canonical fuzzy numbers of dimension two abstract recently several authors have dealt with interactive fuzzy numbers this paper proposes a new approach to interactions between fuzzy numbers by using canonical fuzzy numbers of dimension two

associative monotonic operations in fuzzy set theory abstract the properties of binary operations in a real interval are considered and used in the discussion of generalized operations on fuzzy sets on fuzzy numbers and on fuzzy probabilistic sets

triangular norm based addition of fuzzy intervals triangular norm based addition of fuzzy intervals on the extended real line is reduced to the addition of shapes on 0 the addition of fuzzy intervals including lr fuzzy intervals lr fuzzy numbers lt and tr fuzzy numbers based on limit t norms is recalled for continuous archimedean t norms special types of incoming summands allowing the exact output computation are introduced several examples are given

cpk index estimation using fuzzy numbers process capacity indices pcis were developed and have been successfully used by companies to compete in and dominate the high profit markets by improving the quality and the productivity since the past two decades there is an essential assumption in the conventional application wherein the output process measurements are precise and distributed as normal random variables since the assumption of normal distribution is untenable errors can occur if the cpk index is computed using non normal data in the present study we address the situation that the output of data from measurement of the quality of a product is insufficiently precise or scarce this is possible when the quality measurement refers to the decision maker s subjective determination in such a situation the linguistic variable that is easier to capture the decision maker s subjective perception is applied to construct the pci cpk the present approach can mitigate the effect when the normal assumption is inappropriate and extends the application of cpk index

on the calculation of extended max and min operations between convex fuzzy sets of the real line in this paper we will identify the sets of so called sub and pseudo highest intersection points of convex fuzzy sets of the real line and will explore their properties based on the properties of these sets an algorithm for calculating extended max and min operations between two or more convex fuzzy sets of the real line with general membership functions not necessarily continuous is proposed

on differential equations with interactive fuzzy parameter via t norms abstract in this paper we study fuzzy differential equations with uncertain parameters modeled by interactive fuzzy numbers the interactivity is formalized with the help of upper semicontinuous t norms to obtain solutions to fuzzy differential equations we use two different approaches the first uses a family of differential inclusions while the second is the fuzzification of the deterministic problem using the zadeh extension principle we show that the solutions obtained by the two methods are equal interactivity among the parameters and variable of the problem are studies with respect two methods we show that a hierarchy in uncertainties of the solutions arises when we chose one of the basic t norm the minimum the t norm of the product the t norm of lukasiewicz and t norm of the drastic product to model the interaction between parameters finally to illustrate the concepts introduced in the paper we study the malthusian model with interactive parameters

a simple computation of min and max operations for fuzzy numbers in this paper we propose a new method to implement the operations min and max for fuzzy numbers easily and quickly those considered fuzzy numbers in the operations can be of any shape

falscal a fuzzy multidimensional scaling algorithm the conventionally adopted alternating least squares scaling alscal procedure of multidimensional scaling mds is a valuable mathematical scheme for analyzing data in areas where organized concepts and underlying dimensions are inadequately defined or developed fuzzy set theory fst attempts to formulate human reasoning and perceptions therefore targeting problems in areas where human factors significantly impact the result of decision making to our knowledge the fst and alscal approaches have not yet been integrated this study integrates and modifies the fst and alscal procedures fuzzy data collected from fuzzy questionnaires are adopted as the input of the mds ensuring that the uncertainty of input data can be incorporated into the analysis the conventionally adopted alscal procedure is then modified to cope with fuzzy input data by adopting the notion of fuzzy distances fuzzy disparities and fuzzy ranking to represent the similarities between fuzzy data related approximation operations of the triangular fuzzy number are also introduced to facilitate computation in fuzzy alscal

fuzzy arithmetic with requisite constraints abstract the purpose of this paper is to show that the standard fuzzy arithmetic does not take into account known constraints when applied to states of linguistic variables these constraints referred to as requisite constraints represent additional information when they are ignored as in the standard fuzzy arithmetic the obtained results exhibit in general information deficiency it is thus important as argued in the paper to revise fuzzy arithmetic to take relevant requisite constraints into account some typical requisite constraints are overviewed with a more extensive examination of the requisite equality constraint crisp or fuzzy

