set valued measure and fuzzy set valued measure abstract fuzzy set valued measure and set valued measure are two different subjects in this paper we shall introduce a couple of new results regarding set valued measure and establish the relation between set valued measure and fuzzy set valued measure lastly we offer a theorem which illustrates the application of set valued measure to fuzzy set valued measure

deterministic fuzzy time series model for forecasting enrollments the fuzzy time series has recently received increasing attention because of its capability of dealing with vague and incomplete data there have been a variety of models developed to either improve forecasting accuracy or reduce computation overhead however the issues of controlling uncertainty in forecasting effectively partitioning intervals and consistently achieving forecasting accuracy with different interval lengths have been rarely investigated this paper proposes a novel deterministic forecasting model to manage these crucial issues in addition an important parameter the maximum length of subsequence in a fuzzy time series resulting in a certain state is deterministically quantified experimental results using the university of alabama s enrollment data demonstrate that the proposed forecasting model outperforms the existing models in terms of accuracy robustness and reliability moreover the forecasting model adheres to the consistency principle that a shorter interval length leads to more accurate results

effective lengths of intervals to improve forecasting in fuzzy time series abstract length of intervals affects forecasting results in fuzzy time series unfortunately the issue of how to determine effective lengths of intervals has not been touched in previous studies this study proposes distribution and average based length to approach this issue distribution based length is the largest length smaller than at least half the first differences of data average based length is set to one half the average of the first differences of data empirical analyses show that distribution and average based lengths are simple to calculate and can greatly improve forecasting results in particular they are superior to the randomly chosen lengths used in previous studies

a proposal for a defuzzification strategy by the concept of sensitivity analysis abstract a systematic procedure is proposed for defuzzifying fuzzy subsets and interval values employing the concept of sensitivity analysis with a kind of minmax principle such that the defuzzification minimizes the sensitivity rating the discrepancy between a would be most appropriate defuzzified value and the unknown ideal value of defuzzification in the possible worst case a criterion of defuzzification can be built into the sensitivity to give a rationale to the defuzzified value as examples defuzzification with respect to a criterion of distance and minimization problems of two types of functions with fuzzy parameters are discussed

fuzzy stochastic fuzzy time series and its models in this paper as an extension of the concept of time series we will present the definition and models of fuzzy stochastic fuzzy time series fsfts both of whose values and probabilities with which the fsfts assumes its values are fuzzy sets and which may not be modeled properly by the concept of time series to investigate fsfts the definition of fuzzy valued probability distributions is considered and discussed when the fsfts is time invariant several preliminary conclusions are derived

successive identification of a fuzzy model and its applications to prediction of a complex system abstract a successive identification method of a fuzzy model is suggested the identification mechanism consists of two levels one is the supervisor level and the other is the adjustment level the supervisor level determines a policy of parameter adjustment using a set of fuzzy adjustment rules the adjustment rules are derived from the fuzzy implications of a fuzzy model and are extended to fuzzy adjustment rules by using an extended concept of zadeh s contrast intensification the adjustment level executes the policy of parameter adjustment determined with the fuzzy adjustment rules the parameter adjustment consists of premise parameter adjustment and consequent parameter adjustment both of them are realized by the weighted recursive least square algorithm finally it is shown from two examples that the method is very useful for modeling complex systems

modeling temporal functions with granular regression and fuzzy rules modeling of temporal functions has been studied extensively in last few decades temporal functions or time series are found practically in the gamut of applications ranging from engineering analysis to financial and commercial transactions numerous time series models been proposed and they can be found in the relevant time series literature deterministic and stochastic models have dominated much of the research in this area nonetheless these models have their limitations and particularly specific models solve specific problem domains therefore there is no general mechanism that can address the issues of modeling of temporal functions granular information is now being used to address a few of the problems in the theory of time series this paper proposes two models that use the concepts of regression and interleaved information granules intervals and fuzzy sets to identify the structure existing in a given time series in brevity we are attempting to combine regression and fuzzy rules to model temporal systems

forecasting enrollments with fuzzy time series part ii abstract there have been a good many methods to forecast university enrollments in the literature however none of them could be applied when the historical data are linguistic values fuzzy time series is an effective tool to deal with such problems in this paper as an application of fuzzy time series in educational research the forecast of the enrollments of the university of alabama is carried out in so doing a fuzzy time series model is developed using historical data a complete procedure is proposed which includes fuzzifying the historical data developing a fuzzy time series model and calculating and interpreting the outputs to evaluate the forecasting model the robustness of the fuzzy time series model is tested advantages and problems of the forecasting method are also discussed

the theory of fuzzy stochastic processes abstract in this paper we deal with the general theory of fuzzy stochastic processes we give the suitable definitions of fuzzy random function fuzzy stochastic process and their fall shadow distribution functions the concepts of separability and measurability of a fuzzy random function are introduced and some properties of these new concepts are derived we investigate the continuity of fuzzy sample function of a fuzzy stochastic process

fuzzy reasoning and fuzzy relational equations l a zadeh first suggested a method of fuzzy reasoning called compositional rule of inference cri for short instead of sup min composition we use a more general composition called sup t composition in cri according to the criteria gmp and gmt the fuzzy implication r must satisfy the sup t composite fuzzy relational equations email protected r s and email protected r 1 q in this paper we discuss the solution of these equations and point out that email protected composition and the implication r n a used to cri will be more suitable under criteria gmp and gmt

