fuzzy versus statistical linear regression abstract statistical linear regression and fuzzy linear regression have been developed from different perspectives and thus there exist several conceptual and methodological differences between the two approaches the characteristics of both methods in terms of basic assumptions parameter estimation and application are described and contrasted their descriptive and predictive capabilities are also compared via a simulation experiment to identify the conditions under which one outperforms the other it turns out that statistical linear regression is superior to fuzzy linear regression in terms of predictive capability whereas their comparative descriptive performance depends on various factors associated with the data set size quality and proper specificity of the model aptness of the model heteroscedasticity autocorrelation nonrandomness of error terms specifically fuzzy linear regression performance becomes relatively better vis a vis statistical linear regression as the size of the data set diminishes and the aptness of the regression model deteriorates fuzzy linear regression may thus be used as a viable alternative to statistical linear regression in estimating regression parameters when the data set is insufficient to support statistical regression analysis and or the aptness of the regression model is poor e g due to vague relationship among variables and poor model specification

note on fuzzy regression abstract regression analysis has been widely used in several areas for many years fuzzy linear regression was introduced in 1980 by h tanaka s uejima and k asai in this paper the general form of regression equations is developed for fuzzy numbers it is showed that the problem of fuzzy regression can be formulated as a mathematical programming problem the special case of linear regression yields a linear programming problem different measures of vagueness are introduced to define the best estimate two simple numerical examples illustrate the methodology and allow a partial comparison among the different measures of vagueness

fuzzy regression based on asymmetric support vector machines this paper presents a modified framework of support vector machines which is called asymmetric support vector machines asvms and is designed to evaluate the functional relationship for fuzzy linear and nonlinear regression models in earlier works in order to cope with different types of input output patterns strong assumptions were made regarding linear fuzzy regression models with symmetric and asymmetric triangular fuzzy coefficients excellent performance is achieved on some linear fuzzy regression models however the nonlinear fuzzy regression model has received relatively little attention because such nonlinear fuzzy regression models having certain limitations this study modifies the framework of support vector machines in order to overcome these limitations the principle of asvms is applying an orthogonal vector into the weight vector in order to rotate the support hyperplanes the prime merits of the proposed model are in its simplicity understandability and effectiveness consequently experimental results and comparisons are given to demonstrate that the basic idea underlying asvms can be effectively used for parameter estimation

bicriteria variable selection in a fuzzy regression equation abstract by considering two criteria of minimum total sum of vagueness and minimum total sum of squares in estimation this article proposes a variable selection method for a fuzzy regression equation with crisp input and fuzzy output a branch and bound algorithm is designed and the least resistance principle is adopted to determine the set of compromised solutions numerical examples are provided for illustration

fuzzy linear regression and its applications to forecasting in uncertain environment abstract linear regression has been used for many years in developing mathematical models for application in marketing management and sales forecasting in this paper two different sales forecasting techniques are discussed the first technique involves non fuzzy abstract methods of linear regression and econometrics a study of the international market sales of cameras done in 1968 by john scott armstrong utilized these non fuzzy forecasting techniques the second sales forecasting technique uses fuzzy linear regression introduced by h tanaka s uejima and k asai in 1980 in this paper a study of the computer and peripheral equipment sales in the united states is discussed using fuzzy linear regression moreover fuzzy linear regression is applied to forecasting in an uncertain environment finally some possible improvements and suggestions for further study are mentioned

membership function as an evaluation abstract after giving an overview of the different kinds of mathematical forms of the membership functions we extract the different demands and determine the rational class of the membership functions from the generalisation of our result we can determine it giving four parameters the internal a b the sharpness and the decision level we show the correspondence of this membership function to the zimmermann zysno model and using their empirical data we also test our mathematical model we also show the connections between the operators of the evaluation and membership functions which gives the generalisation of this concept in a more general form as a special case we can get a linear form

