extending yager s orness concept for the owa aggregators to other mean operators abstract in this paper we address the problem of defining the orness closeness to the maximum and andness closeness to the minimum of fuzzy aggregation operators in particular we center our study in fuzzy mean aggregators as defined by dubois prade and yager for this purpose we propose the introduction of the orness distribution function orness average value orness extension measure and orness sequence which we believe are valid concepts to characterize this type of aggregation operators we study their application to several well known mean operators and prove as well that in the case of yager s owa operators the orness average value that we propose coincides with yager s original orness definition we also introduce a method for the construction of mean operators from a predefined orness distribution function and make some considerations about the extension of these concepts to the cases of weighted aggregations or aggregations based on fuzzy measures

characterizations of discrete sugeno integrals as polynomial functions over distributive lattices we give several characterizations of discrete sugeno integrals over bounded distributive lattices as particular cases of lattice polynomial functions that is functions which can be represented in the language of bounded lattices using variables and constants we also consider the subclass of term functions as well as the classes of symmetric polynomial functions and weighted infimum and supremum functions and present their characterizations accordingly moreover we discuss normal form representations of these functions

on viewing fuzzy measures as fuzzy subsets we introduce the concept of a fuzzy measure discuss some of their basic properties and look at some notable examples we introduce a correspondence between a fuzzy measure on x and a fuzzy subset over the power set of x these fuzzy subsets are required to have special properties on the space 2x and we refer to these as measure type fuzzy sets we take advantage of this correspondence between a fuzzy measure and a fuzzy set to suggest the formulation of various set operations on fuzzy measures

convergence rates of the truncated euler maruyama method for stochastic differential equations influenced by higham et al 2002 several numerical methods have been developed to study the strong convergence of the numerical solutions to stochastic differential equations sdes under the local lipschitz condition these numerical methods include the tamed euler maruyama em method the tamed milstein method the stopped em the backward em the backward forward em etc recently we developed a new explicit method in mao 2015 called the truncated em method for the nonlinear sde d x t f x t d t g x t d b t and established the strong convergence theory under the local lipschitz condition plus the khasminskii type condition x t f x p 1 2 g x 2 k 1 x 2 however due to the page limit there we did not study the convergence rates for the method which is the aim of this paper we will under some additional conditions discuss the rates of l q convergence of the truncated em method for 2 q p and show that the order of l q convergence can be arbitrarily close to q 2

higher order implicit strong numerical schemes for stochastic differential equations higher order implicit numerical methods which are suitable for stiff stochastic differential equations are proposed these are based on a stochastic taylor expansion and converge strongly to the corresponding solution of the stochastic differential equation as the time step size converges to zero the regions of absolute stability of these implicit and related explicit methods are also examined

weighted minimum and maximun operations in fuzzy sets theory abstract this short note comments on the interpretation of weighted minimum and maximum operations introduced in a previous paper as medians and corrects a misleading statement about it

on sugeno integral as an aggregation function the sugeno integral for a given fuzzy measure is studied under the viewpoint of aggregation in particular we give some equivalent expressions of it we also give an axiomatic characterization of the class of all the sugeno integrals some particular subclasses such as the weighted maximum and minimum functions are investigated as well

benchmarking in linguistic importance weighted aggregations in this work we concentrate on the issue of weighted aggregations and provide a possibilistic approach to the process of importance weighted transformation when both the importances interpreted as benchmarks and the ratings are given by symmetric triangular fuzzy numbers we will show that using the possibilistic approach i small changes in the membership function of the importances can cause only small variations in the weighted aggregate ii the weighted aggregate of fuzzy ratings remains stable under small changes in the nonfuzzy importances iii the weighted aggregate of crisp ratings still remains stable under small changes in the crisp importances whenever we use a continuous implication operator for the importance weighted transformation we illustrate the proposed method by some simple examples

on four noncommutative fuzzy connectives and their axiomatization in most of the query languages conjunctive and disjunctive combinations of conditions remain the usual way for aggregation fuzzy query languages also offer trade off operators such as means in order to compensate between elementary conditions in this paper we would like to introduce a new type of condition basically founded on the interaction between two predicates thus enriching the panoply of tools the user is provided with and the power of query languages

a note on the conditional probability of fuzzy subsets of a continuous domain abstract the notion of a mass assignment corresponding to a discrete fuzzy set is generalised to include all fuzzy sets the definition is motivated by considering a possible mechanism by which an intelligent agent could extend set theoretic operations to fuzzy sets this same mechanism also suggests an alternative definition for the conditional probability of fuzzy sets it is noted that this definition is probability possibility consistent and it is shown that in the case where the probability distribution on the domain has a density function then the conditional probability of f given g can be expressed as the probability of f calculated relative to a conditional density function dependent on g this result is used to develop an analytical method for calculating conditional probabilities of fuzzy subsets of the reals where the membership functions of f and g and the density function are continuous piecewise linear functions such a method has applications to the development of a general semantic unification in fril