calibration sufficiency and domination considerations for bayesian probability assessors abstract degroot and fienberg 1982a recently considered various aspects of the problem of evaluating the performance of probability appraisers after briefly reviewing their notions of calibration and sufficiency we introduce related ideas of semicalibration and domination and consider their relationship to the earlier concepts we then discuss some simple bayesian mechanisms for making probability assessments and study their calibration semicalibration sufficiency and domination properties finally several results concerning the comparison of finite dichotomous experiments relevant to the present work are collected in an appendix

defuzzification filters and applications to power system stabilization problems defuzzification is a very important step in fuzzy systems applications there are a number of different defuzzification methods reported in the literature in this paper the concept of defuzzification filters in a control system setting is first discussed and a methodology for designing such filters considered as will be seen the design of such filters requires the knowledge of the plant model and its inverse a reference control signal is computed and then is used to generate the actual defuzzified control signal which will be applied to control the plant the application of the defuzzification filter is made by introducing the filter into a power system in which a neuro fuzzy self learning controller was applied to stabilize the system but success could not always be guaranteed with the defuzzification filter however the system is always stabilized simulation results are presented

some properties of defuzzification neural networks abstract fuzzy systems have gained more and more attention from researchers and practitioners of various fields in such systems the output represented by a fuzzy set sometimes needs to be transformed into a scalar value and this task is known as the defuzzification process several analytic methods have been proposed for this problem but lately the neural network approach has been used for this purpose when employed as defuzzifiers a neural network is called a defuzzification neural network in this paper some preliminary results on properties of such defuzzification networks will be reported

on the decomposition problem of fuzzy sets in this paper we consider an important problem that is frequently encountered and yet almost universally ignored both in the application and in the theoretic studies of fuzzy sets we refer to this problem as the decomposition of fuzzy sets in nearly all applications of fuzzy sets theory e g fuzzy decision making fuzzy control fuzzy forecasting etc the output is in general a fuzzy set this is then defuzzified before it is applied although defuzzification may be necessary if a crisp quantity is definitely needed when a fuzzy output is appropriate desired or required in an application then the defuzzification step becomes unnecessary yet in this case one finds that it is some times difficult to correctly interpret a fuzzy quantity or identify the true meaning of this fuzzy output using a family of predefined fuzzy sets thus how to match the fuzzy output and the predefined fuzzy sets is the problem of concern in this paper to address this problem we first present and review some definitions and then proceed with an investigation of the preliminary properties of these concepts complementing them with illustrative examples finally we propose some algorithms for the solution of this problem

a new hybrid artificial neural networks and fuzzy regression model for time series forecasting quantitative methods have nowadays become very important tools for forecasting purposes in financial markets as for improved decisions and investments forecasting accuracy is one of the most important factors involved in selecting a forecasting method hence never has research directed at improving upon the effectiveness of time series models stopped artificial neural networks anns are flexible computing frameworks and universal approximators that can be applied to a wide range of forecasting problems with a high degree of accuracy however anns need a large amount of historical data in order to yield accurate results in a real world situation and in financial markets specifically the environment is full of uncertainties and changes occur rapidly thus future situations must be usually forecasted using the scant data made available over a short span of time therefore forecasting in these situations requires methods that work efficiently with incomplete data although fuzzy forecasting methods are suitable for incomplete data situations their performance is not always satisfactory in this paper based on the basic concepts of anns and fuzzy regression models a new hybrid method is proposed that yields more accurate results with incomplete data sets in our proposed model the advantages of anns and fuzzy regression are combined to overcome the limitations in both anns and fuzzy regression models the empirical results of financial market forecasting indicate that the proposed model can be an effective way of improving forecasting accuracy

fuzzy arima model for forecasting the foreign exchange market considering the time series arima p d q model and fuzzy regression model this paper develops a fuzzy arima farima model and applies it to forecasting the exchange rate of nt dollars to us dollars this model includes interval models with interval parameters and the possibility distribution of future values is provided by farima this model makes it possible for decision makers to forecast the best and worst possible situations based on fewer observations than the arima model c 2001 elsevier science b v all rights reserved

a simple method of forecasting based on fuzzy time series in fuzzy time series forecasting various methods have been developed to establish the fuzzy relations on time series data having linguistic values for forecasting the future values however the major problem in fuzzy time series forecasting is the accuracy in the forecasted values the present paper proposes a new method of fuzzy time series forecasting based on difference parameters the proposed method is a simplified computational approach for the forecasting the method has been implemented on the historical enrollment data of university of alabama adapted by song and chissom and the forecasted values have been compared with the results of the existing methods to show is superiority further the proposed method has also been implemented on a real life problem of crop production forecast of wheat crop and the results have been compared with other methods

