbb r f n t eta n t dt for every sufficiently smooth function f where h is a self adjoint operator defined in a separable hilbert space and v is a self adjoint operator in the n th schatten von neumann ideal sn existence and summability of 1 and 2 were established by krein mat sb 33 597 626 1953 and koplienko sib mat zh 25 62 71 1984 respectively whereas for n 2 the problem was unresolved we show that n h v exists integrable and vert eta n vert l 1 mathbb r leq c n vert v vert s n n for some constant cn depending only on n our results for n rely on estimates for multiple operator integrals obtained in this paper our method also applies to the general semi finite von neumann algebra setting of the perturbation theory

the iwasawa main conjectures for gl2 we prove the one two and three variable iwasawa greenberg main conjectures for a large class of modular forms that are ordinary with respect to an odd prime p the method of proof involves an analysis of an eisenstein ideal for ordinary hida families for gu 2 2

inequality relation between fuzzy numbers and its use in fuzzy optimization the inequality relation between two fuzzy numbers is investigated a certain type of such a relation motivated by practical interpretation is proposed and its correspondence with the usual lattice type relation generated by the extended maximum and minimum operators and its possible interpretation are discussed the concept of r l fuzzy number is introduced the class of all r l fuzzy numbers covering practically the whole set of normal convex fuzzy numbers comparing two r l fuzzy numbers of the same type the relation introduced in the paper may be replaced by four ordinary inequalities this fact may be taken advantage of in optimization problems with linear fuzzy constraints

stackelberg solutions for fuzzy random two level linear programming through probability maximization with possibility this paper considers stackelberg solutions for decision making problems in hierarchical organizations under fuzzy random environments taking into account vagueness of judgments of decision makers fuzzy goals are introduced into the formulated fuzzy random two level linear programming problems on the basis of the possibility and necessity measures that each objective function fulfills the corresponding fuzzy goal together with the introduction of probability maximization criterion in stochastic programming we propose new two level fuzzy random decision making models which maximize the probabilities that the degrees of possibility and necessity are greater than or equal to certain values through the proposed models it is shown that the original two level linear programming problems with fuzzy random variables can be transformed into deterministic two level linear fractional programming problems for the transformed problems extended concepts of stackelberg solutions are defined and computational methods are also presented a numerical example is provided to illustrate the proposed methods

motives and siegel modular forms for a motive m over q we define the fundamental periods of m using invariant theory our definition generalizes deligne s periods we show that if a motive m is constructed from motives m 1 m 2 m n by a standard algebraic operation then the fundamental periods of m can be expressed as monomials of the fundamental periods of m 1 m 2 m n applying this theory we discuss two hypothetical motives attached to a siegel modular form we show that a siegel modular form of degree m has at most m 1 period invariants

multiplicity one theorems in the local characteristic 0 non archimedean case we consider distributions on gl n 1 which are invariant under the adjoint action of gl n we prove that such distributions are invariant by transposition this implies multiplicity at most one for restrictions from gl n 1 to gl n similar theorems are obtained for orthogonal or unitary groups

on fuzzy random multiobjective quadratic programming in this paper a multiobjective quadratic programming problem having fuzzy random coefficients matrix in the objective and constraints and the decision vector are fuzzy pseudorandom variables is considered first we show that the efficient solutions of fuzzy quadratic multiobjective programming problems are resolved into series optimal solutions of relative scalar fuzzy quadratic programming some theorems are proved to find an optimal solution of the relative scalar quadratic multiobjective programming with fuzzy coefficients having decision vectors as fuzzy variables at the end numerical examples are illustrated in the support of the obtained results

koplienko spectral shift function on the unit circle the note shows that for every pair of contractions a trace formula of koplienko holds with a summable spectral shift function see theorem 1 below this answers a question by f gesztesy a pushnitski b simon see zh mat fiz anal geom 4 1 63 107 202 2008 open question 11 2

