numerical solutions to compressible flows in a nozzle with variable cross section compressible flows in a nozzle can be modeled by the gas dynamics equations in one dimensional space with source terms it turns out that along stationary waves the entropy is conserved investigating properties of the system leads us to the determination of stationary waves relying on this analysis we construct a numerical scheme which takes into account the use of stationary waves our scheme is shown to be capable of maintaining equilibrium states this demonstrates the efficiency of the new scheme over classical ones which usually give unsatisfactory results when reducing the refinement of the mesh size moreover our scheme converges much faster than the classical ones in most cases

a review of some methods for ranking fuzzy subsets this paper deals with the problem of ranking n fuzzy subsets of the unit interval a number of methods suggested in the literature is reviewed and tested on a group of selected examples where the fuzzy sets can be nonnormal and or nonconvex the ranking is obtained from i the index of strict preference defined by watson ii three indexes proposed by yager iii the algorithm used by chang iv three versions of the a preference index suggested by adamo v the index defined by baas and kwakernaak vi three modified versions used by baldwin and guild vii the method proposed by kerre viii three forms of the index suggested by jain ix the four grades of dominance studied by dubois and prade in simple cases the results are good for all the methods with some exceptions in questionable cases where the decision must be probably modelled in accordance with the context in which it is imbedded the best indexes seem to be the dominances suggested by dubois and prade these indexes do not force any particular choice but clearly describe the situation hence allowing the decision maker himself to make his best choice

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

on the maximum entropy parameterized interval approximation of fuzzy numbers this paper extends the interval valued weighted possibilistic mean of a fuzzy number of fuller and majlender to a general weighting function without the monotonic increasing assumption this weighting function determines a weighted average aggregation of the cuts of the fuzzy number according to the preference of a decision maker some properties of the weighting function are provided and a preference index that qualifies this aggregation and can serve as a parameter for the definition of interval approximation of a fuzzy number is proposed a special class of parameterized weighting functions satisfying the maximal entropy principle is proposed

reasonable properties for the ordering of fuzzy quantities ii as a continuation of the first part related to the first and second class of ordering approaches this paper deals with the fulfilment of reasonable properties in the third class of ordering approaches to do so we briefly introduce fuzzy relations on which the third class of approaches is based then we recall some transitivity related concepts and an ordering procedure based on a acyclic fuzzy relation acyclicity is a very weak restriction on a fuzzy relation we prove that many fuzzy relations used for the comparison of fuzzy quantities satisfy some conditions stronger than acyclicity so we give a widely applicable formulation to derive a total ranking order from a fuzzy relation with our formulation we examine all the ordering indices in the third class with respect to the proposed axioms in part i

nonlinear resonance in systems of conservation laws the riemann problem for a general inhomogeneous system of conservation laws is solved in a neighborhood of a state at which one of the nonlinear waves in the problem takes on a zero speed the inhomogeneity is modeled by a linearly degenerate field the solution of the riemann problem determines the nature of wave interactions and thus the riemann problem serves as a canonical form for nonlinear systems of conservation laws generic conditions on the fluxes are stated and it is proved that under these conditions the solution of the riemann problem exists is unique and has a fixed structure this demonstrates that in the above sense resonant inhomogeneous systems generically have the same canonical form the wave curves for these systems are only lipschitz continuous in a neighborhood of the states where the wave speeds coincide and so in contrast to strictly hyperbolic systems the implicit function theorem cannot be applied directly to obtain existence and uniqueness here we show that existence

echocardiogram analysis using fuzzy sets and relations abstract this paper describes part of a larger project whose objective is to obtain completely automated analysis of a set of time sequenced echocardiogram images to yield such heart function parameters as chamber and stroke volumes ejection fraction and indices of regional myocardial function the research reported here is concerned with identifying collections of local regions in different frames which have similar characteristics and hence comprise a global region and those global regions which add together to form other known global regions the local regions are described by a fuzzy vector whose components are fuzzy numbers an equality like relation is defined on the set of local regions and equivalence classes are used to define the global regions a similar technique is used to decide which global regions add to larger global regions the end result is used by a fuzzy expert system which classifies the global regions according to their anatomical significance or as artifacst the results here reported suggest the utility of the fuzzy set techniques employed the possible application of our methods to other pattern recognition problems is discussed

fuzzy scores of technical efficiency abstract this paper suggests to extend scores of technical efficiency as used in for example data envelopment analysis dea to efficiency scores defined as so called fuzzy intervals fuzzy scores allow the decision maker to use scores of technical efficiency in combination with other sources of available performance information e g expert opinions key figures etc in this sense fuzzy scores become formal images of the evaluation otherwise done implicitly by the decision maker and may therefore enhance a more consistent evaluation it is shown how to rank a set of fuzzy scores

fuzzy analytic hierarchy process fallacy of the popular methods abstract the fuzzy analytic hierarchy process fuzzy ahp is a very popular decision making method and literally thousands of papers have been published about it however we find the basic logic of this approach has problems from its methodology the definition and operational rules of fuzzy numbers not only oppose the main logic of fuzzy set theory but also oppose the basic principles of the ahp in dealing with the outcomes fuzzy ahp does not give a generally accepted method to rank fuzzy numbers and a way to check the validity of the results besides we discuss the validity of the analytic hierarchy network process ahp anp in complex and uncertain environments and find that fuzzy anp is a false proposition because there is no fuzzy priority in the super matrix which provides the basis for the anp although fuzzy ahp has been applied in many cases and cited hundreds of times we hoped that those who use fuzzy ahp would understand the problems associated with this method