taiex forecasting based on fuzzy time series and fuzzy variation groups in this paper we present a new method to forecast the daily taiwan stock exchange capitalization weighted stock index taiex based on fuzzy time series and fuzzy variation groups where the main input factor is the previous day s taiex and the secondary factor is either the dow jones the nasdaq the m 1b or their combination first the proposed method fuzzifies the historical training data of the taiex into fuzzy sets to form fuzzy logical relationships second it groups the fuzzy logical relationships into fuzzy logical relationship groups flrgs based on the fuzzy variations of the secondary factor third it evaluates the leverage of the fuzzy variations between the main factor and the secondary factor to construct fuzzy variation groups fourth it gets the statistics of the fuzzy variations appearing in each fuzzy variation group fifth it calculates the weights of the statistics of the fuzzy variations appearing in each fuzzy variation group respectively finally based on the weights of the statistics of the fuzzy variations appearing in the fuzzy variation groups and the flrgs it performs the forecasting of the daily taiex because the proposed method uses both fuzzy variation groups and flrgs to analyze in detail the historical training data it gets higher forecasting accuracy rates to forecast the taiex than the existing methods

handling forecasting problems using fuzzy time series abstract in 6 9 song et al proposed fuzzy time series models to deal with forecasting problems in 10 sullivan and woodall reviewed the first order time invariant fuzzy time series model and the first order time variant model proposed by song and chissom 6 8 where the models are compared with each other and with a time invariant markov model using linguistic labels with probability distributions in this paper we propose a new method to forecast university enrollments where the historical enrollments of the university of alabama shown in 7 8 are used to illustrate the forecasting process the average forecasting errors and the time complexity of these methods are compared the proposed method is more efficient than the ones presented in 7 8 10 due to the fact that the proposed method simplifies the arithmetic operation process furthermore the average forecasting error of the proposed method is smaller than the ones presented in 2 7 8

a robust method of forecasting based on fuzzy time series present study proposes an improved and versatile method of forecasting based on the concept fuzzy time series forecasting the developed model has been presented in a form of simple computational algorithms it utilizes various difference parameters being implemented on current state for forecasting the next state values to accommodate the possible vagueness in the data in a better way and making it a robust method the developed model has been implemented on the historical student enrollments data of university of alabama adapted by song and chissom and the obtained forecasted values have been compared with the existing methods to show its superiority the robustness of the model has also been tested in comparison the suitability of the developed model has also been examined in the crop production forecasting by implementing it on historical time series data of rice production of pantnagar farm india

a note on fuzzy time series model recently song et al fuzzy sets and systems 73 1995 341 348 proposed a homogeneous fuzzy time series model to model dynamic process whose observations are fuzzy sets or linguistic values by means of defining some new operations on fuzzy numbers in this paper we considered expanding the results to the nonhomogeneous fuzzy time series and the general fuzzy time series by using the weakest t norm based algebraic fuzzy operations and solved the open problem suggested by song et al in their conclusion of the paper

a refined fuzzy time series model for forecasting abstract fuzzy time series models have been used to model observations where each one of them contains multiple values the formulation of fuzzy relationships and the lengths of intervals are considered to be two of the critical factors that affect forecasting results unfortunately the lengths of the intervals were determined during the early stages of forecasting in these models and they thus often failed to reflect the distribution of observations this study therefore proposes a refined fuzzy time series model to further refine the lengths of intervals this model can refine the lengths of intervals during the formulation of fuzzy relationships and hence capture the fuzzy relationships more appropriately as a result the forecasting results can be improved both the stock index and enrollment are used as the targets in the empirical analysis

adaptive expectation based multi attribute fts model for forecasting taiex in recent years there have been many time series methods proposed for forecasting enrollments weather the economy population growth and stock price etc however traditional time series such as arima expressed by mathematic equations are unable to be easily understood for stock investors besides fuzzy time series can produce fuzzy rules based on linguistic value which is more reasonable than mathematic equations for investors furthermore from the literature reviews two shortcomings are found in fuzzy time series methods 1 they lack persuasiveness in determining the universe of discourse and the linguistic length of intervals and 2 only one attribute closing price is usually considered in forecasting not multiple attributes such as closing price open price high price and low price therefore this paper proposes a multiple attribute fuzzy time series fts method which incorporates a clustering method and adaptive expectation model to overcome the shortcomings above in verification using actual trading data of the taiwan stock index taiex as experimental datasets we evaluate the accuracy of the proposed method and compare the performance with the chen 1996 7 yu 2005 6 and cheng cheng wang 2008 20 methods the proposed method is superior to the listing methods based on average error percentage maer

towards fuzzy differential calculus part 1 integration of fuzzy mappings abstract this paper deals with fuzzy set valued mappings of the real line and more particularly focuses on mappings from the real line to the set of convex normal fuzzy sets of the real line these mappings can also be viewed as fuzzy relations using zadeh s extension principle the integral of such fuzzy mappings over a crisp interval is defined provided a special analytical representation of the fuzzy mapping the practical computation of such an integral is shown to be easy practically speaking it yields the fuzzy surface of a fuzzily bounded area

the completion of a fuzzy measure and its applications this paper discusses first the completion of a fuzzy measure which is defined on a ring then as an application of the complete fuzzy measure both convergence almost everywhere and convergence in fuzzy measure egoroff s theorems are provided

fuzzy relation analysis in fuzzy time series model fuzzy relation is a crucial connector in presenting fuzzy time series model however how to obtain a fuzzy relation matrix to represent a time invariant relation is still a question based on the concept of fuzziness in information theory the concept of entropy is applied to measure the degrees of fuzziness when a time invariant relation matrix is derived finally an example is illustrated to show that the proposed method could obtain more accurate and robust results in forecasting