modification of a finite volume scheme for laplace s equation for laplace s equation we discuss whether it is possible to construct a linear positive finite volume fv scheme on arbitrary unstructured grids dealing with the arbitrary grids we state a control volume which guarantees a positive fv scheme with linear reconstruction of the solution the control volume is defined by a property of the analytical solution to the equation and does not depend on the grid geometry for those problems where the choice of the control volume is prescribed a priori we demonstrate how to improve positivity of the linear fv scheme by using corrected reconstruction stencils the difficulties arising when grids with no geometric restrictions are used for the discretization are discussed numerical examples illustrating the developed approach to the stencil correction are given

weak order stochastic runge kutta methods for commutative stochastic differential equations a new explicit stochastic runge kutta scheme of weak order 2 is proposed under a commutativity condition which is derivative free and which attains order 4 for ordinary differential equations the weak order conditions are derived by utilizing multi colored rooted tree analysis and a solution is found in a transparent way the scheme is compared with other derivative free and weak second order schemes in numerical experiments

temporal scenario modelling and recognition based on possibilistic logic we propose in this paper a new approach for the modelling and recognition of temporal scenarios a scenario is represented by three different structures the first one models the logical dependency between the elements of the scenario using possibilistic logic while the second one is the minimal temporal graph representing all temporal constraints between the events the third structure explains the way the matching between observations and scenarios has to be done the consistency between the three structures is ensured

continuous preference logic for system evaluation in this paper we investigate mathematical models that are suitable for modeling decisions in the area of system evaluation comparison and selection our interest is focused on soft computing models that can be directly related to observable properties of human reasoning and have a record of use in system evaluation practice we analyze various approaches to defining andness and orness and use a generalized conjunction disjunction gcd to build compound preference logic functions and logic models for system evaluation we also present applications of the continuous preference logic in decision models based on the lsp method

on conditions under which some generalized sugeno integrals coincide a solution to dubois problem abstract in the paper we characterize the class of all pairs of fuzzy implications and dual fuzzy implications such that the q integral and q cointegral coincide this gives a solution to the problem posed by didier dubois during the conference fsta 2016 the 13th international conference on fuzzy set theory and applications as a corollary we obtain the necessary and sufficient conditions under which the seminormed fuzzy integral and the semiconormed fuzzy integral are equal for all measurable functions

a monotone finite element scheme for convection diffusion equations a simple technique is given in this paper for the construction and analysis of a class of finite element discretizations for convection diffusion problems in any spatial dimension by properly averaging the pde coefficients on element edges the resulting finite element stiffness matrix is an m matrix under some mild assumption for the underlying generally unstructured finite element grids as a consequence the proposed edge averaged finite element scheme is particularly interesting for the discretization of convection dominated problems this scheme admits a simple variational formulation it is easy to analyze and it is also suitable for problems with a relatively smooth flux variable some simple numerical examples are given to demonstrate its effectiveness for convection dominated problems

strong convergence of the stopped euler maruyama method for nonlinear stochastic differential equations in this paper numerical methods for the nonlinear stochastic differential equations sdes with non global lipschitz drift coefficient are discussed the existing known results have only so far shown that the classical explicit euler maruyama em approximate solutions converge to the true solution in probability 22 23 more recently the authors in 16 proved that the classical em method will diverge in l 2 sense for the underlying sdes in this paper and those sdes with superlinearly growing coefficients these strongly indicate that the classical em method is not good enough for the highly nonlinear sdes however in this paper we introduce a modified em method using stopping time and show successfully that the discrete version of the modified em approximate solution converges to the true solution in the strong sense namely in l 2 with a order arbitrarily close to a half

fuzzy sets and decision analysis abstract this survey points out recent advances in multiple attribute decision making methods dealing with fuzzy or ill defined information fuzzy maut as well as fuzzy outranking methods are reviewed aggregation procedures choice problems and treatment of interactive attributes are covered trends in research and open problems are indicated

finite element approximation of the diffusion operator on tetrahedra linear galerkin finite element discretizations of the laplace operator produce nonpositive stiffness coefficients for internal element edges of two dimensional delaunay triangulations this property also called the positive transmissibility pt condition is a prerequisite for the existence of an m matrix and ensures that nonphysical local extrema are not present in the solution for tetrahedral elements it has already been shown that the linear galerkin approach does not in general satisfy the pt condition we propose a modification of the three dimensional galerkin scheme that if a delaunay triangulation is used satisfies the pt condition for internal edges and if further conditions on the boundary are specified yields an m matrix the proposed approach can also be extended to the general diffusion operator with nonconstant or anisotropic coefficients