stochastic group preference modelling in the multiplicative ahp a model of group consensus this paper proposes a model for the representation of a consensus seeking group decision making process under the multiplicative variant of the analytic hierarchy process ahp in particular it proposes a group preference model which expresses the group s preference intensity judgements as random variables with associated probability distributions and the structure of the multiplicative ahp is exploited to derive interval judgements for the alternatives final impact scores as perceived by the group these interval judgements can be used to determine the probability that a rank reversal may occur amongst alternatives due to the group preference uncertainty i e to assess the stability of the final impact score vector which in turn offers information about the degree of consensus within the group about the decision

unsteady mixed flows in non uniform closed water pipes a full kinetic approach we recall the pressurized and free surface model constructed for the modeling of unsteady mixed flows in closed water pipes where transition points between the free surface and pressurized flow are treated as a free boundary associated to a discontinuity of the gradient of pressure then we present a numerical kinetic scheme for the computations of unsteady mixed flows in closed water pipes this kinetic method that we call fka for full kinetic approach is an easy and mathematically elegant way to deal with multiple transition points when the changes of state between free surface and pressurized flow occur we use two approaches namely the ghost waves approach and the full kinetic approach to treat these transition points we show that this kinetic numerical scheme has the following properties it is wet area conservative under a cfl condition it preserves the wet area positive it treats naturally the flooding zones and most of all it is very easy to implement it finally numerical experiments versus laboratory experiments are presented and the scheme produces results that are in a very good agreement we also present a numerical comparison with analytic solutions for free surface flows in non uniform pipes the numerical scheme has a very good behavior a code to code comparison for pressurized flows is also conducted and leads to a very good agreement we also perform a numerical experiment when flooding and drying flows may occur and finally make a numerical study of the order of the kinetic method

criteria for evaluating fuzzy ranking methods abstract in this paper four criteria for evaluating fuzzy ranking methods are investigated fuzzy preference representation rationality of fuzzy ordering distinguishability and robustness based on these criteria two existing ranking methods baas and kwakernaak s and nakamura s are evaluated and a new improved ranking method is suggested

a godunov type method for the shallow water equations with discontinuous topography in the resonant regime abstract we investigate the riemann problem for the shallow water equations with variable and possibly discontinuous topography and provide a complete description of the properties of its solutions existence uniqueness in the non resonant regime multiple solutions in the resonant regime this analysis leads us to a numerical algorithm that provides one with a riemann solver next we introduce a godunov type scheme based on this riemann solver which is well balanced and of quasi conservative form finally we present numerical experiments which demonstrate the convergence of the proposed scheme even in the resonance regime except in the limiting situation when riemann data precisely belong to the resonance hypersurface

algebraic structure of centered m fuzzy numbers abstract in this paper we discuss the algebraic structure of fuzzy numbers assuming that they are generated by a subset of mappings from r to a lattice ordered monoid particularly to a positive or a negative cone and for every fuzzy number there is a center defined using a special ordering on the set of fuzzy numbers and introducing special binary fuzzy algebraic operations we obtain different structural properties of these fuzzy numbers we study these algebraic structures using different class of generator mappings and establish the isomorphism between the real line and the set of the centered fuzzy numbers

well balanced schemes for the euler equations with gravitation well balanced high order finite volume schemes are designed to approximate the euler equations with gravitation the schemes preserve discrete equilibria corresponding to a large class of physically stable hydrostatic steady states based on a novel local hydrostatic reconstruction the derived schemes are well balanced for any consistent numerical flux for the euler equations the form of the hydrostatic reconstruction is both very simple and computationally efficient as it requires no analytical or numerical integration moreover as required by many interesting astrophysical scenarios the schemes are applicable beyond the ideal gas law both first and second order accurate versions of the schemes and their extension to multi dimensional equilibria are presented several numerical experiments demonstrating the superior performance of the well balanced schemes as compared to standard finite volume schemes are also presented

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

canonical fuzzy bags and bag fuzzy measures as a basis for madm with mixed non cardinal data abstract this contribution introduces what will be called sine analysis a new approach to multiple attribute decision making madm with mixed noncardinal data this approach is based upon the notion of canonical fuzzy bags and their scalar evaluations by bag fuzzy measures

ranking of fuzzy sets based on the concept of existence abstract various approaches have been proposed for the comparison or ranking of fuzzy sets however due to the complexity of the problem a general method which can be used for any situation still does not exist this paper formalizes the concept of existence for the ranking of fuzzy sets many of the existing fuzzy ranking methods are shown to be some application of this concept an improved fuzzy ranking method is then introduced based on this concept this newly introduced method is expanded for treating both normal and nonnormal convex and nonconvex fuzzy sets emphasis is placed on the use of the subjectivity of the decision maker such as the optimistic or the pessimistic view points an improved procedure for obtaining linguistic conclusions is also developed finally some numerical examples are given to illustrate the approach