a new fuzzy time series model of fuzzy number observations fuzzy time series 4 has been proposed to model dynamic processes whose observations are fuzzy sets or linguistic values and some applications have been made with satisfactory results 5 6 in this paper a new fuzzy time series model is proposed by means of defining some new operations on fuzzy numbers the proposed model is in the form of two theorems that relate the current value of a fuzzy time series with its past

fuzzy forecasting based on automatic clustering and axiomatic fuzzy set classification the method can generate clustering based intervals the method can predict the fuzzy trend of forecasted data in advance the afs classification is exploited to yield the semantic interpretation of each fuzzy trend with the proposed method the horizon of prediction can be as long as desired the method has both good interpretability and superior accuracy in spite of the impressive diversity of models of fuzzy forecasting there is still a burning need to arrive at models that are both accurate and highly interpretable this study proposes a new fuzzy forecasting model designed with the use of the two key techniques namely clustering and axiomatic fuzzy set afs classification first clustering algorithm is utilized to generate clustering based intervals second the fuzzy trend labeled training data set is constructed based on fuzzy logic relationships and fuzzy trends of historical samples then the afs classification is exploited to yield the semantic interpretation of each fuzzy trend the main novelty is that the proposed model not only predicts the value but can also capture the trend prevailing in the time series and obtain its semantic interpretation the taiwan stock exchange capitalization weighted stock index taiex inventory demand and spanish electricity prices are used in a series of experiments the results show that the proposed model has both good interpretability and accuracy

a type 2 fuzzy time series model for stock index forecasting abstract most conventional fuzzy time series models type 1 models utilize only one variable in forecasting furthermore only part of the observations in relation to that variable are used to utilize more of that variable s observations in forecasting this study proposes the use of a type 2 fuzzy time series model in such a type 2 model extra observations are used to enrich or to refine the fuzzy relationships obtained from type 1 models and then to improve forecasting performance the taiwan stock index the taiex is used as the forecasting target the study period extends over the 2000 2003 period the taiex from january to october in each year is used for the estimation while that covering november and december is used for forecasting the empirical analyses show that type 2 model outperforms type 1 model

relaxation theorem for the evolution differential inclusions abstract in this paper we use an improved version of baire category method to prove the existence of solutions to the evolution differential inclusion ax ext f t x under the hausdorff noncompactness measure condition we also obtain a density result for the evolution differential inclusion

a model of weather forecast by fuzzy grade statistics abstract a method of classification of weather forecasts is approached by applying fuzzy grade statistical theory this method has been verified with an example and the correct rate for the method is 87

weighted fuzzy time series models for taiex forecasting abstract this study proposes weighted models to tackle two issues in fuzzy time series forecasting namely recurrence and weighting it is argued that recurrent fuzzy relationships which were simply ignored in previous studies should be considered in forecasting it is also recommended that different weights be assigned to various fuzzy relationships in previous studies these fuzzy relationships were treated as if they were equally important which might not have properly reflected the importance of each individual fuzzy relationship in forecasting the weighted models are compared with the local regression models in which weight functions also play an important role both models are different by nature but certain theoretical backgrounds in local regression models are adopted by using the taiwan stock index as the forecasting target the empirical results show that the weighted model outperforms one of the conventional fuzzy time series models

a baire category approach to the bang bang property abstract the aim of this paper is to develop a new technique based on the baire category theorem in order to establish the closedness of reachable sets and the existence of optimal trajectories for control systems without the usual convexity assumptions the bang bang property is proved for a new class of concave multifunctions characterized by the existence of suitable linear selections the proofs rely on lyapunov s theorem in connection with a baire category argument

extreme continuous selectors of multivalued maps and their applications abstract a theorem on the existence of continuous selectors whose values are extreme points is proved for a class of multivalued maps the theorem is used to study existence and properties of solutions to differential inclusions in banach spaces

fast and accurate center of gravity defuzzification of fuzzy system outputs defined on trapezoidal fuzzy partitions in this article three methods are presented to perform the center of gravity cog defuzzification method in the context of linguistic fuzzy models with t norm based inference one well known method the discretisation method and two new methods the slope based method and the modified transformation function method the methods are worked out for trapezoidal membership functions forming a fuzzy partition in the sense of ruspini experimental results show that the newly introduced methods exhibit excellent accuracy at an extremely low computational cost compared to the widely applied discretisation method

a comparison of fuzzy forecasting and markov modeling abstract fuzzy time series models were introduced by song and chissom fuzzy sets and systems 54 1993 269 277 54 1993 1 9 62 1994 1 8 to model and forecast processes whose values are described by linguistic variables song and chissom used as an application the forecasting of educational enrollments this paper reviews the two methods set forth by song and chissom a first order time invariant fuzzy time series model and a first order time variant model these models are compared with each other and with a time invariant markov model using linguistic labels with probability distributions the results of these methods for the enrollment data are compared with three traditional time series models a first order autoregressive ar 1 model and two second order auto regressive ar 2 models all of which are time invariant