on the observability of time discrete conservative linear systems abstract we consider various time discretization schemes of abstract conservative evolution equations of the form z a z where a is a skew adjoint operator we analyze the problem of observability through an operator b more precisely we assume that the pair a b is exactly observable for the continuous model and we derive uniform observability inequalities for suitable time discretization schemes within the class of conveniently filtered initial data the method we use is mainly based on the resolvent estimate given by burq and zworski in n burq m zworski geometric control in the presence of a black box j amer math soc 17 2 2004 443 471 electronic we present some applications of our results to time discrete schemes for wave schrodinger and kdv equations and fully discrete approximation schemes for wave equations

t sum of l r fuzzy numbers abstract the sum of l r fuzzy numbers based on a given archimedian continuous t norm t is studied a series of improving sufficient conditions of several authors ensuring an analytical form of the output sum is completed by a sufficient and necessary condition i e the best sufficient condition some applications are indicated

uniform controllability properties for space time discretized parabolic equations this article is concerned with the analysis of semi discrete in space and fully discrete approximations of the null controllability and controllability to the trajectories for parabolic equations we propose an abstract setting for space discretizations that potentially encompasses various numerical methods and we study how the controllability problems depend on the discretization parameters for time discretization we use schemes with theta in frac 1 2 1 for the proofs of controllability we rely on the strategy introduced by lebeau and robbiano comm partial differ equ 20 335 356 1995 for the null controllability of the heat equation which is based on a spectral inequality we obtain relaxed uniform observability estimates in both the semi discrete and fully discrete frameworks and associated uniform controllability properties for the practical computation of the control functions we follow j l lions hilbert uniqueness method strategy exploiting the relaxed uniform observability estimate algorithms for the computation of the controls are proposed and analysed in the semi discrete and fully discrete cases additionally we prove an error bound between the fully discrete and the semi discrete control functions this bound is however not uniform with respect to the space discretization the theoretical results are illustrated through numerical experimentations

discrete carleman estimates for elliptic operators in arbitrary dimension and applications in arbitrary dimension we consider the semidiscrete elliptic operator partial t 2 mathcal a scriptscriptstyle mathfrak m where mathcal a scriptscriptstyle mathfrak m is a finite difference approximation of the operator nabla x gamma x nabla x for this operator we derive a global carleman estimate in which the usual large parameter is connected to the discretization step size we address discretizations on some families of smoothly varying meshes we present consequences of this estimate such as a partial spectral inequality of the form of that proven by g lebeau and l robbiano for mathcal a scriptscriptstyle mathfrak m and a null controllability result for the parabolic operator partial t mathcal a scriptscriptstyle mathfrak m for the lower part of the spectrum of mathcal a scriptscriptstyle mathfrak m with the control function that we construct whose norm is uniformly bounded we prove that the l 2 norm of the final state converges to zero exponentially as the step size of the discretization goes to zero a relaxed observability estimate is then deduced

on possibilistic correlation in 2004 fuller and majlender introduced the notion of covariance between fuzzy numbers by their joint possibility distribution to measure the degree to which they interact based on this approach in this paper we will present the concept of possibilistic correlation representing an average degree of interaction between marginal distributions of a joint possibility distribution as compared to their respective dispersions moreover we will formulate the classical cauchy schwarz inequality in this possibilistic environment and show that the measure of possibilistic correlation satisfies the same property as its probabilistic counterpart in particular applying the idea of transforming level sets of possibility distributions into uniform probability distributions we will point out a fundamental relationship between our proposed possibilistic approach and the classical probabilistic approach to measuring correlation

fuzzy differential equations with interactive derivative in this paper we introduce and study new concept of differentiability for fuzzy set valued functions this derivative considers possible local interactivity in the process studied several properties of differentiability and integrability are investigated for the new concept and they are compared to similar fuzzy differentiabilities like hukuhara differentiability and generalized hukuhara differentiability furthermore we establish theorems as the fundamental theorem of calculus ultimately we exhibit some results for fuzzy initial value problem and an application

on product sum of triangular fuzzy numbers abstract we study the problem if a i i n are fuzzy numbers of triangular form then what is the membership function of the infinite or finite sum a 1 a 2 defined via the sup product norm convolution

exact controllability for multidimensional semilinear hyperbolic equations in this paper we obtain a global exact controllability result for a class of multidimensional semilinear hyperbolic equations with a superlinear nonlinearity and variable coefficients for this purpose we establish an observability estimate for the linear hyperbolic equation with an unbounded potential in which the crucial observability constant is estimated explicitly by a function of the norm of the potential such an estimate is obtained by a combination of a pointwise estimate and a global carleman estimate for the hyperbolic differential operators and analysis on the regularity of the optimal solution to an auxiliary optimal control problem

