fuzzy inventory model with two warehouses under possibility constraints a multi item inventory model with two storage facilities is developed with advertisement price and displayed inventory level dependent demand in a fuzzy environment purchase cost investment amount and storehouse capacity are imprecise the model is formulated as a single multi objective programming problem under fuzzy constraint constraints are satisfied with some pre defined necessity and the problem is solved via the goal programming method gpm when crisp equivalents of the constraints are available and by a fuzzy simulation based single multi objective genetic algorithm fsga fsmoga otherwise the model is illustrated with some numerical examples and results from different methods are compared in some particular cases

fuzzy portfolio optimization under downside risk measures this paper presents two fuzzy portfolio selection models where the objective is to minimize the downside risk constrained by a given expected return we assume that the rates of returns on securities are approximated as lr fuzzy numbers of the same shape and that the expected return and risk are evaluated by interval valued means we establish the relationship between those mean interval definitions for a given fuzzy portfolio by using suitable ordering relations finally we formulate the portfolio selection problem as a linear program when the returns on the assets are of trapezoidal form

triangular and parametric approximations of fuzzy numbers inadvertences and corrections recent papers were dedicated to approximate fuzzy numbers by triangular trapezoidal or parametric fuzzy numbers with or without additional conditions unfortunately the result of approximation is not always a fuzzy number sometimes it is not a fuzzy set we point out the wrongs and inadvertences in some recent papers then we correct the results

credibilistic markov decision processes the average case using a concept of random fuzzy variables in credibility theory we formulate a credibilistic model for unichain markov decision processes under average criteria and a credibilistically optimal policy is defined and obtained by solving the corresponding non linear mathematical programming also we give a computational example to illustrate the effectiveness of our new model

necessary and sufficient graphical conditions for formation control of unicycles the feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control the directed graph defined by the information flow plays a key role it is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node a similar result is given for formation stabilization to a line and to more general geometric arrangements

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

discrete time credibilistic processes construction and convergences in this paper we discuss a method of constructing a credibilistic process which is a family of fuzzy variables on credibility space applying the extension theorem in credibility theory the finite or infinite horizon credibilistic process is made up from a family of credibilistic kernels also for the markov case convergence theorems are given and credibilistic risk models for reward processes are considered whose risk is completed by the recursive equation

a note on trapezoidal approximations of fuzzy numbers in this paper we propose some generalized and new properties of the trapezoidal approximations of fuzzy numbers first we claim that the trapezoidal approximation operator is linear with respect to the operations of fuzzy numbers second we show a new property concerning the centroid points of fuzzy numbers furthermore a comment for computing the trapezoidal approximations is provided finally some properties about the distance between a fuzzy number and its trapezoidal approximation are proved

approximations of fuzzy numbers by step type fuzzy numbers in this paper the problems of approximations in membership functions space are studied firstly the concept of simple fuzzy numbers is defined which is a special kind of fuzzy numbers with simple structure and give the expressions of the membership function of thus fuzzy numbers then we prove that a fuzzy set of real number field r is a simple fuzzy number if and only if it is a normal step type fuzzy set and obtain a result of that simple fuzzy number space is dense in the fuzzy number space with respect to some metric and then we give two theorems about approximations of fuzzy number membership functions by using simple fuzzy number membership functions at last we investigate the properties of approximation operators given by us

state consensus for multi agent systems with switching topologies and time varying delays in this paper we investigate state consensus problems for discrete time multi agent systems with changing communications topologies and bounded time varying communication delays the analysis in this paper is based on the properties of non negative matrices we first extend the model of networks of dynamic agents to the case with multiple time delays and prove that if the communication topology time delays and weighting factors are time invariant then the necessary and sufficient condition that the multi agent system solves a consensus problem is that the communication topology represented by a directed graph has spanning trees then we allow for dynamically changing communication topologies and bounded time varying communication delays and present some sufficient conditions for state consensus of system finally as a special case of our model the problem of asynchronous information exchange is also discussed

necessity constraint in two plant optimal production problem with imprecise parameters the purpose of this paper is to present and solve a real life problem of two plants producing the same item under fuzzy stochastic environment here an item alongwith random defective units is produced at two different plants situated in different locations under a single management the rates of demand production and defectiveness at these places are different demands of the item are primarily met locally from the respective plants but if a stock out situation occurs in a plant immediately some stock from the other plant if available is rushed to the stock out plant the demands are known but production rates are unknown functions of time are taken as control variables the available budget for the management house is imprecise the holding shortage and transportation costs are assumed to be imprecise and represented by fuzzy numbers which are transformed to corresponding interval numbers following interval mathematics and nearest interval approximation the objective function is changed to respective multi objective functions and thus the single objective fuzzy problem is reduced to a crisp multi objective decision making modm problem the modm problem is then again transformed to a single crisp objective function with the help of weighted sum method using fuzzy relations the imprecise budget constraint expressed in the form of necessity constraint is transformed into an equivalent crisp one then total cost consisting of production holding shortage and transportation from one plant to another costs is expressed as an optimal control problem and solved using weighted sum method the kuhn tucker conditions pontryagin s optimal control principle and generalized reduced gradient grg technique the model has been illustrated by numerical data the optimum results are presented in both tabular and graphical forms