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

elastic solutions for periodically layered strip with perfect bonding or with an interface crack a non homogenization approach to the analysis of a strip consisting of a finite number of isotropic elastic layers arranged periodically is presented the result is obtained by the use of the representative cell method based on the discrete fourier transform two types of problems are addressed in the problems of the first type the bonding between the layers is perfect the solution for this case is found in a closed form in terms of the laplace integrals the numerical results for different boundary conditions are given and a comparison with plate theory is carried out in the problems of the second type there is a flaw crack at one of the interfaces the solution in this case hinges on the analytic expression for the green function corresponding to a single interface dislocation in the uncracked strip by using this expression the crack problem is reduced to a singular integral equation the influence of the elastic mismatch and other problem parameters on the fracture characteristics is examined it is found that similar to the case of the periodic plane when the thinner layeres in the strip are stiffer further increase of their stiffness may lead to the increase or to the decrease of the absolute value of the stress intensity factor depending upon the elastic mismatch between the composite constituents

a fast and stable well balanced scheme with hydrostatic reconstruction for shallow water flows we consider the saint venant system for shallow water flows with nonflat bottom it is a hyperbolic system of conservation laws that approximately describes various geophysical flows such as rivers coastal areas and oceans when completed with a coriolis term or granular flows when completed with friction numerical approximate solutions to this system may be generated using conservative finite volume methods which are known to properly handle shocks and contact discontinuities however in general these schemes are known to be quite inaccurate for near steady states as the structure of their numerical truncation errors is generally not compatible with exact physical steady state conditions this difficulty can be overcome by using the so called well balanced schemes we describe a general strategy based on a local hydrostatic reconstruction that allows us to derive a well balanced scheme from any given numerical flux for the homogeneous problem whenever the initial solver satisfies some classical stability properties it yields a simple and fast well balanced scheme that preserves the nonnegativity of the water height and satisfies a semidiscrete entropy inequality

a new approach for ranking fuzzy numbers by distance method abstract many ranking methods have been proposed so far however there is yet no method that can always give a satisfactory solution to every situation some are counterintuitive not discriminating some use only the local information of fuzzy values some produce different rankings for the same situation for overcoming the above problems we propose a new method for ranking fuzzy numbers by distance method our method is based on calculating the centroid point where the distance means from original point to the centroid point x 0 y 0 and the x 0 index is the same as murakami et al s x 0 however the y 0 index is integrated from the inverse functions of an lr type fuzzy number thus we use ranking function r a x 2 y 2 distance index as the order quantities in a vague environment our method can rank more than two fuzzy numbers simultaneously and the fuzzy numbers need not be normal furthermore we also propose the coefficient of variation cv index to improve lee and li s method comput math appl 15 1988 887 896 lee and li rank fuzzy numbers based on two different criteria namely the fuzzy mean and the fuzzy spread of the fuzzy numbers and they pointed out that human intuition would favor a fuzzy number with the following characteristics higher mean value and at the same time lower spread however when higher mean value and at the same time higher spread or lower mean value and at the same time lower spread exists it is not easy to compare its orderings clearly our cv index is defined as cv standard error mean which can overcome lee and li s problem efficiently in this way our proposed method can also be easily calculated by the mathematica package to solve problems of ranking fuzzy numbers at last we present three numerical examples to illustrate our proposed method and compare with other ranking methods

finite volume schemes with equilibrium type discretization of source terms for scalar conservation laws we develop here a new class of finite volume schemes on unstructured meshes for scalar conservation laws with stiff source terms the schemes are of equilibrium type hence with uniform bounds on approximate solutions valid in cell entropy inequalities and exact for some equilibrium states convergence is investigated in the framework of kinetic schemes numerical tests show high computational efficiency and a significant advantage over standard cell centered discretization of source terms equilibrium type schemes produce accurate results even on test problems for which the standard approach fails for some numerical tests they exhibit exponential type convergence rate in two of our numerical tests an equilibrium type scheme with 441 nodes on a triangular mesh is more accurate than a standard scheme with 50002 grid points

a well balanced flux vector splitting scheme designed for hyperbolic systems of conservation laws with source terms abstract we propose a way to construct robust numerical schemes for the computations of numerical solutions of one and two dimensional hyperbolic systems of balance laws in order to reduce the computational cost we selected the family of flux vector splitting schemes we reformulate the source terms as nonconservative products and treat them directly in the definition of the numerical fluxes by means of generalized jump relations this is applied to a 1d shallow water system with topography and to a 2d simplified model of two phase flows with damping effects numerical results and comparisons with a classical centered discretizations scheme are supplied

on the solution to the riemann problem for the compressible duct flow the quasi one dimensional euler equations in a duct of variable cross section form probably one of the simplest nonconservative systems we consider the riemann problem for it and discuss its properties in particular for some initial conditions the solution to the riemann problem appears to be nonunique in order to rule out the nonphysical solutions we provide two dimensional computations of the euler equations in a duct of corresponding geometry and compare them with the one dimensional 1d results then the physically relevant 1d solutions satisfy a kind of entropy rate admissibility criterion

