optimal multinational capital budgeting under uncertainty this paper discusses the multinational capital budgeting problem when there are some candidate foreign projects which project s should the investor choose in the paper special cash flows and value sources of foreign projects are introduced regarding project parameters such as construction costs annual net operating cash flows terminal values of the projects as well as the foreign exchange rates as uncertain variables the paper proposes one new uncertain zero one integer model for optimal multinational project selection to solve the problem a hybrid intelligent algorithm integrating the 99 methods and genetic algorithm is provided as an illustration an application example is also presented

satisficing solutions and duality in interval and fuzzy linear programming in this paper we introduce a class of fuzzy linear programming problems and define the concepts of feasible and satisficing solutions the necessary tools for dealing with such problems in this way we show that the class of crisp classical lp problems can be embedded into the class of flp ones moreover for flp problems we define the concept of duality and prove the weak and strong duality theorems further we define a class of interval linear programming problems as a special subclass of flp problems and apply the previous results to this special case

further results on invariance of the eigenvalues of matrix products involving generalized inverses abstract it is shown that if m n n n and p m complex matrices a b and c do not satisfy at least one of the range inclusions r a c r b and r ca r b then for each complex number there is a choice of a generalized inverse b such that this number is an eigenvalue of the product ab c combined with criteria derived by baksalary and puntanen 1990 and by baksalary and pukkila 1992 this result implies that the invariance of the magnitude largest eigenvalue and or the magnitude smallest nonzero eigenvalue of ab c respect to the choice of b is equivalent to the invariance of the set of all eigenvalues

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

fuzzy evaluation of cogeneration alternatives in a petrochemical industry this paper derives fuzzy net present value npv and pay back year pby models as decision indexes for cogeneration alternatives decision making the mellin transform is employed to establish the means and variances of the fuzzy indexes in order to rank various cogeneration alternatives it is noted that the mean and variance values depend only on the vertexes of the fuzzy index and are independent of their height the current paper verifies the performance of the proposed models by simulating two numerical examples and by considering a cogeneration program in a petrochemical industry it is shown that the results of the proposed fuzzy economic models are consistent with those of the conventional crisp models and that the developed concepts are straightforward and easily implemented compared to the fuzzy ranking methods proposed in previous studies furthermore the developed methods serve as readily implemented sensitivity analysis tools for use in the arena of uncertain decision making

alternative characterizations of the extended wedderburn guttman theorem let a be a u by v matrix of rank a and let m and n be u by p and v by q matrices respectively where p is not necessarily equal to q or rank m an min p q takane and yanai y takane h yanai on the wedderburn guttman theorem linear algebra appl 410 2005 267 278 investigated the conditions under which rank a an m an m a rank a rank an m an m a this is called the extended wedderburn guttman theorem in this paper we give alternative characterizations of these conditions using the product singular value decomposition psvd of matrix triplets

the fuzzy mathematics of finance this paper develops fuzzy analogues of the elementary compound interest problems in the mathematics of finance we find the fuzzy present value and fuzzy future value of fuzzy cash amounts using fuzzy interest rates over n periods where n may be crisp or fuzzy this paper also develops a method of comparing fuzzy net cash flows in order to rank fuzzy investment alternatives from best to worst

robust solutions of linear programming problems contaminated with uncertain data optimal solutions of linear programming problems may become severely infeasible if the nominal data is slightly perturbed we demonstrate this phenomenon by studying 90 lps from the well known netlib collection we then apply the robust optimization methodology ben tal and nemirovski 1 3 el ghaoui et al 5 6 to produce robust solutions of the above lps which are in a sense immuned against uncertainty surprisingly for the netlib problems these robust solutions nearly lose nothing in optimality

homogenization of an alternating robin neumann boundary condition via time periodic unfolding abstract we consider the homogenization of a parabolic problem in a perforated domain with robin neumann boundary conditions oscillating in time such oscillations must compensate the blow up of the boundary measure of the holes we use the technique of time periodic unfolding in order to obtain a macroscopic parabolic problem containing an extra linear term due to the absorption determined by the robin condition