developing a fuzzy bicluster regression to estimate heat tolerance in plants by chlorophyll fluorescence this paper presents a straightforward and useful fuzzy regression approach to estimate heat tolerance of plants by chlorophyll fluorescence measurement the chlorophyll fluorescence measurement is an indicator of functional change of photosynthesis and is sensitive to temperature using the fluorescence temperature curves the experimenter may determine the heat tolerance tc of plants by intersections of two linear regression lines however as traditional statistical regression analysis shows the experiment may contain uncertain factors or phenomena such as leaf nature and growth environment which concludes that data may vary among individual plants and different species this research presents a fuzzy bicluster regression fbcr analysis with genetic algorithms which helps derive a fuzzy intersection set and fuzzy heat tolerance of plants in addition to the traditional statistical regression analysis a fuzzy clustering concept and simultaneously optimal determination of data clusters is also developed especially when there are nonlinear inflections in data curves due to the imperative use of linear regression models the traditional regression analysis may become unable to sufficiently model the uncertainties exhibited the fbcr analysis can resolve this problem effectively due to the nonlinear tolerance of the system even in a linear model to demonstrate the fbcr analysis it was applied to estimate the heat tolerance of five plant species the results derived appeared to be more suitable than that of the conventional method the approach may provide a useful means for the experimenters to derive more credible results from their chlorophyll fluorescence temperature data

extrapolating internet users in taiwan by risk assessment abstract in a competitive environment most products usually have different stages of life cycle by different sales thus satisfying consumers requirements could make the product competitive from the experiences of experts the analytic hierarchy process has been used to analyze the expected range for a specified plc stage to enable a decision maker to derive proper marketing strategies however in decision theory the belfavior of a decision maker is always affected by her risk perception and risk propensity to result in different decision making in order to cope with this problem a fuzzy forecasting system to the risk perception and risk propensity is derived to extrapolate the internet users for a specified plc stage because of uncertainty and unknown system structure in the future

support vector interval regression networks for interval regression analysis in this paper the support vector interval regression networks svirns are proposed for the interval regression analysis the svirns consist of two radial basis function networks one network identifies the upper side of data interval and the other network identifies the lower side of data intervals because the support vector regression svr approach is equivalent to solving a linear constrained quadratic programming problem the number of hidden nodes and the initial values of adjustable parameters can be easily obtained since the selection of a parameter e in the svr approach may seriously affect the modeling performance a two step approach is proposed to properly select the e value after the svr approach with the selected e an initial structure of svirns can be obtained besides outliers will not significantly affect the upper and lower bound interval obtained through the proposed two step approach consequently a traditional back propagation bp learning algorithm can be used to adjust the initial structure networks of svirns under training data sets without or with outliers due to the better initial structure of svirns are obtained by the svr approach the convergence rate of svirns is faster than the conventional networks with bp learning algorithms or with robust bp learning algorithms for interval regression analysis four examples are provided to show the validity and applicability of the proposed svirns

fuzzy least squares algorithms for interactive fuzzy linear regression models fuzzy regression analysis can be thought of as a fuzzy variation of classical regression analysis it has been widely studied and applied in diverse areas in general the analysis of fuzzy regression models can be roughly divided into two categories the first is based on tanaka s linear programming approach the second category is based on the fuzzy least squares approach in this paper new types of fuzzy least squares algorithms with a noise cluster for interactive fuzzy linear regression models are proposed these algorithms are robust for the estimation of fuzzy linear regression models especially when outliers are present numerical examples are given to detail the effectiveness of this approach

fuzzy regression analysis by support vector learning approach support vector machines svms have been very successful in pattern classification and function approximation problems for crisp data in this paper we incorporate the concept of fuzzy set theory into the support vector regression machine the parameters to be estimated in the svm regression such as the components within the weight vector and the bias term are set to be the fuzzy numbers this integration preserves the benefits of svm regression model and fuzzy regression model and has been attempted to treat fuzzy nonlinear regression analysis in contrast to previous fuzzy nonlinear regression models the proposed algorithm is a model free method in the sense that we do not have to assume the underlying model function by using different kernel functions we can construct different learning machines with arbitrary types of nonlinear regression functions moreover the proposed method can achieve automatic accuracy control in the fuzzy regression analysis task the upper bound on number of errors is controlled by the user predefined parameters experimental results are then presented that indicate the performance of the proposed approach

a mathematical programming approach to fuzzy linear regression analysis most of previous studies on fuzzy regression analysis have a common characteristic of increasing spreads for the estimated fuzzy responses as the independent variable increases its magnitude which is not suitable for general cases in this paper fuzzy linear regression models with fuzzy crisp output fuzzy crisp input are considered and an estimated method along with a mathematical programming based approach is proposed the advantages of the proposed approach are simplicity in programming and computation and minimum difference of total spread between observed and estimated values