stability analysis of numerical schemes for stochastic differential equations stochastic differential equations sdes represent physical phenomena dominated by stochastic processes as for deterministic ordinary differential equations odes various numerical schemes are proposed for sdes in this paper we study the stability of numerical schemes for scalar sdes with respect to the mean square norm which we call ms stability we will show some figures of the ms stability domain or regions for some numerical schemes and present numerical results which confirm it this notion is an extension of absolute stability in numerical methods for odes

choice processes for non homogeneous group decision making in linguistic setting several choice processes of alternatives for non homogeneous group decision making problems assuming linguistic preference relations for expressing the opinions of individuals and linguistic values for expressing their respective power or importance degrees are presented these processes are designed using two choice degrees of alternatives based on the concept of fuzzy majority quantifier guided linguistic dominance degree and quantifier guided linguistic non dominance degree being the last one a generalization of orlovski s non dominated alternative concept in order to deal with non weighted linguistic information the linguistic ordered weighted averaging lowa operator is applied to deal with weighted linguistic information three operators of linguistic weighted information aggregation are used the linguistic weighted disjunction lwd operator the linguistic weighted conjunction lwc operator and the linguistic weighted averaging lwa operator

numerical integration of stochastic differential equations several numerical methods for treating stochastic differential equations are considered both the convergence in the mean square limit and the convergence of the moments is discussed and the generation of appropriate random numbers is treated the necessity of simulations at various time steps with an extrapolation to time step zero is emphasized and demonstrated by a simple example

fuzzy set connectives as combinations of belief structures abstract consonant belief structures provide a representation for fuzzy sets owing to the fact that their plausibility measures are essentially possibility measures we note that two belief structures are equivalent if their plausibility and belief functions are equal this observation leads us to provide a multiple number of equivalent representations for any belief structure commensurate representations can be induced for two different belief structures by forcing the same number of focal elements with the same weights we show that if we represent two consonant belief structures in a commensurate manner then their aggregations are closed with respect to consonance provided that the additional requirement that the underlying probability distributions satisfy a condition of correlation is imposed the results of this work allow us to use belief structure representations for the manipulation of fuzzy subsets under various logical combinations all basic fuzzy set connectives can thus be interpreted in the framework of the theory of evidence

aggregating constraint satisfaction degrees expressed by possibilistic truth values in information systems one often has to deal with constraints in order to compel the semantics and integrity of the stored information or to express some querying criteria hereby different constraints can be of different importance a method to aggregate the information about the satisfaction of a finite number of constraints for a given data instance is presented central to the proposed method is the use of extended possibilistic truth values to express the degree of satisfaction of a constraint and the use of residual implicators and residual coimplicators to model the impact and relevance of a constraint the proposed method can be applied to any constraint based system a database application is discussed and illustrated

a random map implementation of implicit filters implicit particle filters for data assimilation generate high probability samples by representing each particle location as a separate function of a common reference variable this representation requires that a certain underdetermined equation be solved for each particle and at each time an observation becomes available we present a new implementation of implicit filters in which we find the solution of the equation via a random map as examples we assimilate data for a stochastically driven lorenz system with sparse observations and for a stochastic kuramoto sivashinsky equation with observations that are sparse in both space and time

strong predictor corrector euler maruyama methods for stochastic differential equations with markovian switching in this paper numerical methods for solving stochastic differential equations with markovian switching sdewmss are developed by pathwise approximation the proposed family of strong predictor corrector euler maruyama methods is designed to overcome the propagation of errors during the simulation of an approximate path this paper not only shows the strong convergence of the numerical solution to the exact solution but also reveals the order of the error under some conditions on the coefficient functions a natural analogue of the p stability criterion is studied numerical examples are given to illustrate the computational efficiency of the new predictor corrector euler maruyama approximation

reliability estimation and design with insufficient data based on possibility theory early in the engineering design cycle it is difficult to quantify product reliability or compliance to performance targets because of insufficient data or information for modeling the uncertainties design decisions are therefore based on fuzzy information that is vague imprecise qualitative linguistic or incomplete the uncertain information is usually available as intervals with lower and upper limits in this work the possibility theory is used to assess design reliability with incomplete information the possibility theory can be viewed as a variant of fuzzy set theory the formal theories to handle uncertainty are first introduced using the theoretical fundamentals of fuzzy measures a computationally efficient and accurate hybrid global local optimization approach is subsequently described for calculating the confidence level of fuzzy response the method combines the advantages of the commonly used vertex and discretization methods subsequently the possibility theory is used in design a possibility based design optimization method is proposed where all design constraints are expressed in a possibilistic way it is shown that the method gives a conservative solution compared with all conventional reliability based designs obtained with different probability distributions finally a general possibility based design optimization method which handles a combination of random and possibilistic design variables is presented several numerical examples demonstrate the application of possibility theory in design