a dual approach to solve the fuzzy linear programming problem abstract a concept of fuzzy objective based on the fuzzification principle is presented in accordance with this concept the fuzzy linear mathematical programming problem is easily solved a relationship of duality among fuzzy constraints and fuzzy objectives is given the dual problem of a fuzzy linear programming problem is also defined

duality in fuzzy linear programming with possibility and necessity relations a class of fuzzy linear programming flp problems with fuzzy coefficients based on fuzzy relations is introduced the concepts of feasible and a b maximal and minimal solutions are defined the class of crisp classical lp problems can be embedded into the class of flp ones moreover for flp problems a new concept of duality is introduced and the weak and strong duality theorems are derived the introduced concepts and results are illustrated and discussed on a simple numerical example

the price of robustness a robust approach to solving linear optimization problems with uncertain data was proposed in the early 1970s and has recently been extensively studied and extended under this approach we are willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes a concern with such an approach is that it might be too conservative in this paper we propose an approach that attempts to make this trade off more attractive that is we investigate ways to decrease what we call the price of robustness in particular we flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations an attractive aspect of our method is that the new robust formulation is also a linear optimization problem thus we naturally extend our methods to discrete optimization problems in a tractable way we report numerical results for a portfolio optimization problem a knapsack problem and a problem from the net lib library

homogenization results for a coupled system of reaction diffusion equations abstract the macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction diffusion processes in periodic porous media is analyzed our mathematical model can be used for studying several metabolic processes taking place in living cells in which biochemical species can diffuse in the cytosol and react both in the cytosol and also on the organellar membranes the coupling of the concentrations of the biochemical species is realized via various properly scaled nonlinear reaction terms these nonlinearities which model at the microscopic scale various volume or surface reaction processes give rise in the macroscopic model to different effects such as the appearance of additional source or sink terms or of a non standard diffusion matrix

fuzzy interval methods in investment risk appraisal abstract standard financial techniques neglect extreme situations and regards large market shifts as too unlikely to matter this approach may account for what occurs most of the time in the market but the picture it presents does not reflect the reality as major events happen in the residual time and investors are surprised by unexpected market movements an alternative fuzzy approach permits fluctuations well beyond the probability type of uncertainty and allows one to make fewer assumptions about the data distribution and market behaviour we suggest a fuzzy criterion and subsequently derive a measure of the risk associated with each investment opportunity and an estimate of the projects robustness towards market uncertainty the procedure is applied to 35 uk companies traded on the london stock exchange finally neural networks capabilities of approximating the fuzzy appraisal function are investigated as an initial step towards building a soft investment classifier based on the developed alternative ranking technique

more on maximal and minimal ranks of schur complements with applications the maximal and minimal ranks of the schur complement d cgb are determined with respect to generalized inverse g of a matrix a where g is taken respectively as least squares g inverse a 1 3 minimum norm g inverse a 1 4 as well as a 1 2 3 a 1 2 4 and a 1 3 4 various consequences are also presented

chance constrained programming models for capital budgeting with npv as fuzzy parameters in an uncertain economic environment experts knowledge about outlays and cash inflows of available projects consists of much vagueness instead of randomness investment outlays and annual net cash flows of a project are usually predicted by using experts knowledge fuzzy variables can overcome the difficulties in predicting these parameters in this paper capital budgeting problem with fuzzy investment outlays and fuzzy annual net cash flows is studied based on credibility measure net present value npv method is employed and two fuzzy chance constrained programming models for capital budgeting problem are provided a fuzzy simulation based genetic algorithm is provided for solving the proposed model problems two numerical examples are also presented to illustrate the modelling idea and the effectiveness of the proposed algorithm

homogenization of elliptic problems involving interfaces and singular data abstract we prove existence and homogenization results for a family of elliptic problems involving interfaces and a singular lower order term these problems model heat or electrical conduction in composite media