trapezoidal approximations of fuzzy numbers the problem of the trapezoidal approximation of fuzzy numbers is discussed a set of criteria for approximation operators is formulated these constraints can be used for direct operator derivation a new nearest trapezoidal approximation operator preserving expected interval is suggested

group decision making with a fuzzy linguistic majority abstract the determination of solutions in group decision making is considered the point of departure is a collection of individual fuzzy preference relations a solution is derived either directly from the individual fuzzy preference relations or by constructing first a social fuzzy preference relation as opposed to conventional approaches in which a crisp threshold type majority rule is used we employ a fuzzy majority rule specified by a fuzzy linguistic quantifier e g most much more than 50 etc a calculus of linguistically quantified propositions is applied using the fuzzy majority various solution concepts are derived mainly of the type of core minimax opposition set and consensus winner

an evaluation of the eigenvalue approach for determining the membership values in fuzzy sets abstract the membership values of the elements of a fuzzy set of key importance in any theoretical or practical application of fuzzy set theory although there are many methods that evaluate membership values the methd proposed by saaty 8 9 based on matrix of pairwise comparisons and eigenvalue theory is the backbone of many other methods in this paper we evaluate the above method by using a forward error analysis approach with the assumption that the true membership values in a fuzzy set are continuous in the interval 0 1 the results reveal that the eigenvalue method is dramatically inaccurate even for fuzzy sets with few members

conditioned weighted l r approximations of fuzzy numbers we compute the extended weighted l r approximation of a given fuzzy number by a method based on general results in hilbert spaces the weighted average euclidean distance being considered the metric properties of the extended weighted l r approximation of a fuzzy number are proved we elaborate on a general method to study the existence uniqueness and to calculate the l r approximations of fuzzy numbers under the preservation of some parameters we apply the results to find the weighted l r approximations preserving ambiguity and value and respectively width in the general and unimodal case

existence uniqueness and continuity of trapezoidal approximations of fuzzy numbers under a general condition abstract the main aim of this paper is to characterize the set of real parameters associated to a fuzzy number represented in a general form which include the most important characteristics with the following property for any given fuzzy number there exists at least a trapezoidal fuzzy number which preserves a fixed parameter the uniqueness of the nearest trapezoidal fuzzy number with this property is proved the average euclidean distance being considered as an important property each resulting trapezoidal approximation operator is continuous the main results are illustrated by examples

nonlinear finite time bipartite consensus protocol for multi agent systems associated with signed graphs in this paper finite time multi agent consensus problems are considered under networks associated with signed graphs whose edge weights can be not only positive but also negative a nonlinear consensus protocol is proposed to guarantee the states of all agents to converge in a finite time if the signed graph is structurally balanced then the final consensus states of all agents are the same in modulus but not in sign otherwise if the signed graph is structurally unbalanced then the states of all agents converge to zero moreover the final consensus states of agents can be provided uniformly regarding a signed average quantity that depends on both the initial states of agents and the topology structure of the whole multi agent network numerical simulations illustrate that the protocol is effective in achieving the finite time consensus of agents under signed graphs and can particularly solve the finite time average consensus problem of agents when their associated graph has all positive edge weights

solving multi period project selection problems with fuzzy goal programming based on topsis and a fuzzy preference relation project portfolio managers are multi objective decision makers dms who are expected to select the best mix of projects by maximizing profits and minimizing risks over a multi period planning horizon however project portfolio decisions are complex multi objective problems with a high number of projects from which a subset has to be chosen subject to various constraints and a multitude of priorities and preferences we propose a goal programming gp approach for project portfolio selection that embraces conflicting fuzzy goals with imprecise priorities a fuzzy goal with an aspiration level and a predefined membership function is defined for each objective the impreciseness in the priorities of the membership values of the fuzzy goals is modeled with fuzzy relations this leads to type ii fuzzy sets since fuzzy relations are organized between the membership values of the fuzzy goals which are themselves fuzzy sets the proposed model is based on the technique for order preference by similarity to ideal solution topsis and fuzzy preference relations topsis is used to reduce the multi objective problem into a bi objective problem the resulting bi objective problem is solved with fuzzy gp fgp the fuzzy preference relations are used to help dms express their preferences with respect to the membership values of the fuzzy goals the proposed approach is used to solve a real life problem characterized as a fuzzy multi objective project selection with multi period planning horizon mops mpph the performance of the proposed approach is compared with a competing method in the literature we show that our approach generates high quality solutions with minimal computational efforts