necessary and sufficient conditions for the equality of interactive and non interactive extensions of continuous functions abstract in this contribution we find the class of n dimensional joint possibility distributions with the property that the interactive extension principle coincides with the non interactive extension principle as long as the interactive operations are determined by continuous functions strictly increasing in each argument this result completes recent studies by the authors where the particular case of interactive additions and multiplications versus non interactive additions and multiplications were investigated in addition this time we propose results that also cover the cases when we know the fuzzy numbers only from their membership functions it means that we eliminated the limitations that appear when we cannot pass from membership function representation to parametric representation of fuzzy numbers as important new applications we mention the study on the completely correlated fuzzy numbers also of note is that we propose two simple methods to extend bidimensional joint possibility distributions to n dimensional joint possibility distributions one method is based on an inductive construction while the other one is based on a pairwise construction

3 3 lemma and protomodularity abstract the classical 3 3 lemma and snake lemma valid in any abelian category still hold in any quasi pointed the map 0 1 is a mono regular and protomodular category some applications are given in this abstract context concerning the denormalization of kernel maps and the normalization of internals groupoids i e associated crossed modules

on the extension of nullnorms and uninorms to fuzzy truth values abstract in this work by applying zadeh s extension principle we extend type 1 proper nullnorms and proper uninorms to fuzzy truth values the definitions of type 2 nullnorms and uninorms are introduced we mainly discuss in which subalgebras of fuzzy truth values extended proper nullnorms and proper uninorms are type 2 nullnorms and uninorms respectively

propagation observation and control of waves approximated by finite difference methods this paper surveys several topics related to the observation and control of wave propagation phenomena modeled by finite difference methods the main focus is on the property of observability corresponding to the question of whether the total energy of solutions can be estimated from partial measurements on a subregion of the domain or boundary the mathematically equivalent property of controllability corresponds to the question of whether wave propagation behavior can be controlled using forcing terms on that subregion as is often desired in engineering applications observability controllability of the continuous wave equation is well understood for the scalar linear constant coefficient case that is the focus of this paper however when the wave equation is discretized by finite difference methods the control for the discretized model does not necessarily yield a good approximation to the control for the original continuous problem in other words the classical convergence consistency stability property of a numerical scheme does not suffice to guarantee its suitability for providing good approximations to the controls that might be needed in applications observability controllability may be lost under numerical discretization as the mesh size tends to zero due to the existence of high frequency spurious solutions for which the group velocity vanishes this phenomenon is analyzed and several remedies are suggested including filtering tychonoff regularization multigrid methods and mixed finite element methods we also briefly discuss these issues for the heat beam and schrodinger equations to illustrate that diffusive and dispersive effects may help to retain the observability controllability properties at the discrete level we conclude with a list of open problems and future subjects for research

fuzzy cardinality and the modeling of imprecise quantification abstract the concept of cardinality of a fuzzy set has received attention from several researchers and has been defined in several apparently independent manners a systematic investigation of this notion is performed which unifies and improves previous attempts the cardinality of a fuzzy set viewed as a fuzzy integer is related to scalar cardinality indices the closely related question of the probability of a fuzzy event is dealt with lastly the usefulness of fuzzy cardinality for meaning representation of statements or queries involving fuzzy linguistic quantifiers is emphasized

a refined fuzzy time series model for forecasting abstract fuzzy time series models have been used to model observations where each one of them contains multiple values the formulation of fuzzy relationships and the lengths of intervals are considered to be two of the critical factors that affect forecasting results unfortunately the lengths of the intervals were determined during the early stages of forecasting in these models and they thus often failed to reflect the distribution of observations this study therefore proposes a refined fuzzy time series model to further refine the lengths of intervals this model can refine the lengths of intervals during the formulation of fuzzy relationships and hence capture the fuzzy relationships more appropriately as a result the forecasting results can be improved both the stock index and enrollment are used as the targets in the empirical analysis