weak second order splitting schemes for lagrangian monte carlo particle methods for the composition pdf fdf transport equations we study a class of methods for the numerical solution of the system of stochastic differential equations sdes that arises in the modeling of turbulent combustion specifically in the monte carlo particle method for the solution of the model equations for the composition probability density function pdf and the filtered density function fdf this system consists of an sde for particle position and a random differential equation for particle composition the numerical methods considered advance the solution in time with weak second order accuracy with respect to the time step size the four primary contributions of the paper are i establishing that the coefficients in the particle equations can be frozen at the mid time while preserving second order accuracy ii examining the performance of three existing schemes for integrating the sdes iii developing and evaluating different splitting schemes which treat particle motion reaction and mixing on different sub steps and iv developing the method of manufactured solutions mms to assess the convergence of monte carlo particle methods tests using mms confirm the second order accuracy of the schemes in general the use of frozen coefficients reduces the numerical errors otherwise no significant differences are observed in the performance of the different sde schemes and splitting schemes

runge kutta methods for numerical solution of stochastic differential equations the way to obtain deterministic runge kutta methods from taylor approximations is generalized for stochastic differential equations now by means of stochastic truncated expansions about a point for sufficiently smooth functions of an ito process a class of explicit runge kutta schemes of second order in the weak sense for systems of stochastic differential equations with multiplicative noise is developed also two runge kutta schemes of third order have been obtained for scalar equations with constant diffusion coefficients numerical examples that compare the proposed schemes to standard ones are presented

numerical procedures for sample structures on stochastic differential equations procedures are discussed for the numerical construction of sample processes on stochastic differential equations structures of a relevant class of gaussian white noise functionals are analyzed to some closed forms and new numerical algorithms for single noise problems are presented up to the accuracy of o h3 or within errors of o h7 2 in the sense of the mean square norm

the application of fuzzy integrals in multicriteria decision making abstract this paper presents a synthesis on the application of fuzzy integrals as an innovative tool for criteria aggregation in decision problems the main point is that fuzzy integrals are able to model interaction between criteria in a flexible way the methodology has been elaborated mainly in japan and has been applied there successfully in various fields such as design reliability evaluation of goods etc it seems however that this technique is still very little known in europe it is one of the aims of this review to disseminate this emerging technology in many industrial fields

a general framework for explaining the results of a multi attribute preference model the automatic generation of an explanation of the prescription made by a multi attribute decision model is crucial in many applications such as recommender systems this task is complex since the quantitative models are not designed to be easily explainable the major limitation of the previous research is that there is no formal justification of the arguments that are selected in the explanation the goal of this paper is to define a general framework to justify which arguments shall be selected in the case where the decision model is based on weights assigned to the attributes due to the complexity of explaining a preference model based on utility theory several explanation reasonings are necessary to cover all cases ranging from situations where the prescription is trivial to situations where the prescription is much more tight the set of selected arguments is in this framework a non dominated element of a combinatorial structure in the sense of an order relation our general approach is instantiated precisely on three models the probabilistic expected utility model the qualitative pessimistic minmax model and the concordance rule which are all constructed from a weight vector

multi step ranking of alternatives in a multi criteria and multi expert decision making environment in this work we introduce a decision model in the form of a recursive aggregation algorithm that attempts to mimic a multi step ranking process of a set of alternatives in a multi criteria and multi expert decision making environment the main idea is rather intuitive each alternative is initially assigned a list of values representing the group experts opinion about the extent to which the alternative satisfies a set of given criteria then the values for each alternative are combined with the weighted mean operator according to vectors of weights one for each decision maker in the group these weights express the personal judgement of the decision makers about the relative importance of the individual criteria consequently a new vector of values is obtained for each alternative these new values are combined again with the weighted mean operator taking into account the different degrees of influence each decision maker accepts from the rest of the group the latter aggregation step is repeated again and again for each alternative until a consensus is attained

numerical integration of multiplicative noise stochastic differential equations a two stage runge kutta algorithm for vector ito and by transform also stratonovich stochastic differential equations with multiplicative noise has been developed the method is second order accurate but for vanishing drift the algorithm yields a martingale independent of step size several examples are included to illustrate our method a discussion of errors shows that sample size can be as important as truncation