a new version of 2 tuple fuzzy linguistic representation model for computing with words in this paper we provide a new proportional 2 tuple fuzzy linguistic representation model for computing with words cw which is based on the concept of symbolic proportion this concept motivates us to represent the linguistic information by means of 2 tuples which are composed by two proportional linguistic terms for clarity and generality we first study proportional 2 tuples under ordinal contexts then under linguistic contexts and based on canonical characteristic values ccvs of linguistic labels we define many aggregation operators to handle proportional 2 tuple linguistic information in a computational stage for cw without any loss of information our approach for this proportional 2 tuple fuzzy linguistic representation model deals with linguistic labels which do not have to be symmetrically distributed around a medium label and without the traditional requirement of having equal distance between them moreover this new model not only provides a space to allow a continuous interpolation of a sequence of ordered linguistic labels but also provides an opportunity to describe the initial linguistic information by members of a continuous linguistic scale domain which does not necessarily require the ordered linguistic terms of a linguistic variable being equidistant meanwhile under the assumption of equally informative which is defined by a condition based on the concept of ccv we show that our model reduces to herrera and mart spl inodot spl acute nez s translational 2 tuple fuzzy linguistic representation model

a nonlinear merging protocol for consensus in multi agent systems on signed and weighted graphs in this paper we investigate the multi agent consensus for networks with undirected graphs which are not connected especially for the signed graph in which some edge weights are positive and some edges have negative weights and the negative weight graph whose edge weights are negative we propose a novel nonlinear merging consensus protocol to drive the states of all agents to converge to the same state zero which is not dependent upon the initial states of agents if the undirected graph whose edge weights are positive is connected then the states of all agents converge to the same state more quickly when compared to most other protocols while the undirected graph whose edge weights might be positive or negative is unconnected the states of all agents can still converge to the same state zero under the premise that the undirected graph can be divided into several connected subgraphs with more than one node furthermore we also discuss the impact of parameter r presented in our protocol current results can further deepen the understanding of consensus processes for multi agent systems

expected value of fuzzy variable and fuzzy expected value models this paper will present a novel concept of expected values of fuzzy variables which is essentially a type of choquet integral and coincides with that of random variables in order to calculate the expected value of general fuzzy variable a fuzzy simulation technique is also designed finally we construct a spectrum of fuzzy expected value models and integrate fuzzy simulation neural network and genetic algorithms to produce a hybrid intelligent algorithm for solving general fuzzy expected value models

portfolios with fuzzy returns selection strategies based on semi infinite programming this paper provides new models for portfolio selection in which the returns on securities are considered fuzzy numbers rather than random variables the investor s problem is to find the portfolio that minimizes the risk of achieving a return that is not less than the return of a riskless asset the corresponding optimal portfolio is derived using semi infinite programming in a soft framework the return on each asset and their membership functions are described using historical data the investment risk is approximated by mean intervals which evaluate the downside risk for a given fuzzy portfolio this approach is illustrated with a numerical example

on the ramanujan conjecture and finiteness of poles for certain l functions in this paper we prove a number of general results about automorphic l functions which appear in the constant terms of eisenstein series for an arbitrary quasi split connected reductive algebraic group over a number field these l functions were first introduced by langlands for chevalley groups 20 and through them he was led to make some of his deep conjectures 21 one significance of these l functions is that all the automorphic l functions studied so far are among them there are three general results first we obtain a uniform line of absolute convergence for all of these l functions theorem 5 1 a uniform estimate for the hecke eigenvalues of generic cusp forms on many absolutely simple quasi split connected reductive algebraic groups over number fields corollary 5 4 and an improvement on the best available estimate for the fourier coefficients of maass wave forms corollary 5 5 also follow next we establish a meromorphic continuation and functional equation for each of these l functions theorem 6 1 finally in theorem 6 2 we prove finiteness of poles on the whole complex plane for an important class of these l functions corollaries 6 6 through 6 10 more precisely let g be a quasi split connected reductive algebraic group over a number field f set g g a f where a f is the ring of adeles of f fix a borel subgroup b of g over f and let u be its unipotent radical let p be a maximal f parabolic subgroup of g with p d b in the context of the problems studied here nothing new will be obtained if one drops the maximality condition on p write p mn a levi decomposition n c u and let b u p m and n be the corresponding groups of adelic points for every place v of f let gv g fj similarly we have bv us pv me and nv let x xv be a generic character of u f u cf section 3 then each xv is generic let r ov 7tv be a cusp form on m we shall say 7t is