to protect or not to protect bayes decisions with forecasts abstract a complete model structural characterization and analytic representation of the bayes solution is presented for a protection problem it is a sequential stationary finite horizon markov decision process involving at each stage a dichotomous action a binary state and a one period ahead forecast of an independent over time bernoulli input process two types of forecasts categorical and probabilistic are considered along with their limiting cases the naive and perfect forecasts the concept of sufficiency is introduced and operationalized so that consistent comparisons of forecasts can be made with respect to both statistical and economic criteria mappings between the sufficiency ordering and the optimal decision strategy are proven or illustrated numerically

markovian forecast processes abstract a sequential forecast process arises when forecasts of a fixed but uncertain state are prepared with decreasing lead times each subsequent forecast incorporating additional information and therefore updating the previous forecast bayesian markov models of such a process are investigated for purposes of rational decision making the markov structure although not universally valid seems plausible leads to tractable models and implies sequential sufficiency of forecasts roughly speaking each subsequent forecast is less uncertain than the previous one sequential sufficiency in turn has implications on modeling markov stopping control processes the normal model for point categorical forecasts is studied in detail

baire s category and the bang bang property for evolution differential inclusions of contractive type abstract the baire category method is employed in order to establish that the bang bang property holds for a class of evolution differential inclusions of contractive type in reflexive and separable real banach spaces

fuzzy seasonality forecasting abstract in this paper a fuzzy forecasting technique for seasonality in the time series data is presented using the following procedure first with the fuzzy regression analysis the fuzzy trend of a time series is analyzed then the fuzzy seasonality is defined by realizing the membership grades of the seasons to the fuzzy regression model both making fuzzy forecast and crisp forecast are investigated seasonal fuzziness and trends are analyzed the method is applied to the sales forecasting problem of a food distribution company

fuzzy valued measure abstract the main purpose of this paper is to introduce and develop the notion of a fuzzy valued measure in separable banach space this definition of fuzzy valued measure is a natural generalization of the set valued measure radon nikod m theorems for fuzzy valued measure are established

deterministic vector long term forecasting for fuzzy time series in the last decade fuzzy time series have received more attention due their ability to deal with the vagueness and incompleteness inherent in time series data although various improvements such as high order models have been developed to enhance the forecasting performance of fuzzy time series their forecasting capability is mostly limited to short term time spans and the forecasting of a single future value in one step this paper presents a new method to overcome this shortcoming called deterministic vector long term forecasting dvl the proposed method built on the basis of our previous deterministic forecasting method that does not require the overhead of determining the order number as in other high order models utilizes a vector quantization technique to support forecasting if there are no matching historical patterns which is usually the case with long term forecasting the vector forecasting method is further realized by seamlessly integrating it with the sliding window scheme finally the forecasting effectiveness and stability of dvl are validated and compared by performing monte carlo simulations on real world data sets

fuzzy time series forecasting based on fuzzy logical relationships and similarity measures in this paper we propose a new fuzzy time series forecasting method for forecasting the taiwan stock exchange capitalization weighted stock index taiex based on fuzzy time series fuzzy logical relationships particle swarm optimization techniques the k means clustering algorithm and similarity measures between the subscript of the fuzzy set of the fuzzified historical testing datum on the previous trading day and the subscripts of the fuzzy sets appearing in the current states of the fuzzy logical relationships in the chosen fuzzy logical relationship group the particle swarm optimization techniques are used to get the optimal partition of the intervals in the universe of discourse the k means clustering algorithm is used to cluster the subscripts of the fuzzy sets of the current states of the fuzzy logical relationships to get the cluster center of each cluster and to divide the constructed fuzzy logical relationships into fuzzy logical relationship groups the experimental results show that the proposed fuzzy forecasting method gets higher forecasting accuracy rates than the existing methods the advantages of the proposed fuzzy forecasting method is that it uses the particle swarm optimization techniques to get the optimal partition of the intervals in the universe of discourse and uses the k means clustering algorithm to cluster the subscripts of the fuzzy sets of the current states of the fuzzy logical relationships to get the cluster center of each cluster and to divide the constructed fuzzy logical relationships into fuzzy logical relationship groups for increasing the forecasting accuracy rates

fuzzy time series and its models based upon the works by zadeh 1973 1975 in this paper a special dynamic process with linguistic values as its observations is defined and studied this dynamic process is called fuzzy time series to describe fuzzy time series fuzzy relational equations are employed as the models there are two classes of fuzzy time series time variant and time invariant the definition of fuzzy time series is given some properties of fuzzy time series are explored and procedures to develop fuzzy time series models are discussed finally a procedure for using fuzzy time series for foracasting is suggested