upper and lower images of a fuzzy set induced by a fuzzy relation applications to fuzzy inference and diagnosis in fuzzy set theory the image of a fuzzy set induced by a fuzzy relation is usually obtained by a sup t norm composition this corresponds to the upper image which gathers the elements in relation with at least one element of the fuzzy set however the dual point of view leading to the definition of the lower image as the fuzzy set of elements in relation with all the elements of the fuzzy set whose image is computed is not often considered fuzzy sets and fuzzy relations depending on the situations can be interpreted either in a conjunctive manner or as subsets of mutually exclusive possible values for variables whose precise values are ill known disjunctive view the applications of upper and lower images are investigated in both interpretations the generalized modus ponens used in fuzzy rule based systems corresponds to the disjunctive view the interest of upper and lower images is also emphasized for diagnosis problems where the conjunctive interpretation is encountered

inverse average type finite element discretizations of selfadjoint second order elliptic problems etude d une classe de discretisations a elements finis lineaires par morceaux des problemes aux valeurs limites elliptiques du second ordre autoadjoints

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

including importances in owa aggregations using fuzzy systems modeling ordered weighted averaging owa operators are described and are shown to provide a general class of parameterized aggregation operators that include the max min and average we suggest an approach to the inclusion of importances in the owa operator aggregation technique the methodology suggested involves a transformation of the scores to be aggregated by their respective importances we show how we can construct transformation functions with the aid of the fuzzy modeling technology

a haar like construction for the ornstein uhlenbeck process the classical haar construction of brownian motion uses a binary tree of triangular wedge shaped functions this basis has compactness properties which make it especially suited for certain classes of numerical algorithms we present a similar basis for the ornstein uhlenbeck process in which the basis elements approach asymptotically the haar functions as the index increases and preserve the following properties of the haar basis all basis elements have compact support on an open interval with dyadic rational endpoints these intervals are nested and become smaller for larger indices of the basis element and for any dyadic rational only a finite number of basis elements is nonzero at that number thus the expansion in our basis when evaluated at a dyadic rational terminates in a finite number of steps we prove the covariance formulae for our expansion and discuss its statistical interpretation

sampling fuzzy discretization and signal reconstruction abstract the sampling theorem provides the condition under which a continuous time signal can be precisely represented and completely recovered from its instantaneous values equally spaced in time it gives a condition for the signal reconstruction problem the importance of this theorem pertains to the necessity of knowing when a continuous time signal is uniquely represented by its discrete version so that continuous time signals can be properly converted and handled by sampled data systems like digital computers the problem of the equivalence between either continuous time or discrete time signals and their fuzzy descriptions is analyzed here this encompasses the analysis of signal reconstruction when fuzzy systems are used as sampled data systems such as fuzzy filters fuzzy models or fuzzy controllers a necessary and sufficient condition is given for ensuring that the fuzzy system processes the legitimate representations of the signal presented at its interfaces furthermore a sufficient condition suitable for automatic tuning of membership functions is proposed and discussed the discussion encompasses the outline of some requirements that membership functions at fuzzy system interfaces should meet to allow humans to assess their semantic meaning

semantics of quotient operators in fuzzy relational databases abstract the quotient operator plays an important role for query evaluation in relational databases its extension to fuzzy databases raises the question of the intended interpretation of the intermediary degrees attached to the items in the fuzzy relations this note points out that the fuzzy quotient operator should be defined in slightly different ways depending on the possible interpretations of the degrees levels of satisfaction of a gradual property levels of importance of a required property uncertainty pertaining to the membership of an element to a subset

fuzzy integral in multicriteria decision making abstract this paper presents a synthesis on the use of fuzzy integral as an aggregation operator in multicriteria decision making definitions essential properties are given and compared to those of usual aggregation operators a quick survey on applications is given

balanced implicit methods for stiff stochastic systems this paper introduces some implicitness in stochastic terms of numerical methods for solving stiff stochastic differential equations and especially a class of fully implicit methods the balanced methods their order of strong convergence is proved numerical experiments compare the stability properties of these schemes with explicit ones

efficiencies of two stage systems with fuzzy data two stage dea data envelopment analysis models show the performance of individual processes and thus are more informative than the conventional one stage models for making decisions this paper extends this approach from deterministic to uncertain situations where the observations are represented by fuzzy numbers the extension principle is utilized to develop a pair of two level mathematical programs to calculate the lower and upper bounds of the a cut of the fuzzy efficiency by enumerating various values of a the membership functions of fuzzy efficiencies are constructed numerically it is found that the property of the system efficiency being equal to the product of the two process efficiencies which holds for the deterministic case also holds for the fuzzy case this property can be generalized to series systems with more than two processes an example of non life insurance companies in taiwan is used to explain how to calculate the system and process efficiencies and how to derive their relationship when the data is fuzzy

stability of weak numerical schemes for stochastic differential equations abstract this paper considers numerical stability and convergence of weak schemes solving stochastic differential equations a relatively strong notion of stability for a special type of test equations is proposed these are stochastic differential equations with multiplicative noise for different explicit and implicit schemes the regions of stability are also examined