a new approach to the concept of a strong unified least squares matrix abstract for given matrices a b c and d of appropriate sizes a criterion for the range of the product ab c to be a subspace of the range of d irrespective of the choice of a generalized inverse b of b is established this result is crucial in a new approach to the concept of the strong unified least squares matrix which plays an essential role in the theory of estimation in the general gauss markov model

strong unified least squares matrices for a general linear model a necessary and sufficient condition is established for the range of a product ab c to be a subspace of the range of a matrix d irrespective of the choice of a generalized inverse b of b this result is applicable in establishing a characterization of strong unified least squares matrices for a general linear model

a robust approach to the decision rules of npv and irr for simple projects we propose a robust approach to the decision rules of net present value npv and internal rate of return irr by building an analogy between robust optimization approach proposed in the literature and decision rules of npv and irr by considering uncertainty in cash flows as proposed in the literature we assume that the parameters cash inflows and cash outflows in our case belong to a symmetric and bounded interval set and define a series of decision rules of npv and irr by considering robustness

a general model for fuzzy linear programming abstract in the current literature there are several models of fuzzy linear programming problems the aim of this paper is first to describe the more important problems in fuzzy linear programming and second to give a general model of fuzzy linear programming problems involving all of the above ones finally a resolution method for that general model is proposed

generalized and extended fuzzy sets with applications abstract this paper introduces generalized fuzzy sets extended fuzzy sets and generalized extended fuzzy sets and shows how these fuzzy sets may arise naturally in some applications the applications presented are chosen from the areas of decision theory hierarchical analysis and expert systems zadeh s method of reducing a level 2 fuzzy set to a regular fuzzy set is generalized to reduce some of these new fuzzy sets to simpler fuzzy sets what is needed then for applications is an algebra of irreducible generalized extended fuzzy sets

robust solutions to uncertain semidefinite programs in this paper we consider semidefinite programs sdps whose data depend on some unknown but bounded perturbation parameters we seek robust solutions to such programs that is solutions which minimize the worst case objective while satisfying the constraints for every possible value of parameters within the given bounds assuming the data matrices are rational functions of the perturbation parameters we show how to formulate sufficient conditions for a robust solution to exist as sdps when the perturbation is full our conditions are necessary and sufficient in this case we provide sufficient conditions which guarantee that the robust solution is unique and continuous holder stable with respect to the unperturbed problem s data the approach can thus be used to regularize ill conditioned sdps we illustrate our results with examples taken from linear programming maximum norm minimization polynomial interpolation and integer programming

a note on invariance of the eigenvalues singular values and norms of matrix products involving generalized inverses abstract it is shown that the set of singular values of the product ab c as well as any norm of this product is invariant with respect to the choice of a generalized inverse b if and only if ab c is invariant itself this is in contrast with the corresponding invariance property of the set of eigenvalues of ab c for which the invariance of ab c is not necessary

ranking alternatives using fuzzy numbers we investigate the problem of employing expert opinion to rank alternatives across a set of criteria the experts use fuzzy numbers to express their preferences and we employ fuzzy arithmetic to compute an issue s fuzzy ranking this leads to a partition of the alternatives into sets h1 h2 where h1 contains the highest ranked issues h2 has all the second highest ranked alternatives etc the total ranking process is shown to possess a number of important properties an example is presented to illustrate the method

rank invariance criterion and its application to the unified theory of least squares abstract necessary and sufficient conditions are established for the product ab c to have its rank invariant with respect to the choice of a generalized inverse b in particular cases these conditions coincide with the results of mitra they are discussed also in the statistical context of the unified theory of least squares introduced by rao

solving fuzzy equations in economics and finance abstract in this paper we apply our new solution procedure for solving fuzzy equations linear non linear differential to three problems in economics and finance the three applications are 1 leontief s input output model 2 the internal rate of return and 3 a dynamic supply demand model where price and supply are governed by a system of differential equations

on some matrix equalities for generalized inverses with applications abstract necessary and sufficient conditions are derived for the matrix equality a pn q to hold where a and n are generalized inverses of matrices some consequences and applications are also given in particular necessary and sufficient conditions are derived for the additive decompositions c a b and a a 1 a k to hold

