on theoretical pricing of options with fuzzy estimators in this paper we present an application of a new method of constructing fuzzy estimators for the parameters of a given probability distribution function using statistical data this application belongs to the financial field and especially to the section of financial engineering in financial markets there are great fluctuations thus the element of vagueness and uncertainty is frequent this application concerns theoretical pricing of options and in particular the black and scholes options pricing formula we make use of fuzzy estimators for the volatility of stock returns and we consider the stock price as a symmetric triangular fuzzy number furthermore we apply the black and scholes formula by using adaptive fuzzy numbers introduced by thiagarajah et al k thiagarajah s s appadoo a thavaneswaran option valuation model with adaptive fuzzy numbers computers and mathematics with applications 53 2007 831 841 for the stock price and the volatility and we replace the fuzzy volatility and the fuzzy stock price by possibilistic mean value we refer to both cases of call and put option prices according to the black scholes model and also analyze the results to greek parameters finally a numerical example is presented for both methods and a comparison is realized based on the results

a new method for solving interval and fuzzy equations linear case a new approach to the solution of interval and fuzzy equations based on the generalized procedure of interval extension called interval extended zero method is proposed the central for the proposed approach is the treatment of the interval zero as an interval centered around zero it is shown that such proposition is not of heuristic nature but is the direct consequence of the interval subtraction operation some methodological problems concerned with this definition of interval zero are discussed it is shown that the resulting solution of interval linear equations based on the proposed method may be naturally treated as a fuzzy number an important advantage of a new method is that it substantially decreases the excess width effect on the other hand we show that it can be used as a reliable practical tool for solving linear interval and fuzzy equations as well as the systems of them the features of the method are illustrated by the example of the solution of the well known leontief input output problem in the interval setting

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

option valuation model with adaptive fuzzy numbers in this paper we consider moment properties for a class of quadratic adaptive fuzzy numbers defined in dubois and prade d dubois h prade fuzzy sets and systems theory and applications academic press new york 1980 the corresponding moments of trapezoidal fuzzy numbers tr f n s and triangular fuzzy numbers t f n s turn out to be special cases of the adaptive fuzzy number s bodjanova median value and median interval of a fuzzy number information sciences 172 2005 73 89 a numerical example is presented based on the black scholes option pricing formula with quadratic adaptive fuzzy numbers for the characteristics such as volatility parameter interest rate and stock price our approach hinges on a characterization of imprecision by means of fuzzy set theory

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

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

application of levy processes and esscher transformed martingale measures for option pricing in fuzzy framework in this paper we consider the european option valuation problem we assume that the underlying asset follows a geometric levy process the log price is a sum of a brownian motion with drift and a linear combination of poisson processes describing jumps in price in our approach we use martingale method and theory of fuzzy sets to obtain the european call and put option pricing formulas we use the mean correcting and the esscher transformed martingale measures application of the first mentioned measure required deep analysis of transformation of characteristics of levy process we assume that some model parameters cannot be precisely described and therefore we apply fuzzy numbers application of fuzzy arithmetic enables us to consider different sources of uncertainty and introduce experts opinions or imprecise estimates to the model in contradistinction to our previous papers where the european call option price at time zero was analysed we introduce the valuation expressions of the european call and put options for arbitrary time t numerical simulations conducted in the paper are used to analyse and illustrate the theoretical results this numerical approach is based on l r numbers and the exact shape of the fuzzy numbers which give us the possibility of comparing behaviour of option prices for various values of the parameters of the underlying asset

on the algebra of interactive fuzzy numbers abstract this paper discusses basic arithmetic of interactive fuzzy numbers which are values of fuzzy variables we argue that one should use the joint distribution and not necessarily only the marginals in the extension principle to perform these operations since in practice we usually do not know the joint we suggest default methods involving an approximate joint distribution or the classical extension principle to calculate m n m n and evaluate m n m n etc for positively negatively associated fuzzy numbers m and n we also introduce a measure of association between fuzzy variables

towards a general setting for the fuzzy mathematics of finance abstract this paper investigates a possible general setting for the fuzzy mathematics of finance we consider two classes of fuzzy quantities and explore their links with the axiomatic models of financial evaluation following some general purpose theorems about operations on fuzzy quantities we provide conditions for a consistent fuzzy extension of present and future value both with one and several capitals applications to the most common topics of financial mathematics are accordingly discussed

