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

fuzzy dea a perceptual evalution method abstract dea data envelopment analysis is a non parametric technique for measuring and evaluating the relative efficiencies of a set of entities with common crisp inputs and outputs in fact in a real evaluation problem input and output data of entities evaluated often fluctuate these fluctuating data can be represented as linguistic variables characterized by fuzzy numbers for reflecting a kind of general feeling or experience of experts based on the fundamental ccr model a fuzzy dea model is proposed to deal with the efficiency evaluation problem with the given fuzzy input and output data furthermore an extension of the fuzzy dea model to a more general form is also proposed with considering the relationship between dea and ra regression analysis using the proposed fuzzy dea models the crisp efficiency in ccr model is extended to be a fuzzy number to reflect the inherent uncertainty in real evaluation problems

a taxonomy and review of the fuzzy data envelopment analysis literature two decades in the making data envelopment analysis dea is a methodology for measuring the relative efficiencies of a set of decision making units dmus that use multiple inputs to produce multiple outputs crisp input and output data are fundamentally indispensable in conventional dea however the observed values of the input and output data in real world problems are sometimes imprecise or vague many researchers have proposed various fuzzy methods for dealing with the imprecise and ambiguous data in dea in this study we provide a taxonomy and review of the fuzzy dea methods we present a classification scheme with four primary categories namely the tolerance approach the a level based approach the fuzzy ranking approach and the possibility approach we discuss each classification scheme and group the fuzzy dea papers published in the literature over the past 20 years to the best of our knowledge this paper appears to be the only review and complete source of references on fuzzy dea

a geometric analysis of when fixed weighting schemes will outperform ordinary least squares many researchers have demonstrated that fixed exogenously chosen weights can be useful alternatives to ordinary least squares ols estimation within the linear model e g dawes am psychol 34 571 582 1979 einhorn hogarth org behav human perform 13 171 192 1975 wainer psychol bull 83 213 217 1976 generalizing the approach of davis stober dana and budescu psychometrika 75 521 541 2010b i present an analytic method to determine when a choice of fixed weights will incur less mean squared error than ols as a function of sample size error variance and model predictability geometrically i solve for the region of population that favors a choice of fixed weights over ols i derive closed form upper and lower bounds on the volume of this region giving tight bounds on the proportion of population favoring a choice of fixed weights i illustrate this methodology with several examples and provide a matlab the mathworks matlab software version 2009b 2010 programming implementation of the major results

reaction diffusion branching models of stock price fluctuations abstract several models of stock trading bak et al physica a 246 1997 430 are analyzed in analogy with one dimensional two species reaction diffusion branching processes using heuristic and scaling arguments we show that the short time market price variation is subdiffusive with a hurst exponent h 1 4 biased diffusion towards the market price and blind eyed copying lead to crossovers to the empirically observed random walk behavior h 1 2 at long times the calculated crossover forms and diffusion constants are shown to agree well with simulation data

a new ranking method to fuzzy data envelopment analysis due to its wide practical use data envelopment analysis dea has been adapted to many fields to deal with problems that have occurred in practice one adaptation has been in the field of ranking decision making units dmus most methods of ranking dmus assume that all input and output data are exactly known but in real life the data cannot be precisely measured thus this paper will carry out some researches to dea under fuzzy environment a fuzzy comparison of fuzzy variables is defined and the ccr model is extended to be a fuzzy dea model based on credibility measure in order to rank all the dmus a full ranking method will be given since the ranking method involves a fuzzy function a fuzzy simulation is designed and embedded into the genetic algorithm to establish a hybrid intelligent algorithm however it is shown to be possible to avoid some of the need for dealing with these nonlinear problems by identifying conditions under which they can be replaced by linear problems finally we will provide a numerical example to illustrate the fuzzy dea model and the ranking method

dynamic numerical models of stock market price from microscopic determinism to macroscopic randomness abstract a variant of threshold dynamics is introduced to model the behaviors of a large assembly of dealers in a stock market although the microscopic evolution dynamics is deterministic the collective behaviors such as market prices show seemingly stochastic fluctuations the statistical properties of market price change can be well approximated by a simple discrete langevin type equation with random amplification the macroscopic stochastic equation is solved both numerically and analytically showing that the market price change generally follow power law distributions in the steady state the reason for the appearance of rapid decay in the distribution tails are discussed

fuzzy data envelopment analysis dea a possibility approach abstract evaluating the performance of activities or organizations by traditional data envelopment analysis dea models requires crisp input output data however in real world problems inputs and outputs are often imprecise this paper develops dea models using imprecise data represented by fuzzy sets i e fuzzy dea models it is shown that fuzzy dea models take the form of fuzzy linear programming which typically are solved with the aid of some methods to rank fuzzy sets as an alternative a possibility approach is introduced in which constraints are treated as fuzzy events the approach transforms fuzzy dea models into possibility dea models by using possibility measures of fuzzy events fuzzy constraints we show that for the special case in which fuzzy membership functions of fuzzy data are of trapezoidal types possibility dea models become linear programming models a numerical experiment is used to illustrate the approach and compare the results with those obtained with alternative approaches

a fuzzy systems approach in data envelopment analysis abstract the use of fuzzy set theoretic measures is explored here in the context of data envelopment analysis which utilizes a nonparametric approach to measure efficiency three types of fuzzy statics are employed here e g fuzzy mathematical programme fuzzy regression and fuzzy entropy to illustrate the types of decisions and solutions that are achievable when the data are vague and prior information is inexact and imprecise