optimal design for synchronization of cooperative systems state feedback observer and output feedback this technical note studies synchronization of identical general linear systems on a digraph containing a spanning tree a leader node or command generator is considered which generates the desired tracking trajectory a framework for cooperative tracking control is proposed including full state feedback control observer design and dynamic output feedback control the classical system theory notion of duality is extended to networked systems it is shown that unbounded synchronization regions that achieve synchronization on arbitrary digraphs containing a spanning tree can be guaranteed by using linear quadratic regulator based optimal control and observer design methods at each node

transportation projects selection process using fuzzy sets theory government transportation agencies are faced with the problem of efficiently selecting a subset of transportation projects for implementation this selection process is based on multiple objectives which are often measured in incommensurable units usually the problem is treated by neglecting or biasing the qualitative characteristics of the various projects moreover the usual selection methods cannot deal effectively with the decision makers preferences or vagueness fuzzy sets theory is able to cope with inexact information and therefore is believed to be an appropriate tool for use in the projects selection process this work presents an efficient technique for the selection of transportation projects using fuzzy sets theory the selection procedure is a multiple objectives process and projects are rated both on a quantitative and qualitative basis using linguistic variables in order to describe appropriately a given transportation policy both fuzzy weighted average and noncompensatory fuzzy decision rules are used in the proposed approach in addition this work contains a case study of a selection process of interurban road projects in israel the results of the proposed method obtained by a fuzzy expert system are compared with the results obtained by an ordinary crisp process

model reference adaptive fuzzy control a linguistic space approach in this paper a model reference adaptive fuzzy controller with the adaptivity achieved by tuning both the scaling factors and the control rules is presented the proposed tuning strategy includes two parts 1 by referring a reference trajectory created in the linguistic space to tune the scaling factors and 2 by applying an auxiliary correction matrix generated by specific tuning rules to compensate the control rules since only the control signal the output error and change in output error of the plant are needed in the construction of the reference trajectory and the tuning rules the tuning strategy has the advantage of real time property simulation results with a damping process and an oscillating process as the controlled plants show the performance and adaptivity of the proposed controller

approximations by lr type fuzzy numbers recently many scholars investigated interval triangular and trapezoidal approximations of fuzzy numbers these publications can be grouped into two classes euclidean distance class and non euclidean distance class most approximations in euclidean distance class can be calculated by formulas but calculating approximations in the other class is more complicated furthermore approximations in euclidean distance class can be divided into two subclasses one is to study approximations of fuzzy numbers without constraints the other one is to study approximations preserving some attributes in this paper we use lr type fuzzy numbers to approximate fuzzy numbers the proposed approximations will generalize all recent approximations without constraints in euclidean class also an efficient formula is provided

simplifying the search for effective ranking of fuzzy numbers we prove that a ranking index which generates an order on some subset of fuzzy numbers can be reduced to a ranking index with a simpler form and which generates an equivalent order this way the finding of ranking indices generating orders with desirable properties can be essentially simplified such that we need to search only from additive or scale invariant ranking indices we determine exactly making an abstraction of equivalent orders the class of ranking indices on trapezoidal fuzzy numbers which generate orders satisfying all the basic requirements finally ranking indices used to rank trapezoidal fuzzy numbers are extended to ranking indices used to rank arbitrary fuzzy numbers so that the desired properties are preserved

nonvanishing of l functions for gl n mathbf a _q in this work we establish new nonvanishing results for automorphic l functions on glnaq in particular we show that given a cuspidal automorphic form on gl3aq and an arbitrary point s0 c there exist infinitely many dirichlet characters with prescribed ramification such that the twisted completed l functions do not vanish at s0 s0 0

approximation of fuzzy numbers using the convolution method in this study we consider the use of the convolution method for constructing approximations comprising fuzzy number sequences with useful properties for a general fuzzy number we show that this convolution method can generate differentiable approximations in finite steps for fuzzy numbers with finite non differentiable points in previous studies this convolution method was only used for constructing differentiable approximations of continuous fuzzy numbers the possible non differentiable points of which were the two endpoints of the 1 cut the construction of smoothers is a key step in the process for producing approximations we also show that if appropriate smoothers are selected then we can use the convolution method to provide approximations that are differentiable lipschitz and that also preserve the core