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

a priori estimates for operational differential inclusions we prove a set valued gronwall lemma and a relaxation theorem for the semilinear differential inclusion x ax f t x x 0 x0 where a is the infinitesimal generator of a c0 semigroup on a separable banach space x and f 0 t x x is a set valued map this allows us to investigate infinitesimal generators of reachable sets and variational inclusions the results are applied to a semilinear optimal control problem with end point constraints

unity and diversity of fuzziness spl minus from a probability viewpoint like the fields of probability and statistics fuzzy set theory is characterized by a variety of viewpoints adherents of fuzzy methods however consistently maintain that probability is not necessarily the optimal representation of uncertainty we rebut this view

radon nikody m theorem and conditional expectation of fuzzy valued measures and variables abstract the notions of fuzzy valued measure and conditional expectation of a fuzzy valued variable are defined the main result of the paper is a proof of the existence of the radon nikod m derivative of the fuzzy valued measure a convergence theorem for conditional expectations is proved as well

fuzzy decision support system for demand forecasting with a learning mechanism in this paper a new decision support system for demand forecasting dss df is presented a demand forecast is generated in dss df by combining four forecasts values two of them are obtained independently one by a customer and the other by a market expert they represent subjective judgments on future demand given as linguistic values such as demand is around a certain value or demand is not lower than a certain value etc two additional forecasts are crisp values obtained using conventional statistical methods one using time series analysis based on decomposition tsad and the other using an auto regressive integrated moving average arma model the combination of these four forecast values into one improved forecast is made by applying fuzzy if then rules a modified mamdani style inference is used which enables reasoning with fuzzy inputs a new learning mechanism is developed and incorporated into the dss df to adapt the rule bases that combine the individual forecasted values the rule bases are adapted taking into consideration the performance of each of the forecast methods recorded in the past the application of dss df is demonstrated by an illustrative example the forecasts obtained by dss df are compared with results procured by applying the conventional tsad and arma methods separately the results obtained are encouraging and indicate that combining forecasts obtained by different methods may be beneficial

evolutionary algorithm based learning of fuzzy neural networks part 2 recurrent fuzzy neural networks fuzzy neural networks fnn as opposed to neuro fuzzy systems whose main task is to process numerical relationships can process both numerical measurement based information and perception based information in spite of great importance of fuzzy feed forward and recurrent neural networks for solving wide range of real world problems today there are no effective training algorithm for them currently there are two approaches for training of fnn first approach is based on application of the level sets of fuzzy numbers and the back propagation bp algorithm the second approach involves using evolutionary algorithms to minimize error function and determine the fuzzy connection weights and biases the method based on the second approach was proposed by the authors and published in part 1 of this paper r a aliev b fazlollahi r vahidov genetic algorithm based learning of fuzzy neural networks part 1 feed forward fuzzy neural networks fuzzy sets and systems 118 2001 351 358 in contrast to the bp and other supervised learning algorithms evolutionary algorithms do not require nor use information about differentials and hence they are most effective in case where the derivative is very difficult to obtain or even unavailable however the main deficiency of the existing fnn based on the feed forward architecture is its adherence to static problems in case of dynamic or temporal problems there is a need for recurrent fuzzy neural networks rfnn designing efficient training algorithms for rfnn has recently become an active research direction in this paper we propose an effective differential evolution optimization deo based learning algorithm for rfnn with fuzzy inputs fuzzy weights and biases and fuzzy outputs the effectiveness of the proposed method is illustrated through simulation of benchmark forecasting and identification problems and comparisons with the existing methods the suggested approach has also been used for real applications in an oil refinery plant for petrol production forecasting

fuzzy forecasting based on two factors second order fuzzy trend logical relationship groups similarity measures and pso techniques in this paper we propose a new fuzzy forecasting method based on two factors second order fuzzy trend logical relationship groups tsftlrgs particle swarm optimization pso techniques and similarity measures between the subscripts of fuzzy sets fss for forecasting the taiwan stock exchange capitalization weighted stock index taiex and the new taiwan dollar us dollar ntd usd exchange rates first we propose a pso based optimal intervals partition algorithm to get the optimal partition of the intervals in the universe of discourse uod of the main factor taiex and to get the optimal partition of the intervals in the uod of the secondary factor sf where sf dow jones nasdaq m1b based on the proposed pso based optimal intervals partition algorithm the constructed tsftlrgs and similarity measures between the subscripts of fss we propose a new method for forecasting the taiex and the ntd usd exchange rates the main contribution of this paper is that we propose a new fuzzy forecasting method based on tsftlrgs pso techniques and similarity measures between the subscripts of fss for forecasting the taiex and the ntd usd exchange rates to get higher forecasting accuracy rates than the ones of the existing fuzzy forecasting methods

non probabilistic convex model process a new method of time variant uncertainty analysis and its application to structural dynamic reliability problems in this paper we propose a method for time variant uncertainty analysis namely the non probabilistic convex model process which provides an effective mathematical tool for the analysis of structural dynamic uncertainty when lacking relevant information in the convex model process we express the variables at any time with intervals and establish the corresponding auto covariance function and correlation coefficient function to depict the correlation between variables at different times we also define several important characteristic parameters for the uni and bi dimensional convex model processes including the mid value function variance function auto covariance function and cross covariance function we provide the definition for the stationary convex model process and its ergodicity then by combining the convex model process with the first passage failure mechanism we propose a non probabilistic analysis model of structural dynamic reliability and formulate the solving algorithm based on monte carlo simulation finally through the analysis of numerical examples we verify the effectiveness of the convex model process and the model of dynamic reliability analysis proposed in this paper

a probabilistic and statistical view of fuzzy methods fuzzy set theory has primarily been associated with control theory and with the representation of uncertainty in applications in artificial intelligence more recently fuzzy methods have been proposed as alternatives to traditional statistical methods in statistical quality control linear regression and forecasting among other areas we review some basic concepts of fuzzy methods point out some philosophical and practical problems and offer simpler alternatives based on traditional probability and statistical theory applications in control theory and statistical quality control serve as our primary examples

fuzzy measures assuming their values in the set of fuzzy numbers abstract fuzzy valued fuzzy measures are defined in an axiomatic way extending a result of klement j math anal appl 75 1980 330 339 it is shown that they can be characterized by a suitable family of ordinary measures and markov kernels