optimal selection of the service rate for a finite input source fuzzy queuing system finite input source queuing models have a wide range of applications in many practical situations and are frequently found in machine maintenance and repair operations owing to uncontrollable factors finite input source queuing problems parameters may contain uncertainty that is why to begin with in this paper it is proposed the analysis development and design of a fuzzy queuing model with finite input source in which the arrival pattern as well as the service pattern follow an exponential distribution under uncertain parameter in order to design the system the established optimization criterion consists in determining the optimal number of servers so as to minimize the expected total cost function per unit time to choose among uncertain alternatives three techniques to make decisions under uncertainty are proposed this type of systems has a finite waiting line as a result the system of differential equations that governs the model s behaviour consists of a finite number of equations in the second place this feature of the finite input source queuing systems enables us to bring forward in this paper two new contributions i in the first one the following doubt has been raised and solved if the convergence of the probabilities email protected i t obtained from the fuzzy differential equations that govern the behaviour of the finite source system is worked out does the result match the steady state fuzzy probabilities obtained by applying zadeh s extension principle to the classic queuing model and ii it has been performed a fuzzy simulation experiment on the differential equations using bontempi s qua si iii algorithm this enables us to know the time evolution of the probabilities email protected i t and its convergence on the one hand on the other we can compare the results of the simulation to those analytically obtained by applying zadeh s extension principle this way the validity of the proposed procedure for the simulation is verified by means of the theoretical results the extension of queuing decision models to fuzzy environments enables the decision maker to obtain more informing results and wider knowledge on the behaviour of the system since the results obtained in the fuzzy queuing model are fuzzy subsets containing the whole initial information that is why the finite input source queuing models with uncertain data can be of more use and can have a broader range of applications

reformulating decision theory using fuzzy set theory and shafer s theory of evidence abstract utilities and probabilities in decision theory are usually assessed by asking individuals to indicate their preferences between various uncertain choices in this paper we argue that 1 the utility of a consequence can be assessed as the membership function of the consequence in the fuzzy set satisfactory 2 the probability of an event instead of being directly assessed should be inferred from the evidence associated with that event the degree of evidence is quantified using shaferian basic probability assignments in addition we use the heisenberg uncertainty principle to argue for a change in one of the technical assumptions underlying decision theory as a result of this change some kinds of evidence will be observable in certain experiments but unobservable in others since probabilities are defined over the potential outcomes of an experiment they will only be defined over some but not all the evidence as a result the probabilities associated with different experiments could be inconsistent this formulation emphasizes the importance of new distinctions and not just new information in updating probabilities we argue that this formulation addresses many of the observed empirical deviations between decision theory and experiment it also addresses the anomalies of quantum physics we close with a brief discussion of directions for further research

equilibrium schemes for scalar conservation laws with stiff sources we consider a simple model case of stiff source terms in hyperbolic conservation laws namely the case of scalar conservation laws with a zeroth order source with low regularity it is well known that a direct treatment of the source term by finite volume schemes gives unsatisfactory results for both the reduced cfl condition and refined meshes required because of the lack of accuracy on equilibrium states the source term should be taken into account in the upwinding and discretized at the nodes of the grid in order to solve numerically the problem we introduce a so called equilibrium schemes with the properties that i the maximum principle holds true ii discrete entropy inequalities are satisfied iii steady state solutions of the problem are maintained one of the difficulties in studying the convergence is that there are no bv estimates for this problem we therefore introduce a kinetic interpretation of upwinding taking into account the source terms based on the kinetic formulation we give a new convergence proof that only uses property ii in order to ensure desired compactness framework for a family of approximate solutions and that relies on minimal assumptions the computational efficiency of our equilibrium schemes is demonstrated by numerical tests that show that in comparison with an usual upwind scheme the corresponding equilibrium version is far more accurate furthermore numerical computations show that equilibrium schemes enable us to treat efficiently the sources with singularities and oscillating coefficients

hierarchical structures of fuzzy ratings in the analysis of strategic goals of enterprises abstract analysis of strategic goals of enterprises involves simultaneous consideration of various goals subgoals and strategies which are changed according to situations and problems and it is a complex unstructured ill defined process incorporating multiattribute comparisons and impreciseness of the data to cope with this analysis a methodology integrating the analytic hierarchy process ahp procedure what if analysis fuzzy sets and fuzzy arithmetic is proposed in this paper

on static analysis of finite repetitive structures by discrete fourier transform functional solutions for the static response of beam and plate like repetitive lattice structures are obtained by discrete fourier transform the governing equation is set up as a single operator form with the physical stiffness operator acting as a convolution sum and containing a matrix kernel which relates to the mechanical properties of the lattice boundary conditions do not affect the equation form and are taken into account at a subsequent stage of the analysis the technique of virtual load and substructure is proposed to formally close the repetitive lattice into a cyclic structure and to assure the equivalence of responses of the modified cyclic and original repetitive lattices a discrete periodic green s function is introduced for the modified structure and the final displacement solutions are written as convolution sums over the green s function and the actual external and virtual loads several example problems illustrate the approach

hierarchic models for laminated composites the principles governing the formulation of hierarchic models for laminated composites are discussed the essential features of the hierarchic models described herein are a the exact solutions corresponding to the hierarchic sequence of models converge to the exact solution of the corresponding problem of elasticity for a fixed laminate thickness and b the exact solution of each model converges to the same limit as the exact solution of the corresponding problem of elasticity with respect to the laminate thickness approaching zero hierarchic models make the computation of any engineering data possible to an arbitrary level of precision within the framework of the theory of elasticity examples are presented

representations of fuzzy relations with an application to group decision making abstract representations of fuzzy relations of type 1 and type 2 satisfying max and max product transitivities in terms of exact and fuzzy utility functions respectively have been obtained an application to group decision making has been indicated