social choice axioms for fuzzy set aggregation the problem of aggregating n fuzzy sets f1 f2 fn on a set is viewed as one of merging the opinions of n individuals e g experts that rate objects belonging to this approach contrasts with the pure set theoretic point of view and leads to interpreting already known axioms underlying fuzzy connectives in a way different from that of multiple criteria aggregation various natural properties of a voting procedure including the ones proposed by arrow are expressed in the fuzzy set setting a number of conditions limiting the choice of fuzzy set operations are proposed and classified according to whether they are imperative mainly technical or facultative families of solutions are obtained that include those proposed in earlier works the case of non homogeneous groups is briefly examined lastly the application of the voting paradigm to the management of antagonistic local decision rules in knowledge based systems is outlined

on some optimization problems under uncertainty abstract the last ten years show a diversification of the approaches for handling uncertainties in optimization problems by certain relaxations or on the contrary seeking a more conservative solution in this paper we present some new results and points of view in nonlinear inexact and fuzzy mathematical programming possible applications to capital budgeting of interrelated projects and to production planning are also discussed

characterization and comparison of sugeno and choquet integrals abstract starting from the concept of equiordered functions we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure sugeno and choquet integrals the characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals pointing out their formal similarities and their conceptual differences

voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids voronoi cells and the notion of natural neighbours are used to develop a finite difference method for the diffusion operator on arbitrary unstructured grids natural neighbours are based on the voronoi diagram which partitions space into closest point regions the sibson and the laplace non sibsonian interpolants which are based on natural neighbours have shown promise within a galerkin framework for the solution of partial differential equations in this paper we focus on the laplace interpolant with a two fold objective first to unify the previous developments related to the laplace interpolant and to indicate its ties to some well known numerical methods and secondly to propose a voronoi cell finite difference scheme for the diffusion operator on arbitrary unstructured grids a conservation law in integral form is discretized on voronoi cells to derive a finite difference scheme for the diffusion operator on irregular grids the proposed scheme can also be viewed as a point collocation technique a detailed study on consistency is conducted and the satisfaction of the discrete maximum principle stability is established owing to symmetry of the laplace weight a symmetric positive definite stiffness matrix is realized which permits the use of efficient linear solvers on a regular rectangular or hexagonal grid the difference scheme reduces to the classical finite difference method numerical examples for the poisson equation with dirichlet boundary conditions are presented to demonstrate the accuracy and convergence of the finite difference scheme copyright 2003 john wiley sons ltd

numerical treatment of stochastic differential equations we define general runge kutta approximations for the solution of stochastic differential equations sde these approximations are proved to converge in quadratic mean to the solution of an sde with a corrected drift the explicit form of the correction term is given concerning the order of convergence we show that in general it is impossible for the quadratic mean of the one step error to be of an order greater than o h 3 this order is attained e g by the stochastic analogue of heun s method in the n dimensional case the highest order of convergence is in general only o h 2 attained by euler s method the order o h 3 can only be reached if nabla x sigma r sigma s nabla x sigma s sigma r for the diffusion matrix

fuzzy set based methods in instance based reasoning a formal framework of instance based prediction is presented in which the generalization beyond experience is founded on the concepts of similarity and possibility the underlying extrapolation principle is formalized within the framework of fuzzy rules thus instance based reasoning can be realized as fuzzy set based approximate reasoning more precisely our model makes use of so called possibility rules these rules establish a relation between the concepts of similarity and possibility which takes the uncertain character of similarity based inference into account inductive inference is possibilistic in the sense that predictions take the form of possibility distributions on the set of outcomes rather than precise deterministic estimations the basic model is extended by means of fuzzy set based modeling techniques this extension provides the basis for incorporating domain specific expert knowledge thus our approach favors a view of instance based reasoning according to which the user interacts closely with the system

computer simulations of multiplicative stochastic differential equations a class of robust algorithms for the computer simulation of stochastic differential equations with multiplicative noise is investigated excellent agreement is obtained with the known analytic behaviour of the kubo oscillator in the white noise limit the algorithms include a known first order one dimensional explicit method as well as implicit methods of increased stability a distinction is drawn between classes of stochastic differential equations depending on the type of spatial variation or curvature defined by the diffusion tensor this allows greatly simplified numerical implementations of the new algorithms in certain cases the results of different techniques are compared for the case of the kubo oscillator where a semi implicit technique gives the greatest accuracy