defuzzification of fuzzy intervals abstract this paper deals with defuzzification of fuzzy intervals classified as regular or irregular based on the defuzzification method used a fuzzy interval is regular if its membership function is maximized at its defuzzified value otherwise the fuzzy interval is irregular three methods for defuzzification are presented in this paper 1 mean of maxima mom method 2 center of area coa method and 3 fuzzy mean fm method fuzzy intervals with symmetrical membership function are regular and all three defuzzification methods give the same results for any regular fuzzy interval based on the coa method its defuzzified value is equal to the middle point of the corresponding mean value interval for irregular fuzzy intervals two approaches are proposed one is to apply the defuzzification method but relax the reasonable but not necessary rnn requirement another is to apply the rnn requirement but relax the defuzzification method this paper shows that the regularity of a fuzzy interval is preserved after applying an arithmetic operation with a nonzero real number the formulas for calculating the defuzzified value of the arithmetic operations between a regular fuzzy interval and a real number are derived this paper also shows that the regularity of two fuzzy intervals based on the coa method is preserved after applying addition or subtraction operation between them the formulas for calculating the defuzzified value of the sum and the difference of regular fuzzy intervals are derived the properties of fuzzy intervals discussed in this paper can be taken into consideration before or when a defuzzification method is selected

modeling vague beliefs using fuzzy valued belief structures abstract this paper presents a rational approach to the representation and manipulation of imprecise degrees of belief in the framework of evidence theory we adopt as a starting point the non probabilistic interpretation of belief functions provided by smets transferable belief model as well as previous generalizations of evidence theory allowing to deal with fuzzy propositions we then introduce the concepts of interval valued and fuzzy valued belief structures defined respectively as crisp and fuzzy sets of belief structures verifying hard or elastic constraints we then proceed with a generalization of various concepts of dempster shafer theory including those of belief and plausibility functions combination rules and normalization procedures most calculations implied by the manipulation of these concepts are based on simple forms of linear programming problems for which analytical solutions exist making the whole scheme computationally tractable we discuss the application of this framework in the areas of decision making under uncertainty and classification of fuzzy data

a t sum bound of lr fuzzy numbers abstract in this paper we provide an upper bound and a lower bound of t sum of lr fuzzy numbers with different spreads where t is archimedean t norm and also show in three examples how close they are to actual membership functions furthermore we study when the membership function of t sum achieves the upper bound

equivalent conditions for laws of large numbers for t related l r fuzzy numbers in this paper we give some necessary and sufficient conditions for laws of large numbers for sequence of mutually t related l r fuzzy numbers when t is an continuous archimedean t norm and diameter of support of the fuzzy numbers is not uniformly bounded we also consider some necessary and sufficient conditions for laws of large numbers for l r fuzzy random numbers and generalize earlier results of fuller fuzzy sets and systems 45 1992 299 303 triesch fuzzy sets and systems 58 1993 339 342 and hong and lee fuzzy sets and systems 121 2001 537 543

the reduction of interval type 2 lr fuzzy sets type reduction of interval type 2 it2 fuzzy sets is essential in conducting the type 2 fuzzy sets expressed with the resolution forms of it2 fuzzy sets several type reduction methods such as km ekm and centroid flow have been proposed these methods are relatively easy to implement but still computation intensive because they need to invoke an iterative switching point finding procedure this study derives a theorem and proposes a heuristic algorithm which can fast and accurately identify the minimum and maximum switching points of a piecewise smooth it2 fuzzy set it also demonstrates that it is easy to derive the close form expressions of the switching points of a piecewise smooth it2 fuzzy set if both of its upper and lower membership functions can be parameterized as lr fuzzy sets which are defined in this paper then the type reduction of piecewise smooth it2 fuzzy sets can be simplified to solve the close form expressions of their switching points in terms of lr parameters experiments on it2 fuzzy sets with various piecewise smooth membership functions including linear gaussian and hybrid shaped ones were made the results showed that the proposed type reduction method can obtain solutions which accurately approximate to the desired switching points with much lower computational overhead than the karnik mondel km and enhanced km ekm methods

protomodular aspect of the dual of a topos abstract the structure of the dual of a topos is investigated under its aspect of a barr exact and protomodular category in particular the normal monomorphisms in the fibres of the fibration of pointed objects are characterized and the change of base functors with respect to this same fibration are shown to reflect those normal monomorphisms

t sum of bell shaped fuzzy intervals the usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of zadeh s extension principle based on a t norm t a t norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation if this arithmetic operation is closed for this class it is important to know which t norms are consistent with a particular type of fuzzy intervals recently dombi and gyorbiro proved that addition is closed if the dombi t norm is used with two bell shaped fuzzy intervals a result proved by mesiar on a strict t norm based shape preserving additions of lr fuzzy intervals with unbounded support is recalled as applications we define a broader class of bell shaped fuzzy intervals then we study t norms which are consistent with these particular types of fuzzy intervals dombi and gyorbiro s results are special cases of the results described in this paper