methods for decision making with cardinal numbers and additive aggregation abstract for multi attribute decision making with cardinal numbers and additive aggregation the methods additive aggregation and outranking for crisp and fuzzy numbers are connected with the concept of linguistic variables preference ranking a generalization of outranking and preference ranking organization methods such as electre and promethee can be divided into three phases where each of them is defined completely by linguistic variables the derived method preference ranking with additive weighting and individual fuzziness has an improved selectivity or discrimination compared to conventional methods moreover the method fulfils four important requirements preference only for sufficiently large weights considering evaluation differences outside of thresholds and regarding aggregational and substitutional properties the simplified method preference ranking with additive weighting and general fuzziness allows a reduction of computational resources

numerical methods for interval and fuzzy number comparison based on the probabilistic approach and dempster shafer theory there are many different methods for interval and fuzzy number comparison proposed in the literature which provide the results of comparison in the form of a real or boolean value in this paper we use the dempster shafer theory of evidence with its probabilistic interpretation to justify and construct the method which provides the result of comparison in the form of an interval or fuzzy number the complete and consistent set of expressions for inequality and equality relations between intervals and fuzzy numbers has been obtained in the framework of the probabilistic approach these relations make it possible to compare intervals and fuzzy numbers with real values and may be considered as an asymptotic limit of the results we obtain using the dempster shafer theory a natural fuzzy extension of the proposed approach is considered and discussed using some illustrative examples

the r d project selection problem with fuzzy coefficients abstract this paper deals with the multicriteria project selection problem subject to linear constraints with zero one decision variables linguistic rather than numerical values are used in the project appraisals for each criterion with their meanings represented by normal fuzzy sets the grade of membership of a given alternative in the fuzzy set of all nondominated alternatives is computed by an algorithm that converges rapidly on the final solution continuity and normality are the only restrictions imposed on the membership functions an example of the overall procedure and topics for future research are presented

the preference order of fuzzy numbers abstract many fuzzy number ranking approaches are developed in the literature for multiattribute decision making problems almost all of the existing approaches focus on quantity measurement of fuzzy numbers for ranking purpose in this paper we consider the ranking process to determine a decision maker s preference order of fuzzy numbers a new ranking index is proposed to not only take quantity measurement but incorporate quality factor into consideration for the need of general decision making problems for measuring quantity several cuts of fuzzy numbers are used a signal noise ratio is defined to evaluate quality of a fuzzy number this ratio considers the middle point and spread of each cut of fuzzy numbers as the signal and noise respectively a fuzzy number with the stronger signal and the weaker noise is considered better moreover the associated levels are treated as the degree of belief about the cut and used as weights in the index for strengthening the influence of cut with higher levels the membership functions of fuzzy numbers are not necessarily to be known beforehand while applying this index only a few left and right boundary values of cuts of fuzzy numbers are required we have proved the feature of the proposed index in a particular case several examples are also used to illustrate the feature and applicability in ranking fuzzy numbers

ranking alternatives using fuzzy numbers a computational approach abstract the method presented by buckley fuzzy sets and systems 15 1985 21 31 for ranking alternatives by using fuzzy numbers is discussed as far as computational aspects are concerned an alternative procedure is presented which allows for the use of any convex and normalized fuzzy set to assess the contribution of each alternative to some overall objective according to a set of criteria the procedure also allows the criteria to be structured in n level hierarchies an example is presented to illustrate the algorithm

a fuzzy multicriteria group decision making approach to select configuration items for software development selection of configuration items in software configuration management is important to determine the software quality and reduce the development time and cost the objective of this research is to develop a multicriteria group decision making model based on fuzzy set theory to improve the configuration items selection process since most information available in this stage is not numerical fuzzy set theory is used to represent the evaluation ratings of candidate items the developed model ranks candidate items into partial or complete orders that can assist decision makers in selecting more proper set of configuration items the consensus measures are also developed to determine the group acceptability of the obtained ranking orders in addition sensitivity analysis can be performed to examine the solution robustness an example of flight simulator development project is used to illustrate the concept developed

preference relations on a set of fuzzy utilities as a basis for decision making abstract in fuzzy decision problems we often encounter situations of choosing among alternatives which are assigned fuzzy utilities these problems have been approached using fuzzy implications or direct comparisons among fuzzy utilities in the literature however there are few attempts to investigate the issues addressing reasonable choice or reasonable ordering using fuzzy sets theory this paper first introduces some fundamental properties of fuzzy binary relations and certain conditions of reasonable orderings of fuzzy utilities then a method for constructing a fuzzy preference relation on a given set of fuzzy utilities is proposed for the sake of rational decision making this procedure employs the concepts of the extended minimum and the hamming distance between the greatest upper sets or the greatest lower sets of fuzzy utilities finally it is shown that the proposed fuzzy preference relations have reasonable properties as fuzzy orderings for decision making

properties of the aggregation operators related with fuzzy relations abstract the problem of information generalization in multicriteria decision making is considered in this paper the information is unified by fuzzy relations and the generalization is realized with the help of aggregation operators some of the most oftenly used operators are presented and their properties depending on the properties of the fuzzy relations which they aggregate are proved the sensitivity of the operators with respect to variations in their arguments is investigated the numerical example deciding the problem of alternatives ranking is given as well