an empirical analysis of the use of the analytic hierarchy process for estimating membership values in a fuzzy set abstract the analytic hierarchy process ahp is now a popular multicriteria decision making method and has been applied in many diverse areas despite the debate on its theoretical foundations many researchers have been using the pairwise comparison matrix and the eigenvector method suggested by saaty for obtaining priority ratings of the decision alternatives in an ahp hierarchy these priority ratings have been used as estimates of fuzzy membership values of the elements called alternatives in ahp of a fuzzy set triantaphyllou and mann have argued that saaty s scale and the eigenvector method are inadequate for estimating fuzzy membership values this paper points out the limitations in the arguments of triantaphyllou and mann about the eigenvector method it primarily concentrates on two aspects the first pertains to saaty s condition on deleting or combining two alternatives which are near copies alternatives whose priority values are close to each other within a 10 range over all criteria the second aspect concerns the use of the eigenvector method for estimating the membership values of elements of a fuzzy set the use of the eigenvector method for estimating fuzzy membership values in a fuzzy set has been justified using the empirical analysis together with theoretical support it has been amply demonstrated in this paper that the problem lies in saaty s scale and not in the eigenvector method

credibility based chance constrained integer programming models for capital budgeting with fuzzy parameters in this paper we discuss a problem of capital budgeting in a fuzzy environment two types of models are proposed using credibility to measure confidence level since the proposed optimization problems are difficult to solve by traditional methods a fuzzy simulation based genetic algorithm is applied two numerical experiments demonstrate the effectiveness of the proposed algorithm

a class of fuzzy random optimization expected value models fuzzy random variable is a measurable mapping from a probability space to a collection of fuzzy variables this concept may be regard as an extension of both random variable and fuzzy variable in this paper the linearity of a scalar value expected value operator of fuzzy random variable is discussed and a fuzzy random simulation approach is suggested to evaluate the expected value of a fuzzy random variable in addition three types of fuzzy random expected value models are presented to model fuzzy random decision systems moreover a hybrid intelligent algorithm which incorporates simulation neural network and genetic algorithm is designed in order to solve general fuzzy random expected value models at the end of this paper the effectiveness of this algorithm is showed via three numerical examples

application of weighting functions to the ranking of fuzzy numbers this paper proposes a new ranking method for fuzzy numbers which uses a defuzzification of fuzzy numbers and a weighting function following saeidifar and pasha 2008 first we define a weighted distance measure on fuzzy numbers and then by minimizing this distance the weighted interval and point approximations of fuzzy numbers are obtained these indices are applied to rank the fuzzy numbers this method is new and interesting for ranking fuzzy numbers and it can be applied for solving and optimizing engineering and economics problems in a fuzzy environment

natural trapezoidal approximations of fuzzy numbers fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is considered new operators that fulfill additional requirements for the core and support of the fuzzy number are suggested these supplementary conditions guarantee the proper interpretation of the solution even for very skew input fuzzy numbers moreover the trapezoidal approximation without expected interval invariance is also examined and the relationship between these two approximations is discussed

a numerical approach to a multi objective optimal inventory control problem for deteriorating multi items under fuzzy inflation and discounting the optimal production and advertising policies for an inventory control system of deteriorating multi items under a single management are formulated with resource constraints under inflation and discounting in fuzzy environment here the deterioration of the items and depreciation of sales are at a constant rate deteriorated items are salvaged and the effect of inflation and time value of money are taken into consideration the inflation and discount rates are assumed to be imprecise and represented by fuzzy numbers these imprecise quantities are first transformed to corresponding intervals and then following interval mathematics the related objective function is changed to respective multi objective functions using utility function method ufm the multi objective problem is changed to a single objective problem here the production and advertisement rates are unknown and considered as control decision variables the production advertisement and demand rates are functions of time t the total profit which consists of the sales proceeds production cost inventory holding cost and advertisement cost is formulated as an optimal control problem and evaluated numerically using ufm and generalized reduced gradient grg technique finally numerical experiment sensitivity analysis and graphical representation are provided to illustrate the system for the present model expressions and graphical results are presented when the rates of advertisement are constant

minimax chance constrained programming models for fuzzy decision systems abstract the existing chance constrained programming for fuzzy decision systems is essentially a kind of maximax models optimistic models which maximize the maximum possible return this paper presents a spectrum of minimax models as opposed to maximax models based on chance constrained programming as well as chance constrained multi objective programming and chance constrained goal programming in which the minimax models will select the alternative that provides the best of the worst possible return finally a fuzzy simulation based genetic algorithm will be designed for solving minimax models and illustrated by some numerical examples

relations among convergence concepts of uncertain sequences uncertainty theory is a generalization of probability theory and credibility theory the purpose of this paper is to investigate various convergence concepts of uncertain sequences in uncertainty spaces sufficient and necessary conditions for convergence of uncertain sequences are given the relations among various convergence concepts of uncertain sequences are established