development of a cost function for wastewater treatment systems with fuzzy regression abstract a fuzzy linear regression analysis is performed to study the cost function of wastewater that is developed by using a pool of data from 26 municipal wastewater treatment systems in taiwan the choice of a primary or more higher wastewater treatment process is intimately related to financial land availability effluent standards and managerial factors especially financial consideration plays an important role in the planning stage in addition cost estimation is difficult to precisely evaluate in an uncertain environment in the conventional regression model deviations between the observed values and the estimated values are supposed to be due to measurement errors here taking a different perspective these deviations are regarded as the fuzziness of the system s parameters thus these deviations are reflected in a linear function with fuzzy parameters using linear programming algorithm this fuzzy linear regression model might be very convenient and useful for finding a fuzzy structure in an evaluation system in this paper the details of the fuzzy linear regression concept and its applications to the cost function in an uncertain environment are shown and discussed

fuzzy linear systems a general fuzzy linear system is investigated using the embedding approach conditions for the existence of a unique fuzzy solution to n n linear system are derived and a numerical procedure for calculating the solution is designed the applicability of the proposed model is illustrated with examples

on direct construction of fuzzy systems abstract in this paper we show that the fuzzy logic system presented by wang and mendel 1992 is a linear expansion of the fuzzy rule base if fuzzy events are represented by triangular basis functions therefore based on linear regression theory we propose a direct approach for constructing a fuzzy logic system from input output data the effectiveness of this approach is demonstrated by simulations

fuzzy linear regression models with least square errors to estimate the parameters of fuzzy linear regression models with fuzzy output and crisp inputs we develop a mathematical programming model in this paper the method is constructed on the basis of minimizing the square of the total difference between observed and estimated spread values or in other words minimizing the least square errors the advantage of the proposed approach is its simplicity in programming and computation as well as its performance to compare the performance of the proposed approach with the other methods two examples are presented

on the effect of linear data transformations in possibilistic fuzzy linear regression abstract in this paper the effect of linear data transformations is analysed in possibilistic fuzzy regression models in classical linear regression the measure of the goodness of fit is invariant with respect to these transformations but these fuzzy models depend on them

interval regression by tolerance analysis approach in interval linear regression analysis we are given crisp or interval data and we are to determine appropriate interval regression parameters there are various methods for interval regression many of them possess the property that while some of the resulting interval regression parameters are very wide the other parameters are crisp this drawback is the main limiting factor for such methods and much effort has been devoted to overcoming it we propose a method motivated by tolerance analysis in linear systems our method yields intervals for regression parameters the widths of which are proportional to an in advance given vector of parameters moreover the method is computationally very cheap and provides a natural measure of quality of a model first we formulate the method for the basic model of crisp input crisp output data and then extend it to crisp input interval output and interval input interval output models for the interval valued cases we study several formulations of the solution concept possibility strong possibility weak possibility necessity here strong possibility is a new concept proposed as a natural counterpart to the remaining ones we prove that the method provides optimal interval parameters meeting centrality and proportionality requirements we also show that the method provides interval regression parameters satisfying various versions of tanaka lee s inclusion property we also derive a form of a complementarity theorem for the weak possibility and necessity solution concepts since practical problems may be affected by outlying observations we show that our approach is easily adapted to deal with them we illustrate the theory by examples

possibilistic linear regression analysis for fuzzy data abstract fuzzy data given by expert knowledge can be regarded as a possibility distribution by which possibilistic linear systems are defined recently it has become important to deal with fuzzy data in connection with expert knowledge three formulations of possibilistic linear regression analysis are proposed here to deal with fuzzy data since our formulations can be reduced to linear programming problems the merit of our formulations is to be able to obtain easily fuzzy parameters in possibilistic linear models and to add other constraint conditions which might be obtained from expert knowledge of fuzzy parameters this approach can be regarded as a fuzzy interval analysis in a fuzzy environment

interval regression analysis by quadratic programming approach when we use linear programming in possibilistic regression analysis some coefficients tend to become crisp because of the characteristic of linear programming on the other hand a quadratic programming approach gives more diverse spread coefficients than a linear programming one therefore to overcome the crisp characteristic of linear programming we propose interval regression analysis based on a quadratic programming approach another advantage of adopting a quadratic programming approach is to be able to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression by changing the weights of the quadratic function we can analyze the given data from different viewpoints for data with crisp inputs and interval outputs the possibility and necessity models can be considered therefore the unified quadratic programming approach obtaining the possibility and necessity regression models simultaneously is proposed even though there always exist possibility estimation models the existence of necessity estimation models is not guaranteed if we fail to assume a proper function fitting to the given data as a regression model thus we consider polynomials as regression models since any curve can be represented by the polynomial approximation using polynomials we discuss how to obtain approximation models which fit well to the given data where the measure of fitness is newly defined to gauge the similarity between the possibility and the necessity models furthermore from the obtained possibility and necessity regression models a trapezoidal fuzzy output can be constructed