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

on fuzzy number lattice r abstract we give a systematic development of fuzzy number lattice theory many of our results generalize to number lattice over the lattice algebra our first main result is that the real number chain r is a homomorphic image of the fuzzy number lattice r that is r r and the congruence class r is a component of r thus we can be specialized to describe the structure of the fuzzy number lattice r next we study the structure and representation of the congruence class

indicators of fuzzy relations in this paper first we give the definitions of various indicators of fuzzy relations and their basic properties then we investigate the relationships between these indicators particularly between those of t transitivity negative s transitivity t s semitransitivity and t s ferrers property the investigation is divided into three parts results in the general case results under a condition proposed by peng et al and results under special t norms and t conorms on account of our research certain results on fuzzy relations in the literature are extended to the degree description

a well balanced scheme for the numerical processing of source terms in hyperbolic equations in a variety of physical problems one encounters source terms that are balanced by internal forces and this balance supports multiple steady state solutions that are stable typical of these are gravity driven flows such as those described by the shallow water equations over a nonuniform ocean bottom 1 10 qquad h t hu x 0 text and hu t left hu 2 frac gh 2 2 right x ga x x h 0 many classic numerical schemes cannot maintain these steady solutions or achieve them in the long time limit with an acceptable level of accuracy because they do not preserve the proper balance between the source terms and internal forces we propose here a numerical scheme adapted to a scalar conservation law that preserves this balance and that can it is hoped be extended to more general hyperbolic systems the proof of convergence of this scheme toward the entropy solution is given and some numerical tests are reported

ranking and defuzzification methods based on area compensation abstract we present some interesting properties related to the area compensation procedure to compare fuzzy numbers it has been proved that this method produces more than a fuzzy interval order it induces a ranking of fuzzy numbers some further results are given about the transitivity property and about computational aspects extensions to non normal fuzzy numbers and fuzzy quantities are also proposed

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

using fuzzy binary relations for identifying noninterior decision alternatives abstract a fuzzy noninferiority relation is introduced based on this relation fuzzy relations of preference strict preference indifference and incomparability are specified and their properties are investigated a fuzzy noninferior subset is defined and its basic characteristic properties are established an algorithm is presented for identifying a fuzzy set of noninferior alternatives in decision making situations that require the selection of a certain number of noninferior alternatives for more detailed study

rationality of fuzzy reciprocal preference relations we study relationships between different transitivity and acyclicity conditions for fuzzy reciprocal relations such conditions may be treated as rationality conditions for preferences described by such kind of relations

a hyperspatial representation of a particular set of fuzzy preference relations abstract in this paper we study a geometrical representation of a special class of fuzzy preference relations by establishing a one one correspondence between the set of all these relations and a hypercube of an n n 1 2 dimensional space furthermore we study some geometrical figures called h spheres and properties of the points which represent the preference relations in the above mentioned euclidean space

an approximate approach for ranking fuzzy numbers based on left and right dominance this study presents an approximate approach for ranking fuzzy numbers based on the left and right dominance the proposed approach only requires a few left and right spreads at some levels of fuzzy numbers to determine the respective dominance of one fuzzy number over the other the total dominance is then determined by combining the left and right dominance based on a decision maker s optimistic perspectives such a dominance is useful in ranking the fuzzy numbers when membership functions cannot be acquired the approach proposed herein is relatively simple in terms of computational efforts and is efficient when ranking a large quantity of fuzzy numbers by using a few left and right spreads two groups of examples demonstrate the accuracy and applicability of the proposed approach

ranking alternatives with fuzzy weights using maximizing set and minimizing set ranking alternatives both qualitative as well as quantitative in a multicriterion environment employing experts opinion preference structure using fuzzy numbers and linguistic variables are presented in this paper fuzzy weights wj i of alternatives a i are computed using standard fuzzy arithmetic concept of maximizing set and minimizing set is introduced to decide total utility or ordering value of each of the alternatives a numerical example is provided at the end to illustrate the method 1999 published by elsevier science b v all rights reserved

selecting is personnel use fuzzy gdss based on metric distance method abstract in this paper we propose a new approach to rank fuzzy numbers by metric distance for showing our method is a good ranking method we give two examples to compare with other methods the paper also developes a computer based group decision support system fmcgdss to increase the recruiting productivity and to easily compare our method with other fuzzy number ranking methods the fmcgdss includes three ranking methods intuition ranking lee and li s fuzzy mean spread and our metric distance method to help manager make better decision under fuzzy circumstance the result indicates that the new method is coincident with the intuition ranking and the lee and li s fuzzy mean spread method on each type weight

an investigation into relations between some transitivity related concepts abstract there exists a variety of transitivity notions in the literature to eliminate the possible inconsistency adherent to a fuzzy preference relation in ranking fuzzy quantities or alternatives the relationships among max min transitivity restricted max min transitivity quasitransitivity weak transitivity consistency and acyclicity are investigated we point out that max min transitivity and transitivity are very strong restrictions on a fuzzy preference relation and acyclicity is the weakest one with a certain transitivity condition an ordering procedure is suggested to obtain a total order relation among fuzzy quantities or alternatives based on a fuzzy preference relation

convergence of the 2 2 godunov method for a general resonant nonlinear balance law we introduce a generalized solution of the riemann problem for a general resonant nonlinear balance law and we prove the convergence of the 2 x 2 godunov numerical method based on these solutions in particular we obtain generic conditions that guarantee a canonical structure for the elementary waves in the solution of the riemann problem and an interesting multiplicity of time asymptotic wave patterns is observed and characterized