a weighted max min model for fuzzy goal programming abstract after narasimhan s pioneering study of applying fuzzy set theory to goal programming in 1980 many achievements in the field have been recorded most of them followed the max min approach however when objectives have different levels of importance only the weighted additive model of tiwari et al seems to be applicable however the shortcoming of the additive model is that the summation of quasiconcave functions may not be quasiconcave this study proposes a novel weighted max min model for fuzzy goal programming fgp and for fuzzy multiple objective decision making the proposed model adapts well to even the most complicated membership functions numerical examples demonstrate that the proposed model can be effectively incorporated with other approaches to fgp and is superior to the weighted additive approach

the truncated euler maruyama method for stochastic differential equations influenced by higham et al 2003 several numerical methods have been developed to study the strong convergence of the numerical solutions to stochastic differential equations sdes under the local lipschitz condition these numerical methods include the tamed euler maruyama em method the tamed milstein method the stopped em the backward em the backward forward em etc in this paper we will develop a new explicit method called the truncated em method for the nonlinear sde d x t f x t d t g x t d b t and establish the strong convergence theory under the local lipschitz condition plus the khasminskii type condition x t f x p 1 2 g x 2 k 1 x 2 the type of convergence specifically addressed in this paper is strong l q convergence for 2 q p and p is a parameter in the khasminskii type condition

residuated variants of sugeno integrals sugeno integrals and their particular cases such as weighted minimum and maximum have been used in multiple criteria aggregation when the evaluation scale is qualitative this paper proposes two new variants of weighted minimum and maximum where the criteria weights play the role of tolerance thresholds these variants require the use of a residuated structure equipped with an involutive negation we propose residuated counterparts of sugeno integrals where the weights bear on subsets of criteria and we study their properties showing they are analogous to sugeno integrals to a large extent finally we propose dual aggregation operations we call desintegrals where an item is evaluated in terms of its defects rather than in terms of its positive features desintegrals are maximal when no defects at all are present while integrals are maximal when all merits are sufficiently present qualitative integrals and desintegrals suggest a possible approach to bipolar evaluation processes where items are judged both in terms of merits and defects that are not independent of one another

unstructured grid optimization for improved monotonicity of discrete solutions of elliptic equations with highly anisotropic coefficients multipoint flux approximation mpfa techniques are commonly applied for discretizing the porous media flow equations within the context of finite volume numerical procedures although these methods can be applied to heterogeneous anisotropic systems on generally unstructured grids the inverse of the resulting linear operator can suffer from a loss of monotonicity at high permeability anisotropy ratios resulting in spurious oscillations of the pressure solution the purpose of this paper is to develop a method for optimizing unstructured grids in two and three dimensions such that the monotonicity behavior of the mpfa technique is significantly improved the method employs anisotropic triangulation and can be readily combined with permeability upscaling procedures results are presented for a variety of examples and the technique is shown to perform well on problems involving complex grid point distributions and heterogeneous permeability fields with strong anisotropy ratios of o 100 oscillation free pressure solutions are achieved in all cases considered even for examples in which the original grid shows large oscillations

characterization of weighted maximum and some related operations abstract the complete characterization of weighted maximum and minimum operations as well as the ordered weighted maximum and minimum is established the results are obtained via stability properties of the operations these properties are expressed by functional equations solutions of these equations correspond to the studied operations

importance weighting and andness control in de morgan dual power means and owa operators abstract importance weighted aggregation plays a central role in utilization of information resources for information retrieval and fusion pattern and object recognition decision making etc a class of aggregation operators of particular interest is formed by the aggregation operators between the min minimum and the max maximum the so called averaging operators two key issues in the choice of such an operator for a given application are the kind of importance weighting and the andness minness of the operator two main kinds of importance weighting for such operators namely multiplicative and implicative are proposed and discussed the purpose of this paper is to facilitate the choice and application of such operators through providing a systematization of their classes according to their behavior and equipping some classical averaging operators namely the power means and the owa operators with importance weighting schemes and direct parametric andness control for both kinds of importance weighting for increased efficacy and for symmetric behavior by andness and orness 1 andness at the same degree of both measures the two classes of averaging operators are applied in a de morgan dual form the main issue in the choice of underlying the classical averaging operator appears to be the computational cost of its application

penalizing strategic preference manipulation in multi agent decision making we consider the problem of group decision making where the selection process is based upon a group preference function obtained by an aggregation of the participating agents individual preference functions we describe some methods for formulating the group preference from the individual preference functions we note the possibility of the individual agents strategically manipulating the information they provide so as to further their own goal of getting their most preferred alternative selected by the group with this in mind we suggest ways of modifying the formulation of the group decision functions to discourage strategic manipulation by the participating agents