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

parametric representation of fuzzy numbers and application to fuzzy calculus we present several models to obtain simple parametric representations of the fuzzy numbers or intervals based on the use of piecewise monotonic functions of different forms the representations have the advantage of allowing flexible and easy to control shapes of the fuzzy numbers we use the standard cuts setting but also the membership functions are obtained immediately and can be used directly to obtain error controlled approximations of the fuzzy calculus in terms of a finite set of parameters the general setting is the hermite type interpolation where the values and the slopes of the monotonic interpolators are given by appropriate parameters and the overall errors of the fuzzy computations can be controlled within a prefixed tolerance by eventually augmenting the total number of pieces and of the parameters by which the results are obtained the representations are designed to model the lower and the upper extremal values of each cut compact intervals of the fuzzy numbers and are able to produce almost any possible configuration differentiable continuous or with a finite number of discontinuity points by using parametric monotonic functions of different types we show applications in the standard fuzzy calculus and we stress the generality and the applicability of the proposed representation to a large class of problems including the numerical solution of fuzzy differential equations the fuzzy linear regression and the stochastic extensions of the fuzzy mathematics the proposed model is called the lower upper representation and we denote the associated fuzzy numbers or intervals as lu fuzzy

selecting the optimum portfolio using fuzzy compromise programming and sharpe s single index model different approaches besides the traditional markowitz s model have been proposed in the literature to analyze portfolio selection problems among them compromise programming cp is a suitable multiobjective programming technique which allows the handling of several objectives in those situations in which the existence of a high level of conflict between criteria does not permit the simultaneous optimization of all the considered objectives when objectives and constraints are in an imprecise environment fuzzy cp arises as a suitable solving method imprecision will be quantified by means of fuzzy numbers that represent the continuous possibility distributions for fuzzy parameters and hence place a constraint on the possible values the parameters may assume in this paper a new fuzzy compromise programming approach is proposed based on the obtaining of the minimum fuzzy distance to the fuzzy ideal solution of the portfolio selection problem once this fuzzy distance has been obtained the second step consists of finding a crisp decision vector an optimal portfolio implying a fuzzy distance to the ideal solution the more accurate as possible to the fuzzy minimum distance previously obtained

using yager s t norms for aggregation of fuzzy intervals the extension principle is one of the basic ideas in fuzzy set theory in this paper yager s family of t norms is used within the formulation of this principle a generalization for the resulting formulas of extended addition and multiplication to n fuzzy sets is given also a procedure to fix the parameter in yager s t norms using information given by the user of the underlying specific model is presented the paper ends with two applications using the described procedure

a new index for bond management in an uncertain environment within the framework of assets liability management we understand that immunization is the main method to assure a certain yield in a future date departing from an initial portfolio although the objective of passive strategies is to design a portfolio that will achieve the performance of a predetermined benchmark active bond management strategies rely on expectations of interest rate movements or changes in yield spread relationships however the variation of the duration increases the risk of a portfolio that why the decision maker will have to choose the combination of expected return and risk which provides the higher utility finally the construction of a fuzzy return risk map will allow the decision maker to know the over risk and the over return as regards immunization strategy for each duration and for each risk aversion of the decision maker the construction of a risk return map presents the results in an appropriate way it will help the decision maker to choose the best duration for the decision maker interest rate forecast finally this methodology is applied to the spanish debt so that the decision maker can select the duration that brings him a greater preference

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

a dynamic output feedback controller for ncs based on delay estimates the stabilization of a network controlled system including a global time varying delay is investigated in this note this delay is considered to be unknown but it is assumed that a bounded error estimate is available the exponential uncertainty induced by the time varying delay is decomposed into the sum of a polytopic term and an uncertain bounded term sufficient conditions to design a dynamic output feedback controller depending on an estimate of the time varying delay are proposed as linear matrix inequalities an illustration shows how our methodology enlarges the design techniques of the literature

a note on the transformation of possibilistic information into probabilistic information for investment decisions abstract investment decisions of a firm take place in a highly competitive environment any attempt to capture the reality in such decisions often results in fuzzy information behaving like fuzzy restrictions but for decision making probabilistic data may be more effective rather than possibilistic data therefore possibilistic data need to be transformed into probabilistic data and this needs a suitable possibility probability consistency principle ppcp this note provides a ppcp and shows that under certain conditions fuzzy information about cashflows can be approximated by normal probability distribution then the tools of the probability theory can be applied for such decisions

delay dependent sampled data control based on delay estimates in this paper the sampled data stabilization of linear time invariant systems with feedback delay is considered we assume that the delay is time varying and that its value is approximatively known we investigate how to use the available information about the evolution of delays for adapting the control law in real time numerical methods for the design of a delay dependent controller are presented this allows for providing a control for some cases in which the stabilization cannot be ensured using a controller with a fixed structure