a godunov type scheme for the isentropic model of a fluid flow in a nozzle with variable cross section we present a godunov type scheme for the isentropic model of a fluid flow in a nozzle with variable cross section the model is of nonconservative form making it hard for standard numerical discretizations of the nonconservative term in particular the error for a standard numerical scheme with a usual discretization of the nonconservative term may become larger as the mesh size gets smaller we first re investigate the riemann problem of the model pointing out several interesting properties of the wave curves and establishing specific existence domain for each type of solutions then we incorporate local riemann solutions to build a godunov type scheme for the model the scheme is constructed in subsonic and supersonic regions where the system is strictly hyperbolic tests show that our scheme can capture standing waves so that it is well balanced furthermore tests also show that our godunov type scheme can give a good accuracy for numerical approximations of exact solutions our godunov type scheme can resolve the difficulty of other existing schemes for similar models of fluid flows with nonconservative terms

a fuzzy outranking method in energy policy planning abstract natural gas imported coal and nuclear power plants are compared in terms of long term 1996 2010 production economy in this study calculation of an accurate unit production cost of a power plant is generally a hard task especially in countries without any previous production experience unit production cost calculation becomes more difficult therefore it is difficult to determine the best plant alternatives to make a judgment owing to the subjective and incomplete data preference of alternatives is modeled with fuzzy preference relation three preferences models are developed to evaluate the nondominance set from a set of alternatives for further development during the applications of preference models if alternatives are outranked by other alternatives they are removed and are not taken into consideration the approach developed is very much suited for applications in the fuzzy and uncertain environment

fuzzy method in group decision making abstract this paper investigates the problems of decision making with multiple judge multiple criteria in a fuzzy environment where the performance of alternatives and the importance of criteria are imprecisely defined and represented by fuzzy sets a fuzzy model associated with the solution algorithm is proposed on the basis of an level weighted fuzzy preference relation a numerical example is solved for illustration

the multiple judge multiple criteria ranking problem a fuzzy set approach abstract this paper investigates the problem of selecting from a set of issues those which best satisfy a collection of criteria a group of judges have fuzzy sets defined over the issues for each criterion whose values lie in a finite linearly ordered set l these judges also have fuzzy sets defined over the set of criteria the paper discusses methods of aggregating all the fuzzy sets into one fuzzy set defined on the issues so that a l gives the final ranking for issue a

a robust numerical method for approximating solutions of a model of two phase flows and its properties the objective of the present paper is to extend our earlier works on simpler systems of balance laws in nonconservative form such as the model of fluid flows in a nozzle with variable cross section to a more complicated system consisting of seven equations which has applications in the modeling of deflagration to detonation transition in granular materials first we transform the system into an equivalent one which can be regarded as a composition of three subsystems then depending on the characterization of each subsystem we propose a convenient numerical treatment of the subsystem separately precisely in the first subsystem of the governing equations in the gas phase stationary waves are used to absorb the nonconservative terms into an underlying numerical scheme in the second subsystem of conservation laws of the mixture we can take a suitable scheme for conservation laws for the third subsystem of the compaction dynamics equation the fact that the velocities remain constant across solid contacts suggests us to employ the technique of engquist osher s scheme then we prove that our method possesses some interesting properties it preserves the positivity of the volume fractions in both phases and in the gas phase our scheme is capable of capturing equilibrium states preserves the positivity of the density and satisfies the numerical minimum entropy principle numerical tests show that our scheme can provide reasonable approximations for data the supersonic regions but the results are not satisfactory in the subsonic region however the scheme is numerically stable and robust

strong transitivity rationality and weak monotonicity in fuzzy pairwise comparisons strong transitivity and weak monotonicity are two important axioms in the theory of value and utility measurement in this paper we define strong transitivity and weak monotonicity for fuzzy pairwise comparisons matrices using the requirements of strong transitivity we develop a metric for measuring the degree of strong transitivity in fuzzy pairwise comparisons we further demonstrate that a matrix which satisfies the metric of strong transitivity will satisfy the weak monotonicity axiom as well

analysis and approximation of conservation laws with source terms we consider a conservation law of the form cl i ut f u x ax where a cdot is a bounded piecewise smooth source term and f an even convex function we first characterize the solution to the riemann problem through a new lax type formula then we prove that for a cdot fixed the semigroup associated with cl is an l1 contraction and we obtain an existence theorem for weak solutions to cl we conclude by constructing godunov type difference schemes and proving that these schemes are l infty stable and have stable steady solutions similar in structure to those of cl some numerical tests are reported

high order well balanced finite volume schemes for simulating wave propagation in stratified magnetic atmospheres wave propagation in idealized stellar atmospheres is modeled by the equations of ideal mhd together with the gravity source term the waves are modeled as small perturbations of isothermal steady states of the system we consider a formulation of ideal mhd based on the godunov powell form with an embedded potential magnetic field appearing as a parameter the equations are discretized by finite volume schemes based on approximate riemann solvers of the hll type and upwind discretizations of the godunov powell source terms local hydrostatic reconstructions and suitable discretization of the gravity source term lead to a well balanced scheme i e a scheme which exactly preserves a discrete version of the relevant steady states higher order of accuracy is obtained by employing suitable minmod eno and weno reconstructions based on the equilibrium variables to construct a well balanced scheme the resulting high order well balanced schemes are validated on a suite of numerical experiments involving complex magnetic fields the schemes are observed to be robust and resolve the complex physics well