fuzzy approaches for multiple objective linear fractional optimization abstract the problem of finding a solution to a multiple objective linear fractional program arises in several real world situations in this paper we advocate that fuzzy sets theory provides a basis for solving this problem with sufficient consistency and rigorousness after representing imprecise aspirations of the decision maker by structured linguistic variables or converting the original problem via approximations or change of variables into a multiple objective linear program techniques of fuzzy linear programming may be used to reach a satisfactory solution it is shown that under reasonable restrictions this solution is efficient pareto optimal for the original problem numerical examples are also included for illustration

on tensor product l functions for quaternion unitary groups and gl 2 over totally real number fields mixed weight cases abstract we prove an algebraicity of special values of tensor product l functions for quaternion unitary groups and gl 2 in the mixed weight cases over any totally real number field as a consequence we can prove a period relation for automorphic forms of quaternion unitary groups of degree 2 and gsp 4 when these automorphic forms correspond under the conjectural jacquet langlands correspondence and a period relation for endoscopic liftings of gsp 4 in very general situations

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

some remarks on triple l functions we extend the garrett s result i 4 concerning triple l function in two aspects one concerns triple l functions of different weights and the other concerns special values of triple l functions of same weights at inner points of their critical strips let mk fn and sk fn be spaces of siegel modular forms and cuspforms of weight k and of degree n respectively for siegel modular forms f l fro of various degree and a field k we denote by k ft fro the field generated by all the fourier coefficients of f l fro over k we write fourier expansion of f sk f1

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

multiple objective linear fractional programming a fuzzy set theoretic approach abstract a method for optimizing a multiobjective linear fractional programming problem is developed which yields always an efficient solution

the use of parametric programming in fuzzy linear programming in this paper the possibility of the identification of a complete fuzzy decision not only the maximizing alternative in fuzzy linear programming by use of the parametric programming technique is presented also it is shown that this fact can be useful in the zimmermann approach to multiple objective linear programming the presented remarks are illustrated by some numerical examples

a parametric approach to fuzzy linear programming in this paper we discuss how to deal with decision problems that are described with lp models and formulated with elements of imprecision and uncertainty more precisely we will study lp models in which the parameters are not fully known but only with some degree of precision even with incomplete information the model builder or model user is normally able to give a realistic interval for the parameters of an lp model for the constraint vector this is combined with some wishes or some leeway on the constraints even with ambiquity in the objective function there is normally some preference ordering to be found among alternative ways of action we will demonstrate that these modelling complications can be handled with the help of some results developed in the theory of fuzzy sets after an overview of some central contributions to fuzzy linear programming we will develop an lp model in which the parameters are not fully known only with some degree of precision and show that the model can be parametrised in such a way that the optimal solution becomes a function of the degree of precision the fuzzy lp model derived in this way appears to be fairly easy to handle computationally which is demonstrated with a numerical example

on fully operator lipschitz functions abstract let a d be the disc algebra of all continuous complex valued functions on the unit disc d holomorphic in its interior functions from a d act on the set of all contraction operators a 1 on hilbert spaces it is proved that the following classes of functions from a d coincide 1 the class of operator lipschitz functions on the unit circle t 2 the class of operator lipschitz functions on d and 3 the class of operator lipschitz functions on all contraction operators a similar result is obtained for the class of operator c 2 lipschitz functions from a d

optimisation under hybrid uncertainty abstract fuzzy stochastic optimisation is emerging as a subfield of mathematical programming the disciplinary matrix of which consists of analysis of mathematical programs under fuzziness and randomness along with methods for solving them the primum movens of this paper is to describe a unifying methodological approach that is suitable for finding a satisfying solution of a mathematical program in the presence of fuzzy data and random variables properties of fuzzy random variables frvs serve as the backdrop to this approach which also lends itself better to handling mathematical programs with fuzzy random coefficients for the paper to be somewhat self contained the notion of frv is briefly discussed and a synopsis of fuzzy stochastic optimisation provided a systematically solved example aimed at illustrating the proposed approach is also included