flexible queries in relational databases the example of the division operator abstract allowing for flexible queries enables database users to express preferences inside minimal requirements and if necessary priorities inside compound queries in other words clear cut properties can be refined by ordering the interpretations compatible with them according to user s preferences often the representation of these preferences can be viewed as modelling linguistic like terms in requests in this paper the theoretical issues raised by the introduction of flexible queries are studied in the case of the division operator in the framework of fuzzy sets and possibility theory the notion of division is well known in the context of regular relations and the extension of this operation to fuzzy relations induced by the flexible queries is investigated several types of extended divisions can be envisaged depending on the meaning of the grades attached to the tuples of the fuzzy relations degree of fulfillment of gradual properties level of importance of components in a query or uncertainty pervading data we focus on the first two meanings which are associated with different multiple valued logic implications and we examine their properties and their expression in the framework of an extended sql like language where no specific construct for the division is available

an application of aggregation procedures to the definition of measures of similarity between fuzzy sets abstract in this paper we examine four classes of procedures of aggregation of local valued relations with weights these procedures are based on the use of a valued implication or coimplication we highlight the existence of a hierarchy among those procedures and show that some of them preserve the transitivity of local relations these results are applied for the definition of a measure of similarity between fuzzy sets

a possibilistic argument for irreversibility abstract our aim is to explicate the idea of irreversibility by a mathematical representation of irreversible processes occurring in possibilistic dynamical systems with this in mind solutions of the cauchy problem in the space of fuzzy points are examined to meet the correspondence argument solutions of the cauchy problem in the space of concentrated points are examined too

user preferences discovery using fuzzy models user preferences discovery aims to learn the patterns of user preferences for various services or items such as movies preferences discovery is essential to the development of intelligent personalization applications based on decision and utility theories traditional approaches to preferences discovery explicitly query users about the behavior of value function or utility of every outcome with respect to each decision criterion consequently these approaches are generally error prone and labor intensive although implicit elicitation approaches have been proposed to address the above limitations extent approaches largely ignore multi valued nature of item features and uncertainty associated with item features and user preferences to address uncertainty due to vagueness and imprecision this research proposed a general framework for preferences discovery based on fuzzy set theories in addition new fuzzy models were created for preferences discovery and representation further an algorithm was developed to predict user preferences with uncertainty and visualization of item features user feedback and the discovered preferences helped improve the interpretation of the discovered knowledge the results of the simulation evaluation using a benchmark movie dataset revealed that the proposed preference discovery method 1 doubled the accuracy of preference discovery as compared to random prediction and 2 outperformed conventional techniques in making movie recommendation these findings suggest that fuzzy models are effective for preferences patterns discovery and personalized recommendation application

weighted fuzzy pattern matching the fuzzy pattern matching technique has been developed in the framework of fuzzy set and possibility theory in order to take into account the imprecision and the uncertainty pervading values which have to be compared in a matching process this technique has proved very useful for implementing patterns of approximate reasoning in expert system inference engines and for designing retrieval systems capable of managing incomplete and fuzzy information data bases and vague queries in this paper the fuzzy pattern matching procedure is improved by introducing weights assessing the relative importance of atoms in the pattern matching indices are obtained using weighted versions of the minimum and maximum operations of fuzzy set theory this approach is extended to the case of variable weights and is related to aggregation schemes proposed by yager when modeling soft quantified statements such as most of the criteria must be met a notion of soft partial matching is thus modelled

two dimensional exponential fitting and applications to drift diffusion models a class of methods is introduced that generalizes the so called exponential fitting method to two dimensional problems and more specifically to equations of the type operatorname div underset raise0 3em hbox smash scriptscriptstyle nabla u u underset raise0 3em hbox smash scriptscriptstyle nabla psi f with psi given and underset raise0 3em hbox smash scriptscriptstyle nabla psi big in a part of the domain the basic idea is the following i write the equation as operatorname div e psi underset raise0 3em hbox smash scriptscriptstyle nabla rho f through the change of variables u rho e psi ii discretize the symmetric equation by means of a method that uses some kind of harmonic average for the coefficient e psi mixed hybrid etc iii write the discrete scheme in terms of the nodal values of u e psi rho this produces an m matrix

fuzzy inference relation based on the theory of falling shadows abstract in this paper we establish a theoretical approach to define a fuzzy inference relation based on the theory of falling shadows the main characteristic of our definition of fuzzy inference relation is that it is semantically dependent in the sense that the formula of our definition will vary according to the correlation of the antecedent and the consequence of the given implication we shall show that the formulae of fuzzy inference relation given by ukasiewicz zadeh and the probability formula are consequences of our definition under three different correlations of the propositions

on β precision aggregation in this paper we propose an extension of the current fuzzy connectives to precision aggregators which include a certain tolerance towards noise and measurement errors in the values of the aggregated criteria when their cardinality is large to do this we have set our extension proposal in the framework of yager s mam mom and mica operators and study the properties of the new extended operators a simple example illustrates the practical use of the extended aggregators