nearest interval approximation of a fuzzy number the problem of the interval approximation of fuzzy numbers is discussed a new interval approximation operator which is the best one with respect to a certain measure of distance between fuzzy numbers is suggested

on the consensus and bipartite consensus in high order multi agent dynamical systems with antagonistic interactions abstract the aim of this paper is to address consensus and bipartite consensus for a group of homogeneous agents under the assumption that their mutual interactions can be described by a weighted signed connected and structurally balanced communication graph this amounts to assuming that the agents can be split into two antagonistic groups such that interactions between agents belonging to the same group are cooperative and hence represented by nonnegative weights while interactions between agents belonging to opposite groups are antagonistic and hence represented by nonpositive weights in this framework bipartite consensus can always be reached under the stabilizability assumption on the state space model describing the dynamics of each agent on the other hand nontrivial standard consensus may be achieved only under very demanding requirements both on the laplacian associated with the communication graph and on the agents description in particular consensus may be achieved only if there is a sort of equilibrium between the two groups both in terms of cardinality and in terms of the weights of the conflicting interactions amongst agents

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

best lipschitz constant of the trapezoidal approximation operator preserving the expected interval in this paper we prove new distance properties between a fuzzy number and its trapezoidal approximation preserving the expected interval then we find the best lipschitz constant of the trapezoidal approximation operator preserving the expected interval finally we use this result in finding within a reasonable error the trapezoidal approximation of a fuzzy number preserving the expected interval in the case when the direct formula leads to complex calculations

a parametric approach to evaluate fuzzy quantities in this paper we present a new general framework to face the problem of evaluating fuzzy quantities a fuzzy quantity is a fuzzy set that may be non normal and or non convex it is based on the idea of interval approximation of a fuzzy number the classical approach followed for fuzzy numbers is not pursuable in a fuzzy quantity context but anyway our proposal produces an interesting general formulation that offers the opportunity to create many different types of evaluations as it depends on several parameters

metrics and orders in space of fuzzy numbers abstract two classes of metrics p q and p where 1 p 0 q 1 in space of fuzzy numbers are introduced then a method of ranking fuzzy numbers based on these metrics is proposed and investigated not only fuzzy numbers but also the left sided and right sided fuzzy numbers are considered applications in making decisions and statistics are suggested

an approach to computing with words based on canonical characteristic values of linguistic labels herrera and martinez initiated a 2 tuple fuzzy linguistic representation model for computing with words cw which offers a computationally feasible method for aggregating linguistic information that are represented by linguistic variables with equidistant labels through counting indexes of the corresponding linguistic labels lawry introduced an alternative approach to cw based on mass assignment theory that takes into account the underlying definitions of the words recently we provided a new proportional 2 tuple fuzzy linguistic representation model for cw that is an extension of herrera and martinez s model and takes into account the underlying definitions of linguistic labels of linguistic variables in the process of aggregating linguistic information by assigning canonical characteristic values ccvs of the corresponding linguistic labels in this paper we study further into cw based on ccvs of linguistic labels to provide a unifying link between lawry s framework and herrera and martinez s 2 tuple framework as well as allowing for computationally feasible cw our approach is based on a formal definition of ccv functions of a linguistic variable which is introduced under the context of its proportional 2 tuple linguistic representation model as continuation of our earlier works and on a group voting model that is for the probabilistic interpretation of the whole semantics of the ordered linguistic terms set of an arbitrary linguistic variable after the general framework developed in the former part of this paper we focus on a particular linguistic variable probability we show that for a linguistic probability description the expectation of its posterior conditional probability is a canonical characteristic value of the linguistic probability description then a calculus for reasoning with linguistic syllogisms and inference from linguistic information is introduced it is investigated under the context that linguistic quantifiers in such linguistic syllogisms can be arbitrary linguistic probability description and that the related linguistic information can be linguistic facts overfacts or underfacts intrinsically our approach to this calculus is with computing with words based on canonical characteristic values of linguistic labels

existence of interval triangular and trapezoidal approximations of fuzzy numbers under a general condition abstract recently many scholars studied approximations of fuzzy numbers by specific fuzzy numbers under preservation of some operators in fact these approximations may not exist for some linear operators the purpose of this paper is to study necessary and sufficient conditions of linear operators which are preserved by interval triangular symmetric triangular trapezoidal or symmetric trapezoidal approximations of fuzzy numbers in addition an effective method for solving such problems is proposed