interactive random fuzzy two level programming through possibility based probability model this paper considers interactive decision making methods for random fuzzy two level linear programming problems assuming that the decision makers concern about the probabilities that their own objective function values are smaller than or equal to certain target values fuzzy goals of the decision makers for the probabilities are introduced then the possibility based probability model to maximize the degrees of possibility with respect to the attained probability is considered interactive fuzzy nonlinear programming to obtain a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented an illustrative numerical example demonstrates the feasibility and efficiency of the proposed method

an extension of the koplienko neidhardt trace formulae abstract koplienko sibirsk mat zh 25 5 1984 62 found a trace formula for perturbations of self adjoint operators by operators of hilbert schmidt class s 2 a similar formula in the case of unitary operators was obtained by neidhardt math nachr 138 1988 7 in this paper we improve their results and obtain sharp conditions under which the koplienko neidhardt trace formulae hold

multiobjective possibilistic linear programming abstract this paper presents two solutions to multiobjective linear programs when all the parameters may be fuzzy variables whose values are restricted by a possibility distribution in the first solution we first find possibility distribution of the objective function and then a solution consists of those values of the decision variables which produce the largest undominated values of the objective function where these values also have maximum possibility in the second solution we first find the possibility distribution of the undominated sets and then a solution consists of those values of the decision variables which are undominated with maximum possibility but also produce the largest undominated values of the objective function for certain multiobjective possibilistic linear programs we show that the two solution concepts are identical

on special values of certain l functions we prove an algebraicity result concerning special values at critical points in the sense of deligne of tensor product l functions associated to automorphic representations of special orthogonal groups for quadratic forms which are totally definite and cuspidal representations of rm gl 2 corresponding to primitive cusp forms over totally real number fields we also prove the reciprocity law i e the equivariance under the action of rm gal overline bbb q bbb q for the special values in the appendix the second author calculates the deligne periods for such l functions assuming the existence of corresponding motives and the automorphic transfer to a quasi split form of the special orthogonal group our result conforms with the celebrated conjecture of deligne on special values of motivic l functions

on the arithmetic of shalika models and the critical values of l functions for gl2n let pi be a cohomological cuspidal automorphic representation of rm gl 2n bbb a over a totally real number field f suppose that pi has a shalika model we define a rational structure on the shalika model of pi f comparing it with a rational structure on a realization of pi f in cuspidal cohomology in top degree we define certain periods omega epsilon pi f we describe the behavior of such top degree periods upon twisting pi by algebraic hecke characters chi of f then we prove an algebraicity result for all the critical values of the standard l functions l s pi otimes chi here we use the recent work of b sun on the non vanishing of a certain quantity attached to pi infty as applications we obtain algebraicity results in the following cases firstly for the symmetric cube l functions attached to holomorphic hilbert modular cusp forms we also discuss the situation for higher symmetric powers secondly for certain self dual of symplectic type rankin selberg l functions for rm gl 3 times rm gl 2 assuming langlands functoriality this generalizes to certain rankin selberg l functions of rm gl n times rm gl n 1 thirdly for the degree four l functions attached to siegel modular forms of genus 2 and full level moreover we compare our top degree periods with periods defined by other authors we also show that our main theorem is compatible with conjectures of deligne and gross

interactive fuzzy linear programming abstract in this study an interactive fuzzy linear programming approach is investigated to improve the flexibility and robustness of linear programming lp technique this paper provides a practical modelling method which is a symmetric integration of zimmermann s werners s vergegay s and chanas s fuzzy lp approaches and additionally provides a decision support system for solving a specific domain of practical lp problems the interactive concept provides a learning process about the system whereby the decision maker can learn to recognize good solutions relative importance of factors in the system and then design a high productivity system instead of optimizing a given system this interactive fuzzy lp system provides integration oriented adaptation and learning features by considering all the possibilities of a specific domain of lp problems which are integrated in logical order using an if then rule