the theory of approximate prices analytical foundations of experimental cost benefit analysis in a fuzzy decision space abstract the essay presents a theory of efficient prices for cost benefit analysis in a fuzzy space the approach proceeds by taking consumers income and producers outputs and costs as given the price preferences of consumers and producers are elicited and then embedded in a fuzzy space through fuzzy mappings to obtain a fuzzy compact price space where fuzzy price decisions are constructed solutions to the fuzzy price decision problems are abstracted through fuzzy mathematical programming to obtain fuzzy equilibrium prices from the fuzzy price space measures of price disagreement fuzzy consumer surplus and fuzzy producer surplus are advanced theorems of existence and uniqueness are stated the total result is a theory of fuzzy prices for cost benefit analysis for decision problem in general including cases where market imputations of prices may not be available to us as well as those cases where market failure may yield price distortions the theory is not only compactible with either contigent variation method direct information elicitation and revealed preference method market based evaluation but provides a direction for cases where problems may exist in both a computational example is provided to illustrate the working mechanism of the theory

using fuzzy random variables in life annuities pricing this paper develops life annuity pricing with stochastic representation of mortality and fuzzy quantification of interest rates we show that modelling the present value of annuities with fuzzy random variables allows quantifying their expected price and risk resulting from the uncertainty sources considered so we firstly describe fuzzy random variables and define some associated measures the mathematical expectation the variance distribution function and quantiles secondly we show several ways to estimate the discount rates to price annuities subsequently the present value of life annuities is modelled with fuzzy random variables we finally show how an actuary can quantify the price and the risk of a portfolio of annuities when their present value is given by means of fuzzy random variables

solutions of fuzzy equations based on kaucher arithmetic and ae solution sets we introduce and investigate two new types of fuzzy solutions to the equation f a x b where the parameters a and b are described in a fuzzy way the solutions we propose are based on some known solutions to this type of equation with the parameters described by the interval data we adapt to the fuzzy case so called formal interval solutions based on the kaucher interval arithmetic and ae solution sets in order to define fuzzy formal solutions we introduce a definition of fuzzy kaucher arithmetic we investigate the regularity of solutions in the case of linear dependence of f on a and discuss also the problem of interpretation and logical description of formal solutions

a fuzzy decision theory of optimal social discount rate collective choice theoretic abstract in this essay we present a fuzzy decision theory of the optimal social discount rate by combining methods of fuzzy logic consensus combination of expert judgments and fuzzy aggregation algorithms are developed for computing optimal social discount rates from individual and collective time preferences the results are examined against the computation of social discount rate on individual preferences as measured by utilities an example is provided to illustrate the applicational mechanism of the theory the essay is concluded with an appendix which is devoted to examining the properties of the required time set for the construction of the social discount

a fuzzy approach for r d compound option valuation this paper is devoted to propose a random fuzzy methodology in order to value r d investments combining the stochastic approach with the fuzzy analysis as it is commonly known an r d project is characterized by a sequential phase in which each phase gives to the manager the opportunity to realize or not the investment so in real option world this opportunity can be analyzed as a compound american exchange option caeo in this paper the fuzzy approach is used to model two important parameters of r d evaluation the volatility of asset v and the opportunity costs of deferring project v therefore we present a level of fuzzy prices of caeo and the fuzzy mean value of caeo using a pessimistic optimistic weight

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

integral fluctuation theorem for the housekeeping heat the housekeeping heat qhk is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states by analysing the evolution of its probability distribution we prove an integral fluctuation theorem exp qhk 1 valid for arbitrary driven transitions between steady states we discuss gaussian limiting cases and the difference between the new theorem and both the hatano sasa and the jarzynski relation

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

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

towards fuzzy modelling in economics abstract the general methodological framework of fuzzy modelling is considered particular emphasis is set on the analytical approach to building fuzzy models especially linear fuzzy models such models are obtained as a fuzzy extension of usual linear models apart from the known extension principle of zadeh and the so called fuzzy parameter extension a new model of fuzzy combination is also considered

on weighted possibilistic mean and variance of fuzzy numbers dubois and prade defined an interval valued expectation of fuzzy numbers viewing them as consonant random sets carlsson and fuller defined an interval valued mean value of fuzzy numbers viewing them as possibility distributions in this paper we shall introduce the notation of weighted interval valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval valued probabilistic mean we shall also introduce the notations of crisp weighted possibilistic mean value variance and covariance of fuzzy numbers which are consistent with the extension principle furthermore we show that the weighted variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory

difference distance and similarity as a basis for fuzzy decision support based on prototypical decision classes the use of prototypical decision classes as a basis for fuzzy decision support is outlined it is shown that given certain assumptions about the structure of both numeric and non numeric linguistic variables trapezoidal fuzzy sets can be used to model linguistic terms in particular the notion of a fuzzy index is introduced to model sets of linguistic terms for which there is no formal measurement scale the similarity between prototypes and input cases is measured as a function of the difference or distance between fuzzy sets the difference measure is itself a fuzzy set to reflect the underlying uncertainties in the original linguistic model similarity profiles for different decision classes are output as trapezoidal fuzzy sets the approach can be applied to the rapid development of decision aids using standard business software