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

forecasting seasonal time series based on fuzzy techniques abstract this paper is devoted to a method for the forecasting of seasonal time series the core of our approach is based on the fuzzy transform and fuzzy natural logic fnl techniques under the assumption that a time series can be additively decomposed into a trend cycle a seasonal component and an irregular fluctuation the forecasting is a combination of individual forecasting of each of these constituents more precisely the trend cycle and the seasonal component are predicted with the help of fuzzy transform pattern recognition and fuzzy natural logic techniques to model the irregular component we apply the box jenkins approach in the paper we compare the suggested method with two other well known methods namely stl see 14 and arima ones

heuristic models of fuzzy time series for forecasting abstract song and chissom first proposed the definitions of fuzzy time series and time invariant and variant models of fuzzy time series chen then proposed arithmetic operations to replace the complex computations in song and chissom s models this study proposes heuristic models by integrating problem specific heuristic knowledge with chen s model to improve forecasting this is because chen s model was easy to calculate was straightforward to integrate heuristic knowledge and forecast better than the others both university enrollment and futures index are chosen as the forecasting targets the empirical analyses show that the heuristic models reflect the fluctuations in fuzzy time series better and provide better overall forecasting results than the previous models

handling forecasting problems based on two factors high order fuzzy time series in our daily life people often use forecasting techniques to predict weather economy population growth stock etc however in the real world an event can be affected by many factors therefore if we consider more factors for prediction then we can get better forecasting results in recent years many researchers used fuzzy time series to handle prediction problems in this paper we present a new method to predict temperature and the taiwan futures exchange taifex based on the two factors high order fuzzy time series the proposed method constructs two factors high order fuzzy logical relationships based on the historical data to increase the forecasting accuracy rate the proposed method gets a higher forecasting accuracy rate than the existing methods

adaptive learning defuzzification techniques and applications abstract in this paper adaptive learning defuzzification techniques are studied under the consideration of system performance indices by treating defuzzification processes as continuous mappings from space 0 1 n to the real line the concept of the optimal defuzzification mapping can be developed since all the continuous defuzzification mappings considered in this paper form a banach space approximation to the optimal mapping with some known functions can be expressed as the parametric optimization problem to find the optimal parameters adaptive learning of the optimal defuzzification mapping is investigated learning laws for the parameters in the defuzzification mapping are derived in one case numerical results indicate that the adaptive learning defuzzification method can give superior defuzzification results to some popular defuzzification methods

taiex forecasting based on fuzzy time series particle swarm optimization techniques and support vector machines in this paper a new method for forecasting the taiex is presented based on fuzzy time series particle swarm optimization techniques and support vector machines the proposed method to forecast the taiex is based on the slope of one day variation of the taiex and the slope of two days average variation of the taiex because the slope of two days average variation of the taiex is smoother than the slope of one day variation of the taiex it is chosen to define the universe of discourse the particle swarm optimization techniques are used to get optimal intervals in the universe of discourse the support vector machine is used to classify the training data set the first feature and the second feature of the support vector machine are the slope of one day variation and the slope of two days average variation of the taiex respectively the experimental results show that the proposed method outperforms the existing methods for forecasting the taiex

on the issue of defuzzification and selection based on a fuzzy set abstract we are concerned with the problem of selecting a crisp element based on information provided by a fuzzy set a problem which manifests itself in the defuzzification step in fuzzy logic controllers we provide a unifying approach to this selection process among other characteristics this unification puts the defuzzification methods of mean of maxima and center of gravity in the same framework we show that this selection can be viewed as a three step operation transformation of the decision fuzzy set normalization to probability distribution selection based on the probability distribution a number of different procedures for selection are discussed

a method for multiple periodic factor prediction problems using complex fuzzy sets multiple periodic factor prediction mpfp problems exist widely in multisensor data fusion applications development of an effective prediction method should integrate information for multiple periodically changing factors because the uncertainty and periodicity coexist in the information used the prediction method should be able to handle them simultaneously in this study complex fuzzy sets are used to represent the information with uncertainty and periodicity a product sum aggregation operator psao is developed for a set of complex fuzzy sets which is used to integrate information with uncertainty and periodicity and a psao based prediction psaop method is then proposed to generate a solution of mpfp problems this study illustrates the details of the psaop method through two real applications in annual sunspot number prediction and bushfire danger rating prediction experiments indicate that the proposed psaop method effectively handles the uncertainty and periodicity in the information of multiple periodic factors simultaneously and can generate accurate predictions for mpfp problems