the efficacy of fuzzy representations of uncertainty advocates of the theory of fuzzy sets as a system for representing uncertainty have based their case on five basic arguments these are 1 the reality hypothesis which holds that imprecision is an inherent property of the world external to an observer 2 the subjectivity hypothesis which holds that probability is an exclusively objective measure of uncertainty and that therefore subjective uncertainty can only be represented with fuzzy sets 3 the behaviorist hypothesis which claims that uncertainty systems should emulate rather than prescribe human behavior in the face of uncertainty 4 the probability as fiction hypothesis which claims that probability does not comprise a field of study in its own right and 5 the superset hypothesis which holds that fuzzy set theory includes probability as a special case and thus provides a richer uncertainty modeling environment we discuss and criticize all five we then criticize the argument that fuzziness represents a type of uncertainty distinct from probability and also the inordinate complexity of fuzzy methods we present a method for assessing the efficacy of fuzzy representations of uncertainty and apply this method in three examples

extended support vector interval regression networks for interval input output data in many applications it is natural to use interval data because of uncertainty existence in the measurements variability in defining terms such as the temperature during a given day description for extremely behavior such as the maximum wind speed in a given area etc in order to handle such interval data a novel approach called the interval support vector interval regression networks isvirns is proposed the isvirns is extended from our previous work the support vector interval regression networks svirns it is easy to find that svirns can handle interval output data but for input data they must be crisp in this study the hausdorff distance is employed as the distance measure of interval data and is incorporated into the kernel functions of svirns to determine the initial structure of isvirns because the proposed approach can provide a better initial structure for isvirns it can have a faster convergent speed the experimental results with real data sets show the validity of the proposed isvirns

fuzzy data analysis by possibilistic linear models abstract since fuzzy data can be regarded as distribution of possibility fuzzy data analysis by possibilistic linear models is proposed in this paper possibilistic linear systems are defined by the extension principle fuzzy parameter estimations are discussed in possibilistic linear systems and possibilistic linear models are employed for fuzzy data analysis with non fuzzy inputs and fuzzy outputs defined by fuzzy numbers the estimated possibilistic linear system can be obtained by solving a linear programming problem this approach can be regarded as fuzzy interval analysis

higher level fuzzy numbers arising from fuzzy regression consider a fuzzy random variable y with expectation symbol b x where b is an unknown fuzzy number and an unknown real number for n observations yi xi there is a model yi b xi ei i 1 2 n where ei are fuzzy valued errors independently and identically distributed in some sense the aim is to obtain estimates of b when all fuzzy numbers are triangular and the ei are uniformly distributed maximum likelihood estimators emerge naturally as a special form of higher level fuzzy number thus mle can be interpreted as an estimation procedure which transforms randomness into higher levels of fuzziness

interval regression analysis using support vector networks support vector machines svms have been very successful in pattern classification and function estimation problems for crisp data in this paper the v support vector interval regression network v svirn is proposed to evaluate interval linear and nonlinear regression models for crisp input and output data as it is difficult to select an appropriate value of the insensitive tube width in e support vector regression network the proposed v svirn alleviates this problem by utilizing a new parametric insensitive loss function the proposed v svirn automatically adjusts a flexible parametric insensitive zone of arbitrary shape and minimal size to include the given data besides the proposed method can achieve automatic accuracy control in the interval regression analysis task for a priori chosen v at most a fraction v of the data points lie outside the interval model constructed by the proposed v svirn to be more precise v is an upper bound on the fraction of training errors and a lower bound on the fraction of support vectors hence the selection of v is more intuitive moreover the proposed algorithm here is a model free method in the sense that we do not have to assume the underlying model function experimental results are then presented which show the proposed v svirn is useful in practice especially when the noise is heteroscedastic that is the noise strongly depends on the input value x