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

weighted trapezoidal and triangular approximations of fuzzy numbers in 2007 zeng and li proposed a weighted triangular approximation of a fuzzy number unfortunately this approximation may fail to be a fuzzy number in this paper we improve this approximation and propose a generalization by the name of weighted trapezoidal approximation their algorithms are also presented finally some examples and relevant properties are discussed

seeking consensus in networks of linear agents communication noises and markovian switching topologies the stochastic consensus problem of linear multi input multi output mimo multi agent systems mass with communication noises and markovian switching topologies is studied in this technical note the agent s full state is first estimated by the state observer and then the estimated state is exchanged with neighbor agents through a noisy communication environment the communication topology is randomly switching and the switching law is described by a continuous time markovian chain then a consensus protocol is proposed for this mas and some sufficient conditions are obtained for ensuring the mean square and almost sure consensus in addition if the communication topology is fixed some necessary and sufficient conditions for the mean square consensus can be obtained according to whether or not each agent in the system has parents

nearest piecewise linear approximation of fuzzy numbers abstract the problem of the nearest approximation of fuzzy numbers by piecewise linear 1 knot fuzzy numbers is discussed by using 1 knot fuzzy numbers one may obtain approximations which are simple enough and flexible to reconstruct the input fuzzy concepts under study they might be also perceived as a generalization of the trapezoidal approximations moreover these approximations possess some desirable properties apart from theoretical considerations approximation algorithms that can be applied in practice are also given

weighted trapezoidal approximation preserving cores of a fuzzy number recently various researchers have proved that approximations of fuzzy numbers may fail to be fuzzy numbers in this contribution we suggest a new weighted trapezoidal approximation of an arbitrary fuzzy number which preserves its cores we prove that the weighted trapezoidal approximation preserving core is always a fuzzy number we then discuss properties of the approximation strategy including translation invariance scale invariance identity and continuity the advantage is that the method presented here is simpler than other methods computationally

on convergence rate of leader following consensus of linear multi agent systems with communication noises this note further studies the previously proposed consensus protocol for linear multi agent systems with communication noises each agent is allowed to have its own time varying gain to attenuate the effect of communication noises therefore the common assumption that all agents have the same noise attenuation gain is not necessary it has been proved that if all noise attenuation gains are infinitesimal of the same order then the mean square leader following consensus can be reached furthermore the convergence rate of the multi agent system has been investigated if the noise attenuation gains belong to a class of functions which are bounded above and below by t beta beta in 0 1 asymptotically then the second moment of the relative state between each follower agent and the leader agent is characterized by a function bounded above by t beta asymptotically

fuzzy quadratic minimum spanning tree problem in this paper a fuzzy quadratic minimum spanning tree problem is formulated as expected value model chance constrained programming and dependent chance programming according to different decision criteria then the crisp equivalents are derived when the fuzzy costs are characterized by trapezoidal fuzzy numbers furthermore a simulation based genetic algorithm using prufer number representation is designed for solving the proposed fuzzy programming models as well as their crisp equivalents finally a numerical example is provided for illustrating the effectiveness of the genetic algorithm

weighted pseudometric approximation of 2 dimensional fuzzy numbers by fuzzy 2 cell prismoid numbers preserving the centroid abstract up to now there have been many research results about approximations of fuzzy numbers by specific fuzzy numbers under preservation of some operators however there are few investigations about approximations of n dimensional fuzzy numbers the main reason is that the structure of n dimensional fuzzy numbers are more complex this paper devotes to seek an approximation operator that produces a special kind of 2 dimensional fuzzy number which is the nearest one to the given 2 dimensional fuzzy number along the direction k the concept of four edges approximation for 2 dimensional fuzzy numbers is defined which is a special kind of 2 dimensional fuzzy numbers at the same time the concept of fuzzy 2 cell prismoid numbers is introduced and the nearest fuzzy 2 cell prismoid numbers of 2 dimensional fuzzy numbers which preserve the centroid of the core for the 2 dimensional fuzzy numbers with respect to the weighted pseudometric are discussed finally with respect to the criteria scale invariance identity criterion and nearness criterion some properties of the approximation operator are presented

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 mean value of a fuzzy number abstract the notion of expectation is defined for fuzzy numbers of intervals viewing them as consonant random sets this expectation is interval valued and remains additive in the sense of fuzzy interval addition as a by product some light is shed on the debate between probability and possibility theory and the problem of how to carry measure theoretic notions into the field of possibility theory

on the relation between a fuzzy number and its centroid in this paper we answer the following question if the centroid and the left right spread of an unknown fuzzy number are given how do we find this fuzzy number

chance constrained programming with fuzzy parameters this paper extends chance constrained programming from stochastic to fuzzy environments analogous to stochastic programming some crisp equivalents of chance constraints in fuzzy environments are presented we also propose a technique of fuzzy simulation for the chance constraints which are usually hard to be converted to their crisp equivalents finally a fuzzy simulation based genetic algorithm is designed for solving this kind of problems and some numerical examples are discussed

median alpha levels of a fuzzy number three median alpha levels of a fuzzy number a are introduced two of them are based on the vertical and horizontal dimensions of a one on the cardinality of a approximation of fuzzy numbers by alpha cuts associated with the median alpha levels is discussed percentile characterizations of alpha cuts with respect to the selected properties of fuzzy numbers are proposed