group velocity in finite difference schemes the relevance of group velocity to the behavior of finite difference models of time dependent partial differential equations is surveyed and illustrated applications involve the propagation of wave packets in one and two dimensions numerical dispersion the behavior of parasitic waves and the stability analysis of initial boundary value problems

a note on the convergence of t sum series of l r fuzzy numbers abstract we prove the existence of the limit of series a 1 a 2 a n of l r fuzzy numbers where addition is defined via the sup t norm convolution and show uniform continuity of the limit this generalizes the earlier result by triesch 1993

a note to the addition of fuzzy numbers based on a continuous archimedean t norm abstract a simple method of computing the t sum of special types of fuzzy numbers is introduced for the lukasiewicz t norm tl the proposed method can be applied to the addition of fuzzy numbers with convex membership functions the classes of fuzzy numbers leading to t idempotents are studied for continuous t norms

maximum and minimum between fuzzy symbols in non interactive and weakly non interactive situations abstract we define fuzzy symbols as particular fuzzy sets whose membership functions operate between two linearly ordered spaces and study the operations of maximum and of minimum between two fuzzy symbols we consider the membership functions of the fuzzy symbols as possibility distributions we study those of the maximum and the minimum of two non interactive and weakly non interactive variables

an axiomatic survey of diagram lemmas for non abelian group like structures abstract it is well known that diagram lemmas for abelian groups and more generally in abelian categories used in algebraic topology can be suitably extended to non abelian structures such as groups rings loops etc moreover they are equivalent to properties which arise in the axiomatic study of these structures for the five lemma this is well known and in the present paper we establish this for the snake lemma and the 3 3 lemma which when suitably formulated turn out to be equivalent to each other for all pointed algebraic structures and also in general categories of a special type in particular we show that among varieties of universal algebras they are satisfied precisely in the so called pointed ideal determined varieties

on various approaches to normalization of interval and fuzzy weights abstract the paper deals with the problem of fuzzification of the procedure of normalization of weights first the existing methods for normalization of interval and fuzzy weights are reviewed second we study the problem of normalization of a fuzzy vector of weights that expresses the joint possibility distribution of initial weights we show that a correct way is to apply the extension principle proposed by zadeh since the result of such normalization is the fuzzy vector of normalized weights that expresses the true joint possibility distribution of normalized weights further we establish some properties of this approach to normalization that are important from the point of view of real applications finally since an n tuple of non interactive interval or fuzzy weights can be viewed as a fuzzy vector of weights of a special kind we investigate normalization of such kind of fuzzy vectors of weights according to the extension principle we show that from the point of view of the way of modelling uncertain normalized weights the result of this approach can be directly compared only with the result of normalization proposed by wang and elhag 2006 35 we find out that it is not sufficient to express the result of normalization only by an n tuple of normalized interval or fuzzy weights together with the constraint that the sum of the weights is equal to 1 since it can cause a false increase of uncertainty in the model this fact is illustrated by an example

topological semi abelian algebras given an algebraic theory t whose category of models is semi abelian we study the category top t of topological models of t and generalize to it most classical results on topological groups in particular top t is homological which includes barr regularity and forces the mal cev property every open subalgebra is closed and every quotient map is open we devote special attention to the hausdorff compact locally compact connected totally disconnected and profinite t algebras c 2004 elsevier inc all rights reserved

regranulation a granular algorithm enabling communication between granular worlds abstract in this paper we describe a granular algorithm for translating information between two granular worlds represented as fuzzy rulebases these granular worlds are defined on the same universe of discourse but employ different granulations of this universe in order to translate information from one granular world to the other we must regranulate the information so that it matches the information granularity of the target world this is accomplished through the use of a first order interpolation algorithm implemented using linguistic arithmetic a set of elementary granular computing operations we first demonstrate this algorithm by studying the common fuzzy pd rulebase at several different granularities and conclude that the 3 3 granulation may be too coarse for this objective we then examine the question of what the natural granularity of a system might be this is studied through a 10 fold cross validation experiment involving three different granulations of the same underlying mapping for the problem under consideration we find that a 7 7 granulation appears to be the minimum necessary precision