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

solving linear and quadratic fuzzy equations abstract we present necessary and sufficient conditions for some linear and quadratic equations to have a solution when the parameters are either real or complex fuzzy numbers the solution will be a real or complex fuzzy number applications in chemistry economics finance and physics are presented for these types of equations

interval and fuzzy average internal rate of return for investment appraisal in investment appraisal uncertainty can be managed through intervals or fuzzy numbers because the arithmetical properties and the extension principle are well established and can be successfully applied in a rigorous way we apply interval and fuzzy numbers to the average internal rate of return airr recently introduced for overcoming the problems of the traditional internal rate of return irr in the setting of interval and fuzzy arithmetic we establish relations between the interim capitals invested the profits and the cash flows which are the ingredients of the airr and shed lights on the different ways uncertainty propagates depending on which variable is known and which one is derived the relations between fuzzy airr and fuzzy net present value are also investigated

approximate fuzzy arithmetic operations using monotonic interpolations abstract we suggest the use of piecewise monotonic interpolations to approximate and represent a fuzzy number or interval and to derive a procedure to control the absolute error associated to the arithmetic operations between fuzzy numbers in order to reduce the distance between the true result of the operation and its approximation the monotonic functions are then used to define a parametric representation of a large class of fuzzy numbers having general shapes of the membership function and a simple and accurate procedure is introduced for the fuzzy arithmetic several computational experiments are given to show the good performance of the proposed procedure

physical origins of entropy production free energy dissipation and their mathematical representations a unifying mathematical theory of nonequilibrium thermodynamics of stochastic systems in terms of master equations is presented as generalizations of isothermal entropy and free energy two functions of state play central roles the gibbs entropy s and the relative entropy f which are related via the stationary distribution of the stochastic dynamics s satisfies the fundamental entropy balance equation ds dt e p ensuremath h d t with entropy production rate e p ensuremath ge 0 and heat dissipation rate h d while df dt ensuremath f d ensuremath le 0 for closed systems that satisfy detailed balance t e p t f d t for open systems one has t e p t f d t q hk t where the housekeeping heat q hk ensuremath ge 0 was first introduced in the phenomenological nonequilibrium steady state thermodynamics put forward by oono and paniconi q hk represents the irreversible work done by the surrounding to the system that is kept away from reaching equilibrium hence entropy production e p consists of free energy dissipation associated with spontaneous relaxation i e self organization f d and active energy pumping that sustains the open system q hk the amount of excess heat involved in the relaxation q ex h d ensuremath q hk f d ensuremath t ds dt two kinds of irreversibility and the meaning of the arrow of time emerge quasistationary processes adiabaticity and maximum principle for entropy are also generalized to nonequilibrium settings

fluctuation theorem for stochastic systems the fluctuation theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics it has been proved in a number of different ways for thermostatted deterministic nonequilibrium systems in the present paper we show that the fluctuation theorem is also valid for a class of stochastic nonequilibrium systems the theorem is therefore not reliant on the reversibility or the determinism of the underlying dynamics numerical tests verify the theoretical result

controller synthesis for networked control systems this paper presents a discrete time model for networked control systems ncss that incorporates all network phenomena time varying sampling intervals packet dropouts and time varying delays that may be both smaller and larger than the sampling interval based on this model constructive lmi conditions for controller synthesis are derived such that stabilizing state feedback controllers can be designed besides the proposed controller synthesis conditions a comparison is made between the use of parameter dependent lyapunov functions and lyapunov krasovskii functions for stability analysis several examples illustrate the effectiveness of the developed theory