value at risk methodology under soft conditions approach fuzzy stochastic approach the paper describes methodology of dealing with financial modelling under uncertainty with risk and vagueness aspects an approach to modelling risks by the value at risk methodology under imprecise and soft conditions is solved it is supposed that the input data and problem conditions is difficult to determine as real numbers or as some precise distribution function thus vagueness is modelled through the fuzzy numbers of the linear t number type the combination of risk and vagueness is solved by fuzzy stochastic methodology illustrative example is introduced

fuzzy linear fractional goal programming applied to refinery operations planning abstract chemical process plant operations planning in an oil refinery has been modelled as fuzzy linear fractional multiple goal programming problem a variant of the fuzzy linear fractional goal programming model of dutta et al fuzzy sets and systems 52 1992 39 45 has been developed and used in the present study to solve the problem which has two fuzzy fractional goals and 22 crisp constraints linear membership functions have been assumed and min operator has been used as the aggregator linguistic variable has been taken as close throughout the paper following dutta et al 1992 a software has been developed in turbo c to implement the model the software takes the parameters defining the fuzziness and crisp data from the input field and solves the crisp equivalent to the fuzzy linear fractional goal programming problem the parameters defining fuzziness are subjectively chosen by the user decision maker the software finally outputs satisfying decision variables satisfying fuzzy fractional goal values optimal values of the profit numerator and the capacities of the primary unit and cracker denominators which are involved in the fuzzy fractional goals the results indicate that the present model yielded a more efficient solution compared to the crisp solution of allen british chem eng 16 1971 685 691 as far as the fractional objectives are concerned this demonstrates the efficacy of the present model however a paltry decrement of 1 3 in the profit is noticed in the present study in comparison to the crisp solution of allen 1971

on a fuzzy set approach to solving multiple objective linear fractional programming problem in 1984 luhandjula used a linguistic variable approach in order to present a procedure for solving multiple objective linear fractional programming problem molfpp in 1992 dutta et al fuzzy sets and systems 52 1 1992 39 45 modified the linguistic approach of luhandjula such as to obtain efficient solution to problem molfpp the aim of this paper is to point out certain shortcomings in the work of dutta et al and give the correct proof of theorem which validates the obtaining of the efficient solutions we notice that the method presented there as a general one does only work efficiently if certain hypotheses restrictive enough and hardly verified are satisfied the example considered by dutta et al is again used to illustrate the approach

feasibility and pareto optimality for multiobjective nonlinear programming problems with fuzzy parameters abstract in this paper we focus on multiobjective nonlinear programming problems with fuzzy parameters and extend the ordinary feasibility and pareto optimality concepts based on the concepts of possibility and necessity for fuzzy numbers using the four indices for ranking two fuzzy numbers four types of feasibility and pareto optimality are defined and the relationships among them are examined in detail these concepts can be viewed as quite generalized versions of the well known feasibility and pareto optimality concepts and the generalized pareto optimal solutions for the multiobjective nonlinear programming problems with fuzzy parameters may be obtained on the basis of the method of nonlinear programming

an interactive fuzzy satisficing method for multiobjective stochastic linear programming problems through an expectation model abstract for decision making problems involving uncertainty both stochastic programming as an optimization method based on the theory of probability and fuzzy programming representing the ambiguity by fuzzy concept have been developing in various ways in this paper we focus on multiobjective linear programming problems with random variable coefficients in objective functions and or constraints for such problems as a fusion of these two approaches after incorporating fuzzy goals of the decision maker for the objective functions we propose an interactive fuzzy satisficing method for the expectation model to derive a satisficing solution for the decision maker an illustrative numerical example is provided to demonstrate the feasibility of the proposed method

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

perturbation formulas for traces on normed ideals we prove perturbation results for traces on normed ideals in semifinite von neumann algebra factors this includes the case of dixmier traces in particular we establish existence of spectral shift measures with initial operators being dissipative or bounded and show that these measures can have singular components in the case of dixmier traces we also establish a linearization formula for a dixmier trace applied to perturbed operator functions a result that does not typically hold for normal traces

fuzzy random variable valued exponential function logarithmic function and power function this paper introduces concepts of fuzzy random variable valued exponential function logarithmic function and power function their fundamental properties are also discussed