predicting daily ozone concentration maxima using fuzzy time series based on a two stage linguistic partition method abstract air pollution is a result of global warming greenhouse effects and acid rain especially in highly industrialization areas air pollution has become a major environmental issue poor air quality has both acute and chronic effects on human health the detrimental effects of ambient ozone on human health and the earth s ecosystem continue to be a national concern in taiwan the pollutant standard index psi has been adopted to assess the degree of air pollution in taiwan the standardized daily air quality report provides a simple number on a scale of 0 to 500 related to the health effects of air quality levels the report focuses on health and the current psi subindices to reflect measured ozone o 3 concentrations therefore this study uses the o 3 attribute to evaluate air quality in an effort to forecast daily maximum ozone concentrations many researchers have developed daily ozone forecasting models however this continuing worldwide environmental problem suggests the need for more accurate models this paper proposes two new fuzzy time series based on a two stage linguistic partition method to predict air quality with daily maximum o 3 concentration stage 1 use the fuzzy time series based on the cumulative probability distribution approach cpda to partition the universe of discourse into seven intervals stage 2 use two linguistic partition methods the cpda and the uniform discretion method udm to repartition each interval into three subintervals to verify the forecasting performance of the proposed methods in detail the practical collected data is used as and evaluating dataset five other methodologies ar ma arma chen s and yu s are used as comparison models the proposed methods both show a greatly improved performance in daily maximal ozone concentration prediction accuracy compared with the other models

slide a simple adaptive defuzzification method we introduce a parameterized family of defuznfica tion operators called the semi linear defuzzification slide method this method is based upon a simple transformation of the fuzzy output set of the controller we suggest an algorithm for the learning of the parameter from a data set in an attempt to simplify the parameter learning we suggest a modified version of the slide method which results in a simple learning algorithm the development of the learning algorithm is based upon the use of the kalman filter n fuzzy logic control systems l 2 the defuzzification i step involves the selection of one value as the output of the controller more specifically starting with a fuzzy subset possibility distribution f over the output space x of the controller the defuzzification step uses this fuzzy subset to select a representative element x the two most often used methods of defuzzification found in the literature are the center of area coa and mean of maxima mom 3 6 methods we recall that the mom method takes as its defuzzified value the mean of the elements that attain the maximum membership grade in f the coa method takes as its defuzzified value d ci ui xi where ui f xi cj f xj in 7 and 8 we formulated a general defuzzification method via basic defuzzification distribution badd transformations the main idea of this badd approach is to transform the possibility distribution f into a probability distribution p and then the defuzzified value is the expected value of the probability distribution the process of transforming f into p was seen as a two step process the first step was to transform f into a new possibility distribution e and then to normalize e to obtain p the step of obtaining e from f involved the use of a badd transformation in which e xi f z where 6 e o co it was shown in 7 that the generalized badd method implies the coa and mom methods as special cases in particular the coa method is obtained for a 1 and the mom is obtained for 6 00 when s 0 we get a defuzzified value that is the unweighted mean of the output space d xi xi the badd transformation has the advantage of being based on a single parameter which allows us the potential of adaptively learning the best method of defuzzification for a given controller while the family of all defuzzified values that can be obtained by the generalized badd defuzzification method was parameterized an undesirable property of the method was the nonlinear

a fuzzy seasonal arima model for forecasting this paper proposes a fuzzy seasonal arima fsarima forecasting model which combines the advantages of the seasonal time series arima sarima model and the fuzzy regression model it is used to forecast two seasonal time series data of the total production value of the taiwan machinery industry and the soft drink time series the intention of this paper is to provide business which are affected by diversified management with a new method to conduct short term forecasting this model includes both interval models with interval parameters and the possible distribution of future value based on the results of practical application it can be shown that this model makes good forecasts and is realistic furthermore this model makes it possible for decision makers to forecast the best and worst estimates based on fewer observations than the sarima model

a unified approach to asymptotic behaviors for the autoregressive model with fuzzy data we propose a unified estimator for the autoregressive model with fuzzy input output variables based on the least squares method the least squares estimation is investigated in presence of a unified r distance defined on the space of fuzzy numbers we investigate asymptotic properties of the unified estimator under some simple conditions as well as a generalization which reduces to the asymptotic properties under those distances when the distances are the special cases of r distance some simulation studies are included to compare the asymptotic properties of estimators formed under several distances being the special cases of r distance

fuzzy transforms method in prediction data analysis we present a prediction method based on fuzzy transforms for forecasting problems and we compare it with the well known wang mendel s one another comparison is made on the local linear wavelet neural network method via forecasting time series we apply these concepts to a mackey glass chaotic time series and to the monthly nao climatic index time series

picture fuzzy regression functions approach for financial time series based on ridge regression and genetic algorithm abstract recent years fuzzy inference systems are efficient tools for solving forecasting problems fuzzy inference systems are based on fuzzy sets and use membership values besides original data so a data augmentation mechanism is employed in the fuzzy inference picture fuzzy sets provide additional information to original data via positive degree membership negative degree membership neutral degree membership and refusal degree membership apart from fuzzy sets the data augmentation with this additional information will be provided to build a better inference system than fuzzy inference systems in this study picture fuzzy inference system is proposed for forecasting purpose by using ridge regression and genetic algorithm ridge regression method is used to obtain picture fuzzy functions and genetic algorithm is used to emerge different information coming from systems which are designed for positive degree membership negative degree membership and neutral degree membership in the proposed method picture fuzzification is provided by picture fuzzy clustering the proposed inference system is tested by various stock exchange data sets the forecasting of the proposed method is compared with well known forecasting methods the obtained results are evaluated according to different error measures such as root of mean square error and mean of absolute percentage error