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

the expected value of a fuzzy number abstract the notions of expected interval and expected value of fuzzy number are introduced the expected interval is defined as the expected value of an interval random set generated by the fuzzy number and the expected value of this number is defined as the centre of the expected interval the linearity of the expected interval is studied

the possibilistic moments of fuzzy numbers and their applications this paper introduces the nearest weighted interval and point approximations of a fuzzy number and then suggests weighted possibilistic moments about these points of fuzzy numbers the possibilistic moments play an important role in fuzzy sets and systems specifically in physics mathematics and statistics we provide the definition of the moments of fuzzy numbers as well as the definition of moments in probability theory some of their applications are mentioned

weighted semi trapezoidal approximations of fuzzy numbers recently many scholars investigated interval triangular and trapezoidal approximations of fuzzy numbers these publications can be grouped into two classes euclidean distance class and non euclidean distance class most approximations in euclidean distance class can be calculated by formulas but calculating approximations in the other class is more complicated in the present paper we study a special class of non linear approximations with respect to a weighted euclidean distance we call it weighted semi trapezoidal approximations the proposed approximations generalize all recent approximations in euclidean distance class first we embed fuzzy numbers into a hilbert space then compute weighted semi trapezoidal approximations by means of best approximations in a closed convex subset of the hilbert space finally we propose formulas of matrix type which is more clear than the previous contributions

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

approximation of fuzzy numbers by max product bernstein operators in this paper firstly we extend to an arbitrary compact interval the definition of the nonlinear bernstein operators of max product kind by proving that their order of uniform approximation is the same as in the particular case of the unit interval then similarly to the particular case of the unit interval we will prove that these operators preserve the quasi concavity too since these properties will help us to generate in a simple way fuzzy numbers of the same support it turns out that these results are very suitable in the approximation of fuzzy numbers moreover these operators approximate the non degenerate segment core with a good order of approximation in addition in the case when the fuzzy numbers are given in parametric form the bernstein max product operator generates a sequence of fuzzy numbers whose widths expected intervals ambiguities and values approximate with a convergent rate the width the expected interval the ambiguity and the value of the approximated fuzzy number finally we obtain a quantitative approximation with respect to a well known integral type metric for some subclasses of functions leading to applications to the approximation of some subclasses of fuzzy numbers

fuzzy linguistic pert a model for program evaluation and review technique pert under fuzzy linguistic contexts is introduced in this fuzzy linguistic pert network model each activity duration is represented by a fuzzy linguistic description aggregation and comparison of the estimated linguistic expectations of activity durations are manipulated by the techniques of computing with words cw to provide suitable contexts for this purpose we first introduce several variations of basic linguistic labels of a linguistic variable such as weighted linguistic labels generalized linguistic labels and weighted generalized linguistic labels etc and then based on the notion of canonical characteristic value ccv function of a linguistic variable we develop some related cw techniques for aggregation and comparison of these linguistic labels afterward using a computing technique of linguistic probability introduced by zadeh and based on the new developed cw techniques for weighted generalized linguistic labels we investigate the associated linguistic expectation pert network of a fuzzy linguistic pert network also throughout the paper several examples are used to illustrate related notions and applications

possibility and necessity constraints and their defuzzification a multi item production inventory scenario via optimal control theory abstract in this paper analogous to chance constraints real life necessity and possibility constraints in the context of a multi item dynamic production inventory control system are defined and defuzzified following fuzzy relations hence a realistic multi item production inventory model with shortages and fuzzy constraints has been formulated and solved for optimal production with the objective of having minimum cost here the rate of production is assumed to be a function of time and considered as a control variable also the present system produces some defective units along with the perfect ones and the rate of produced defective units is constant here demand of the good units is time dependent and known and the defective units are of no use the space required per unit item available storage space and investment capital are assumed to be imprecise the space and budget constraints are of necessity and or possibility types the model is formulated as an optimal control problem and solved for optimum production function using pontryagin s optimal control policy the kuhn tucker conditions and generalized reduced gradient grg technique the model is illustrated numerically and values of demand optimal production function and stock level are presented in both tabular and graphical forms the sensitivity of the cost functional due to the changes in confidence level of imprecise constraints is also presented