a two stage logarithmic goal programming method for generating weights from interval comparison matrices a two stage logarithmic goal programming tlgp method is proposed to generate weights from interval comparison matrices which can be either consistent or inconsistent the first stage is devised to minimize the inconsistency of interval comparison matrices and the second stage is developed to generate priorities under the condition of minimal inconsistency the weights are assumed to be multiplicative rather than additive in the case of hierarchical structures a nonlinear programming method is used to aggregate local interval weights into global interval weights a simple yet practical preference ranking method is investigated to compare the interval weights of criteria or rank alternatives in a multiplicative aggregation process the proposed tlgp is also applicable to fuzzy comparison matrices when they are transformed into interval comparison matrices using a level sets and the extension principle six numerical examples including a group decision analysis problem with a group of comparison matrices a hierarchical decision problem and a fuzzy decision problem using fuzzy comparison matrix are examined to show the applications of the proposed methods comparisons with other existing procedures are made whenever possible

convergence of an inverse problem for discrete wave equations it is by now well known that one can recover a potential in the wave equation from the knowledge of the initial waves the boundary data and the flux on a part of the boundary satisfying the gamma conditions of j l lions we are interested in proving that trying to fit the discrete fluxes given by discrete approximations of the wave equation with the continuous one one recovers at the limit the potential of the continuous model in order to do that we shall develop a lax type argument usually used for convergence results of numerical schemes which states that consistency and uniform stability imply convergence in our case the most difficult part of the analysis is the one corresponding to the uniform stability that we shall prove using new uniform discrete carleman estimates where uniform means with respect to the discretization parameter we shall then deduce a convergence result for the discrete inverse problems our analysis will be restricted to the 1 d case for space semi discrete wave equations discretized on a uniform mesh using a finite differences approach

on the algebra of interactive fuzzy numbers the continuous case abstract in 1 we discussed default methods involving an approximate joint distribution or the extension principle to calculated m n m n and evaluate m n m n etc for positively and negatively associated discrete fuzzy numbers m and n this paper continues that research where now m and n are continuous fuzzy numbers we also discuss default procedures for extended max and min

oblique fuzzy vectors and their use in possibilistic linear programming in this paper we propose oblique fuzzy vectors to treat the interactivity among fuzzy numbers oblique fuzzy vectors are extensions of fuzzy numbers and vectors of non interactive fuzzy numbers the interactivity among fuzzy numbers can be treated by a non singular matrix in an oblique fuzzy vector we discuss characterization of an oblique fuzzy vector and the tractability of manipulation of oblique fuzzy vectors in fuzzy linear functions moreover we discuss possibilistic linear programming problems with oblique fuzzy vectors it is shown that the possibilistic linear programming problems are reduced to linear programming problems with a special structure

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

a convexity problem and a new proof for linearity preserving additions of fuzzy intervals in this paper we propose a new sufficient condition for convexity of function this result provides a simple new proof for linearity preserving additions of fuzzy intervals obtained by the author in 2002 which was a conjecture suggested by mesiar in 1997

the use of fuzzy variables in pert abstract in this paper we present a method called fpert for estimating a project completion time in the situation when activity duration times in the project network model are given in the form of fuzzy variables fuzzy sets on time space theoretical foundations of the method as well as results of calculations derived from a simple example are included

some results on the addition of fuzzy intervals abstract a simple new method of computing t sum of fuzzy intervals having the same results as the sum of fuzzy intervals based on the weakest t norm t w is introduced this work extends that of mesiar fuzzy sets and systems 91 1997 231 237 and markova fuzzy sets and systems 91 1997 253 258

explicit observability inequalities for the wave equation with lower order terms by means of carleman inequalities in this paper by means of carleman estimates and the usual energy estimate we obtain directly two observability inequalities for the linear wave equation with time variant nonsmooth lower order terms we do not need any unique continuation property of the linear equation a priori since this is actually one of the by products of our analysis furthermore the constant in the observability inequality is estimated by an explicit function of the norm of the involved coefficients in the equation also we apply our observability estimates to exact controllability for wave equations

boundary controllability of a linear semi discrete 1 d wave equation derived from a mixed finite element method in this article one discusses the controllability of a semi discrete system obtained by discretizing in space the linear 1 d wave equation with a boundary control at one extremity it is known that the semi discrete models obtained with finite difference or the classical finite element method are not uniformly controllable as the discretization parameter h goes to zero see 8 here we introduce a new semi discrete model based on a mixed finite element method with two different basis functions for the position and velocity we show that the controls obtained with these semi discrete systems can be chosen uniformly bounded in l 2 0 t and in such a way that they converge to the hum control of the continuous wave equation i e the minimal l 2 norm control we illustrate the mathematical results with several numerical experiments