process efficiency of two stage systems with fuzzy data abstract in this paper a new approach to compute estimations of the process efficiencies in two stage systems with fuzzy data is presented the first step is to compute the upper and lower limits of the cuts of the system efficiency using the corresponding models in kao and liu 2011 14 the second step consists in computing the upper and lower limits of the cuts of the efficiency of each of the processes the upper limit of the cuts of the efficiency of each process is computed subject to the upper limit of the system efficiency while the lower limit of the process efficiency is computed subject to the lower limit of the system efficiency the proposed approach takes into account the inherent uncertainty regarding the process efficiencies even in the crisp data case the approach is illustrated with a dataset from the literature

preferential growth solution and application to modeling stock market abstract we consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles a new particle can either form a new cluster with probability q or join an already existing cluster with a probability proportional to the size thereof we calculate exactly the probability p i k t that the size of the i th cluster at time t is k we applied our model as a background for a microscopic economic model

interval efficiency assessment using data envelopment analysis this paper studies how to conduct efficiency assessment using data envelopment analysis dea in interval and or fuzzy input output environments a new pair of interval dea models is constructed on the basis of interval arithmetic which differs from the existing dea models handling interval data in that the former is a linear ccr model without the need of extra variable alternations and uses a fixed and unified production frontier i e the same constraint set to measure the efficiencies of decision making units dmus with interval input and output data while the latter is usually a nonlinear optimization problem with the need of extra variable alternations or scale transformations and utilizes variable production frontiers i e different constraint sets to measure interval efficiencies ordinal preference information and fuzzy data are converted into interval data through the estimation of permissible intervals and a level sets respectively and are incorporated into the interval dea models the proposed interval dea models are developed for measuring the lower and upper bounds of the best relative efficiency of each dmu with interval input and output data which are different from the interval formed by the worst and the best relative efficiencies of each dmu a minimax regret based approach mra is introduced to compare and rank the efficiency intervals of dmus two numerical examples are provided to show the applications of the proposed interval dea models and the preference ranking approach

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

price fluctuations from the order book perspective empirical facts and a simple model abstract statistical properties of an order book and the effect they have on price dynamics were studied using the high frequency nasdaq level ii data it was observed that the size distribution of marketable orders transaction sizes has power law tails with an exponent 1 market 2 4 0 1 the distribution of limit order or quote sizes was found to be consistent with a power law with an exponent close to 2 a somewhat better fit to this distribution was obtained by using a log normal distribution which has an effective power law exponent equal to 2 in the middle of the observed range the depth of the order book measured as a price impact of a hypothetical large market order was observed to be a non linear function of its size a large imbalance in the number of limit orders placed at bid and ask sides of the book was shown to lead to a predictable short term price change which is in accord with the law of supply and demand

fuzzy efficiency without convexity in this paper we develop a fuzzy version of the crisp free disposal hull fdh method for measuring technical efficiency for samples of similar production units the fdh method is basically data envelopment analysis dea without the underlying assumption of convexity of the technology set our approach builds directly upon the definition of farrell s indexes of technical efficiency used in crisp fdh therefore we do not require the use of fuzzy programming techniques but only utilize ranking probabilities of intervals as well as a related definition of dominance between pairs of intervals we illustrate the approach using a data set of 200 lithuanian family farms for the period of 2004 2009 2014 elsevier b v all rights reserved

a simple approximation of productivity scores of fuzzy production plans this paper suggests a simple approximation procedure for the assessment of productivity scores with respect to fuzzy production plans the procedure has a clear economic interpretation and all the necessary calculations can be performed in a spreadsheet making it highly operational

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

mean field approximation for a limit order driven market model a mean field variant of the model of limit order driven market introduced recently by maslov is formulated and solved the agents do not have any strategies and the memory of the system is kept within the order book we show that the evolution of the order book is governed by a matrix multiplicative process the resulting stationary distribution of step to step price changes is calculated it exhibits a power law tail with exponent 2 we obtain also the price autocorrelation function which agrees qualitatively with the experimentally observed negative autocorrelation for short times

fuzzy efficiency measures in data envelopment analysis abstract the existing data envelopment analysis dea models for measuring the relative efficiencies of a set of decision making units dmus using various inputs to produce various outputs are limited to crisp data to deal with imprecise data the notion of fuzziness has been introduced this paper develops a procedure to measure the efficiencies of dmus with fuzzy observations the basic idea is to transform a fuzzy dea model to a family of conventional crisp dea models by applying the cut approach a pair of parametric programs is formulated to describe that family of crisp dea models via which the membership functions of the efficiency measures are derived since the efficiency measures are expressed by membership functions rather than by crisp values more information is provided for management by extending to fuzzy environment the dea approach is made more powerful for applications

the interacting gaps model reconciling theoretical and numerical approaches to limit order models we consider the emergence of power law tails in the returns distribution of limit order driven markets we explain a previously observed clash between the theoretical and numerical studies of such models we introduce a solvable model that interpolates between the previous studies and agrees with each of them in the relevant limit c

efficiency of parallel production systems with fuzzy data this paper investigates the problem of efficiency measurement for parallel production systems where a number of processes are operating independently within the system and some input output data are fuzzy numbers when all observations have precise values previous studies found that the system efficiency measured from a relational data envelopment analysis model is a weighted average of the process efficiencies based on the extension principle of fuzzy theory this paper constructs a pair of two level programming models to calculate the lower and upper bounds of the a cuts of the fuzzy system and process efficiencies it is shown that the fuzzy system efficiency is still a weighted average of the fuzzy process efficiencies however the weights need not be the same at different a levels the case of measuring the teaching and research efficiencies of chemistry departments in uk universities with a qualitative factor of research quality discussed in the literature is used as an example to explain the idea of this paper fuzzy measures obtained from fuzzy observations are more informative than crisp measures obtained from assuming the fuzzy observations to be precise