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

the resonant cases and the riemann problem for a model of two phase flows abstract the resonant cases in the riemann problem for a model of two phase flows with resonance are investigated which complete the construction of riemann solutions the model is given by a nonconservative hyperbolic system of balance laws the phase decomposition method is developed to construct solutions in each phase in a relatively separated way but still glued to each other via the contact discontinuities composite wave curves can be built and intersections of wave curves in each phase plane help to determine various configurations of riemann solutions in particular solutions containing multiple waves propagating with the same shock speed are constructed

tool steel materials selection under fuzzy environment a fuzzy set multiple criteria decision making approach is proposed to help selecting the most suitable tool steel materials for a specific manufacturing application such as die design jig and fixture design the important weights of different criteria and the material suitability ratings of various alternatives under different criteria are given in linguistic terms subsequently they are represented in fuzzy linguistic values and fuzzy numbers through aggregation and ranking of fuzzy numbers the most suitable tool steel material is determined a hypothetical example is illustrated further by computerizing the proposed method and incorporating appropriate interface design together with a data base of tool steel materials assessment information from the handbook a decision support system can be constructed

weak and graded properties of fuzzy relations in the context of aggregation process we study graded properties a properties of fuzzy relations which are parameterized versions of properties of a fuzzy relation defined by l a zadeh namely we take into account fuzzy relations which are a reflexive a irreflexive a symmetric a antisymmetric a asymmetric a connected a transitive where a 0 1 we also pay our attention to the composed versions of these basic properties e g an a equivalence a orders we also consider the so called weak properties of fuzzy relations which are the weakest versions of the standard properties of fuzzy relations we take into account the same types of properties as in the case of the graded ones using functions of n variables we consider an aggregated fuzzy relation of given fuzzy relations we give conditions for functions to preserve graded and weak properties of fuzzy relations

comparison of clusters from fuzzy numbers fuzzy numbers are used for representation of numerical quantities in a vague environment their comparison or ranking is important for application purposes a new index for comparing of fuzzy numbers based on their geometrical properties is suggested in this paper this geometrical index is tested on a group of selected examples and compared with the other well known indexes a method for comparison of m tuples of fuzzy numbers and an algorithm for comparison of subsets clusters of similar closed m tuples of trapezoidal fuzzy numbers are presented

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

linear programming with fuzzy parameters an interactive method resolution this paper proposes a method for solving linear programming problems where all the coefficients are in general fuzzy numbers we use a fuzzy ranking method to rank the fuzzy objective values and to deal with the inequality relation on constraints it allows us to work with the concept of feasibility degree the bigger the feasibility degree is the worst the objective value will be we offer the decision maker dm the optimal solution for several different degrees of feasibility with this information the dm is able to establish a fuzzy goal we build a fuzzy subset in the decision space whose membership function represents the balance between feasibility degree of constraints and satisfaction degree of the goal a reasonable solution is the one that has the biggest membership degree to this fuzzy subset finally to illustrate our method we solve a numerical example

a well balanced approximate riemann solver for compressible flows in variable cross section ducts a well balanced approximate riemann solver is introduced in this paper in order to compute approximations of one dimensional euler equations in variable cross section ducts the interface riemann solver is grounded on the vfroe ncv scheme and it enforces the preservation of riemann invariants of the steady wave the main properties of the scheme are detailed we provide numerical results to assess the validity of the scheme even when the cross section is discontinuous a first series is devoted to analytical test cases and the last results correspond to the simulation of a bubble collapse

constructing a godunov type scheme for the model of a general fluid flow in a nozzle with variable cross section a godunov type scheme for the model of a general fluid flow in a nozzle with variable cross section is presented the model has the form of a nonconservative system of balance laws which poses many challenging questions for study first exact riemann solvers in computing form are described in both subsonic and supersonic regions second the computable exact solutions of local riemann problem are incorporated into a godunov type scheme third the scheme is shown to be well balanced in the sense that it can capture exactly stationary waves finally numerical tests for data belong to both subsonic and supersonic regions are presented these tests show that the scheme has a very fine accuracy especially the scheme can give very good approximations to the exact solutions even in the resonant phenomenon where the solution contains three waves of the same speed

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

fuzzy preferences in the graph model for conflict resolution a new framework for the graph model for conflict resolution is developed so that decision makers dms with fuzzy preferences can be included in conflict models a graph model is both a formal representation for multiple participant multiple objective decision problems and a set of analysis procedures that add insights into them within the new framework graph models can include and integrate into the analysis both certain and uncertain information about dms preferences one key contribution of this study is to extend the four basic stability definitions for two or more dms to models with fuzzy preferences together fuzzy nash stability fuzzy general metarationality fuzzy symmetric metarationality and fuzzy sequential stability provide anuanced description of human behavior a state is fuzzy stable for a dm if a move to any other state is not sufficiently likely to yield an outcome which the dm prefers where sufficiency is measured according to a fuzzy satisficing threshold that is the characteristic of the dm a fuzzy equilibrium which is an outcome that is fuzzy stable for all dms therefore represents a possible resolution of the strategic conflict the practical application and interpretation of these new stability definitions are illustrated with an example

on the interval approximation of a fuzzy number the notion of an approximation interval of a fuzzy number is introduced it is the interval which fulfills two conditions in the first its width is equal to the width of a fuzzy number being approximated in the second the hamming distance between this interval and the approximated number is minimal the introduced notion is compared with the notion of expected interval of a fuzzy number known in literature