invariance properties of a triple matrix product involving generalized inverses abstract given complex valued matrices a b and c of appropriate dimensions this paper investigates certain invariance properties of the product axc with respect to the choice of x where x is a generalized inverse of b different types of generalized inverses are taken into account the purpose of the paper is three fold first to review known results scattered in the literature second to demonstrate the connection between invariance properties and the concept of extremal ranks of matrices and third to add new results related to the topic

evaluating r d projects as investments by using an overall ranking from four new fuzzy similarity measure based topsis variants research and development r d project ranking as investments is a well known problem that is made difficult by incomplete and imprecise information about future project profitability this paper shows how profitability results of r d project evaluation with the fuzzy pay off method can be ranked with four new variants of fuzzy topsis each using a different fuzzy similarity measure an overall project ranking that incorporates the four new variants rankings with three different ideal solutions totaling 12 subrankings is presented the implementation of the created methods is illustrated with a numerical example

upper and lower bounds for ranks of matrix expressions using generalized inverses abstract the maximal and minimal ranks of the matrix expression a 1 b 1 x 1 c 1 b 2 x 2 c 2 with respect to x 1 and x 2 are presented as applications the maximal and minimal ranks of a 1 b 1 xc 1 subject to a consistent matrix equation b 2 xc 2 a 2 are also determined in addition the maximal and minimal ranks of the schur complement d ca b with respect to the generalized inverse a of a and their various consequences are also considered

an ant colony optimization approach for binary knapsack problem under fuzziness in this paper we represent a novel ant colony optimization algorithm to solve binary knapsack problem in the proposed algorithm for n objects n candidate groups are created and each candidate group has exactly m values for m ants as 0 or 1 for each candidate value in each group a pheromone is initialized by the value between 0 1 and 0 9 and each ant selects a candidate value from each group therefore the binary solution is generated by each ant by selecting a value from each group in each generation pheromone update and evaporation is done during the execution of algorithm after certain number of generation the best solution is stored as a temporary population after that crossover and mutation is performed between the solution generated by ants we consider profit and weight are fuzzy in nature and taken as trapezoidal fuzzy number fuzzy possibility and necessity approaches are used to obtain optimal decision by the proposed ant colony algorithm computational experiments with different set of data are given in support of the proposed approach

fuzzy capital budgeting fuzzy equivalents of all the classical capital budgeting investment choice methods are generalised or proposed these equivalents can be used to evaluate and compare projects in which the cash ows duration time and required rate of return cost of capital are given imprecisely in the form of a fuzzy number c 2000 elsevier science b v all rights reserved

fuzzy capital rationing model in this paper we study the fuzzification of weingartner s pure capital rationing model and its analysis we develop a primal dual pair based on t norm t conorm relation for the constraints and objective function for a fully fuzzified pure capital rationing problem except project selection variables we define the a interval under which the weak duality is proved we perform sensitivity analysis for a change in a budget level or in a cash flow level of a non basic as well as a basic variable we analyze the problem based on duality and complementary slackness results we illustrate the proposed model by computational analysis and interpret the results

evolutionary algorithm solution to fuzzy problems fuzzy linear programming in this paper we wish to find solutions to the fully fuzzified linear program where all the parameters and variables are fuzzy numbers we first change the problem of maximizing a fuzzy number the value of the objective function into a multi objective fuzzy linear programming problem we prove that fuzzy flexible programming can be used to explore the whole undominated set to the multi objective fuzzy linear program an evolutionary algorithm is designed to solve the fuzzy flexible program and we apply this program to two applications to generate good solutions

estimating a fuzzy term structure of interest rates using fuzzy regression techniques abstract several papers in the financial literature propose using fuzzy numbers fns to model interest rate uncertainty however in our opinion the first problem to be solved is how to estimate these rates with fns in this paper we attempt to provide a solution to this question with a method for adjusting the temporal structure of interest rates tsir that is based on fuzzy regression techniques this method will enable to quantify the anticipated rates in the fixed income markets for the future with fns in particular we discuss how to estimate the tsir with triangular fuzzy numbers because of their desirable properties