fuzzy linear regression models for assessing risks of cumulative trauma disorders abstract cumulative trauma disorders ctds are a major problem in industry and today s office environments especially for keyboard users since comprehensive knowledge about individual or a combination of risk factors contributing to ctds of the hand and forearm is still lacking developing methodologies to quantify relationships of risk factors is greatly needed the purpose of this research was to build fuzzy linear regression models to reveal the relationship of ctd risk factors to predict the injuries and to evaluate risk levels of individuals twenty seven keyboard users twenty two for model building and five for model validation and three ctd experts participated in the model building four fuzzy models were built corresponding to four risk categories and a final fuzzy linear model was established using ahp pairwise comparisons multicolinearity effects were addressed and a partial standard deviation scaling method was used to eliminate the effects from a methodological point of view fuzzy linear regression models provide useful insight into risk factors ctd relationship

an orderwise polynomial regression procedure for fuzzy data a procedure for polynomial fit with fuzzy data is presented as in real case studies there is often dependence between modes and spreads we propose a regression polynomial model capable to take into account possible interactions between the estimated spreads and modes this method finds applications in several fields such as reliability quality control psychometrics marketing image processing etc an application to a software reliability problem is also presented

resolution of fuzzy regression model abstract fuzzy linear regression was originally introduced by tanaka et al to cope with different types of input output information several approaches to fuzzy linear regression have been proposed in this paper a type of problem with crisp input and fuzzy output described by tanaka is considered of which a modified fuzzy least square method was proposed for solution it shows that with such an approach the predictability in the new model is better than tanaka s and its computation efficiency is better than the conventional fuzzy least square method

an approach to causal modeling in fuzzy environment and its application abstract this paper suggests an approach to building a causal model in fuzzy environment the fuzzy vector autoregressive fvar model is defined and a causality definition in the fuzzy environment is provided three types of causality namely nonfuzzy non causality nonfuzzy causality and fuzzy causality are defined based on the fuzzy causality relation introduced in this paper necessary and sufficient conditions for the three types of causality are also provided when fuzzy parameters have triangular membership functions a procedure to implement the fuzzy causal modeling is also suggested we applied the procedure to real data and compared it with other conventional empirical studies

the fuzzy gmdh algorithm by possibility models and its application abstract it is the purpose of this paper to formulate the group method of data handling gmdh by the possibility model the gmdh formulated by the possibility model is called the fuzzy gmdh to formulate the fuzzy gmdh we discuss possibilistic linear regression by the lp problem called min problem in the fuzzy gmdh the estimated model by using possibilistic linear regression with a multilayer procedure is a non linear system with parameters in the form of fuzzy numbers the estimation by the fuzzy gmdh can be obtained in fuzzy numbers thus this approach can be regarded as fuzzy interval analysis

approximation of functional relationships to fuzzy observations abstract for approximating functional relationships to fuzzy observations there exist several approaches joining some communities the functional relationship is still kept a fuzzy function even if the observations are crisp the case of crisp observations often requires specific considerations in this paper an approximation method using hausdorff like distances is proposed naturally containing the crisp observation case and leading to a crisp function for crisp observations additional the proposed method leads to well known approximation principles from classical theory and can be realized by standard computer software a simple example completes the considerations

fuzzy linear regression analysis for fuzzy input output data using shape preserving operations abstract in this paper we have presented a new method to evaluate fuzzy linear regression models based on tanaka s approach where both input data and output data are fuzzy numbers using t w based fuzzy arithmetic operations this method simplifies the computation of fuzzy arithmetic operations general linear program is applied to derive the solutions we also prove scale independent property of our models and discuss the effects of outliers

optimal smoothing and interpolating splines with constraints abstract this paper considers the problem for designing optimal smoothing and interpolating splines with equality and or inequality constraints the splines are constituted by employing normalized uniform b splines as the basis functions namely as weighted sum of shifted b splines of degree k then a central issue is to determine an optimal vector of the so called control points by employing such an approach it is shown that various types of constraints are formulated as linear function of the control points and the problems reduce to quadratic programming problems we demonstrate the effectiveness and usefulness by numerical examples including approximation of probability density functions approximation of discontinuous functions and trajectory planning

on the possibilistic approach to linear regression models involving uncertain indeterminate or interval data abstract we consider linear regression models where both input data the observations of independent variables and output data the observations of the dependent variable are affected by loss of information caused by uncertainty indeterminacy rounding or censoring instead of real valued crisp data only intervals are available we study a possibilistic generalization of the least squares estimator so called ols set for the interval model investigation of the ols set allows us to quantify whether the replacement of real valued crisp data by interval values can have a significant impact on our knowledge of the value of the ols estimator we show that in the general case very elementary questions about properties of the ols set are computationally intractable assuming p np we also focus on restricted versions of the general interval linear regression model to the crisp input case taking the advantage of the fact that in the crisp input interval output model the ols set is a zonotope we design both exact and approximate methods for its description we also discuss special cases of the regression model e g a model with repeated observations