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

splitting of the rate matrix as a definition of time reversal in master equation systems motivated by recent progress in nonequilibrium fluctuation relations we present a generalized time reversal for stochastic master equation systems with discrete states which is defined as a splitting of the rate matrix into irreversible and reversible parts an immediate advantage of this definition is that a variety of fluctuation relations can be attributed to different matrix splittings additionally we find that the accustomed total entropy production formula and conditions of the detailed balance must be modified appropriately to account for the reversible rate part which was previously ignored

option price sensitivities through fuzzy numbers the main motivation in using fuzzy numbers in finance lies in the need for modelling the uncertainty and vagueness that are implicit in many situations however the fuzzy approach should not be considered as a substitute for the probabilistic approach but rather as a complementary way to describe the model peculiarities here we consider in particular the black and scholes model for option pricing and we show that the fuzzification of some key parameters enables a sensitivity analysis of the option price with respect to the risk free interest rate the final value of the underlying stock price the volatility and also better forecasts see thavaneswaran et al 2009 12 for details the sensitivities with respect to the variables of the model are represented by different letters of the greek alphabet and they play an important role in the definition of the shape of the fuzzy option price

estimating a term structure of interest rates for fuzzy financial pricing by using fuzzy regression methods abstract several papers in the financial literature propose using fuzzy numbers to model interest rate uncertainty however in our opinion the first problem to be solved is how to estimate these rates with fuzzy numbers 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 the extension proposed by ishibuchi and nii fuzzy sets and systems 119 2001 273 of the fuzzy regression methods exposed in savic and predrycz fuzzy regression analysis physica verlag heidelberg 1992 pp 91 100 tanaka fuzzy sets and systems 24 1987 363 375 and tanaka and ishibuchi fuzzy regression analysis physica verlag heidelberg 1992 pp 47 this method will enable to quantify the anticipated rates in the fixed income markets for the future with fuzzy numbers in particular we discuss how to estimate the tsir with triangular fuzzy numbers because of the desirable properties of this kind of fuzzy numbers

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

solving fuzzy equations we start in the next section 10 2 with looking at possible solutions to the simple fuzzy linear equation overline a cdot overline x overline b overline c we discuss three different types of solution which we have studied before in solving fuzzy equations then we present a fourth type of solution based on our fuzzy monte carlo method in section 10 2 2 this new solution is based on random fuzzy numbers in section 10 3 we look at only classical solutions to the fuzzy quadratic equation and apply our fuzzy monte carlo method to obtain new solutions then in section 10 4 we consider the fuzzy matrix equation overline a cdot overline x overline b and a number of solution types for overline x and then another solution based on fuzzy monte carlo techniques the last section contains a brief summary and our conclusions

fuzziness in valuing financial instruments by certainty equivalents abstract our aim is to use the utility theory of von neumann and morgenstern and the approach of certainty equivalent c e in a fuzzy framework for pricing a future uncertain amount the fuzzy theory is more adaptable to represent this problem because the financial evaluations depend on perspectives which are fuzzy known then we define a seller and buyer fuzzy financial c e

on the fuzzy difference equations of finance in this paper our intention is to demonstrate the applicability of fuzzy difference equations in the field of finance in order to achieve that we follow the work done by deeba et al and papashinopoulos et al and we study the existence of positive solutions to fuzzy financial difference equations initially we appose a method realized by buckley that deals with fuzzy analogues of the elementary compound interest problem afterwards we approach this case via the fuzzy difference equations method after making a comparison between the two methods we notice that they end up to the same general formula the main contribution of this paper is the simplicity of the method presented which gives us the opportunity to create formulas for cases which are specialized and also more realistic than the very basic one of the compound interest moreover by using difference equations we can study the factors which cause the change in the value of money in different time periods as a source for these cases of finance we use the work of kwapisz and we study a well known problem of financial mathematics this problem deals with the time value of money and as a direct application of it we study the balance of bank deposits finally a numerical example is presented for better understanding

an efficient approach to solving fuzzy madm problems abstract an approach using defuzzifying methods is proposed for the fuzzy multiple attribute decision making madm problem the computational effectiveness and efficiency of six defuzzifying methods combined with the simple additive weighting saw method are evaluated based on a comparison to the improved fuzzy weighted average ifwa followed by four fuzzy ranking methods numerical examples are discussed to demonstrate the implementation and effectiveness of the methods

robust stability analysis of networked systems with varying delays this article is concerned with networked controlled systems ncs with uncertain varying bounded transmission delays and asynchronous discrete time static control laws it is first shown that the delay variation gives rise to a discrete time uncertain ncs model robust stability analysis is carried out via a linear matrix inequality approach which when combined with a directed parameter search yields an estimate of robust stability bounds against any variations of the maximum allowable delay constrained within one sampling period that the closed loop system can tolerate the derived bounds are compared with other techniques relying on the singular values of the perturbed ncs model the presented simulation results prove the efficacy of the proposed control scheme

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