properties of certain fuzzy linear regression methods abstract fuzzy linear regression was originally introduced by tanaka uejima and asai ieee trans systems man cybern 12 1982 903 907 in subsequent years several different approaches to fuzzy linear regression have been proposed the purpose of this paper is to review and examine some of these formulations to discuss their strengths and weaknesses relative to each other and to suggest possible improvements in addition we compare and contrast these methods to the method of ordinary least squares regression

numerical solutions of fuzzy differential and integral equations using the embedding method numerical procedures for solving fuzzy differential equations fdes and fuzzy integral equations fies with arbitrary kernels have been investigated sufficient conditions for convergence of the proposed algorithms are given and their applicability is illustrated with examples this work and its conclusions may narrow the gap between the theoretical research on fdes and fies and the practical applications already existing in the design of various fuzzy dynamical systems

the use of fuzzy set theory for forecasting corporate tax revenues the system based on the fuzzy set theory for forecasting the florida corporate income tax revenue was developed in response to several years of unsuccessful forecasts generated by the conventional econometric methods the system consists of two parts 1 a the first part utilizes time series of revenue and of the real per capita gnp both time series are transformed into trend vectors through the utilization of moving average technique both vectors are divided into strings of growth patterns such as accelerating growth decelerating growth and negative growth the system checks for several indications of systematic relationship between the gnp vector and the tax revenue vector based on that relationship the forecast of the corporate tax revenues is generated in fuzzy such as very rapid growth slightly negative growth etc 2 b the fuzzy forecast from the first part of the system constitutes input into the second part which in turn generates the range of forecasted revenue in millions of dollars a control mechanism which is built into the system continously checks forecasted rates of change in tax revenues against the actuals throughout the history of the time series to make sure that the cumulative forecasting error will not reach unacceptable magnitude

fuzzy rough regression with application to wind speed prediction accurate wind speed prediction is a prerequisite of large scale wind power generation there are several uncertain factors which degrade the performance of the current wind speed prediction systems fuzzy rough sets are considered as a powerful tool to deal with uncertainty and have been widely discussed and applied in classification learning in this work we describe a regression algorithm based on fuzzy rough sets consisting of fuzzy partition fuzzy approximation and estimation of regression values in this algorithm the training set is divided into k fuzzy classes with fuzzy partition and then the predicted values of test samples are determined in the finite intervals with fuzzy rough approximation finally they are estimated with lower and upper limits of the intervals numerical experiments on uci data sets and wind speed prediction show the effectiveness of the proposed algorithm

approximation of uncertain functional relationships in this paper we consider methods for the linguistic modelling of vague functional relationships where the linguistic model is supposed to be given as a set of rules two approaches for deriving a fuzzy valued function from such models are proposed it is argued that both approaches can be interpreted as a generalization of ordinary methods for the interpolation and approximation of functions mathematical properties of fuzzy functions associated with a set of rules are investigated particularly for the second approach a universal approximation property is shown

on assessing the h value in fuzzy linear regression abstract there are certain circumstances under which the application of statistical regression is not appropriate or even feasible because it makes rigid assumptions about the statistical properties of the model fuzzy regression a nonparametric method can be quite useful in estimating the relationships among variables where the available data are very limited and imprecise and variables are interacting in an uncertain qualitative and fuzzy way thus it may have considerable practical applications in many management and engineering problems in this paper the relationship among the h value membership function shape and spreads of fuzzy parameters in fuzzy linear regression is determined and the sensitivity of the spread with respect to the h value and membership function shape is examined the spread of a fuzzy parameter increases as a higher value of h and or a decreasingly concave or increasingly convex membership function is employed by utilizing the relationship among the h value membership function and spreads of the fuzzy parameters a systematic approach to assessing a proper h parameter value is also developed the approach developed and illustrated enables a decision maker s beliefs regarding the shape and range of the possibility distribution of the model to be reflected more systematically and consequently should yield more reliable and realistic results from fuzzy regression the resulging regressing equations could for example also be used as constraints in a fuzzy mathematical optimization model such as in quality function deployment