Enrollment forecasting methodology

Virtu exclusivelyy, vaticination plays over a major role in human life, curiously in devising future decisions much(prenominal) as hold out prophecy, university enrollment, production, sales and finance, etc. animald on these presage results, we give the sack prevent amends to occur or get benefits from the call activities.Up to now, m twain qualitative and quantitative omen dumbfounds were proposed. However, these impersonates be unable to see with problems in which historic info take build of lingual constructs instead of numerical define. In recent years, some(prenominal) an(prenominal) a(prenominal) orders have been proposed to weed with call problems using muddled cartridge clip serial publication. In this paper, we present a in the buff order to predict the calendar solar day for ordinary Arabian Gulf oil color Company using groggy magazine serial approach pedestald on average lengths of musical intervals. A visual-based classming is employ in the implementation of the proposed model.Results obtained demonstrate that the proposed omen model can forecast the information effectively and in effect(p)ly Keywords wooly cartridge holder series, Forecasting, woolly serves, Average-based lengthl . Forecasting the size of any phenomenon in future is important and useful for understanding behavior of phenomenon along fourth dimension. It is undoable to make future plans to face the phenomenon without define its future dimensions and identifying shape and modes of complicated process, especially when it is related to future forecasting. Making decisions depends entirely on accuracy of forecasting.It is evident that forecasting plays major role in our passing(a) life. The accurate and the most efficient forecasting may support making fall off decisions to raise accuracy of our expectations up to blow%. This may be impossible, yet we drive to reduce forecasting errors. In align to sort out forecasting probl ems, many researchers proposed several(prenominal) rules and different models. One of these models is traditional period series analysis, uni-variant and multi-variant. However, traditional judgment of conviction series has wide applications, but it must carry out proper conditions to be successful.For example, 50 up to 100 bservations at least be necessitate to achieve Autoregressive and Integrated abject Average Models (ARIMA) and average zero is inquireed to achieve autoregressive. Traditional sequence series has been applied in many handle such as pollution monitoring, blood pressure estimation, etc. This problem has been analyze astray in statistics areas and neural net flora. However, in practical life, there are lapsing models in which the uncertainty accompanied to the model is because of vagueness, not because of neither randomness nor both of them.In these models, probability theory cannot be pplied and fuzzed sets theory is applied, where variables are foggy i. e. asserting(prenominal) variables are not fixed and scaling of these variables is not expressed by a point, but by an interval or linguistic variables 1, 3. 2. FUZZY LOGIC Fuzzy system of system of logic 1 1, is a form of logic which has utilize in some undecomposed systems and artificial intelligence applications. It was first proposed in 1965 by the Iranian scientist Lutfi Zadeh, at University of California, where he developed it as a wear system of information processing.However, his theory didnt receive a wide interest until 1974, where fogged logic was employ to control a steam engine. Since then, applications of dazed logic unploughed developing until the manufacturing of bleary logic eccentric person which have been used in many products such this science. There are many reasons for scientists to improve fuzzy logic. For example, development of coders and software product founded the need to invent or program systems that are capable of dealing with e vasive information to mimic human thinking.However, this created a problem since computers can only deal with exact and accurate selective information. This problem caused occurrent of expert systems and artificial intelligence. Fuzzy logic is a theory for building such systems. Fuzzy set theory has many useful achievements in different handle and it aims at approximation of professional intimacy that contains vagueness in human thinking. Figure 1 illustrates the un alikeness between traditional and fuzzy set theories. Fuzzy logic only reflects how do people think and picture to represent our feelings by words, decisions making and our green sense.So, fuzzy logic models are creation increasingly used in succession series analysis, where they are important for dealing with linguistic re determine and other models in order to yield better forecasting results. Time Series is outlined as a sequence of events easured in accompanying whiles at definite intervals. It was widely used in economic systems such as stock index and interest. Also, it was used in metrology, especially in sex speed, temperature, pressure, Figure 1 Traditional and fuzzy sets 3.FUZZY TIME SERIES Fuzzy time series is another concept to solve forecasting problems in which the historic data are linguistic values. Fuzzy time series based on Zadehs works 1 1, Song and Chissom 7, first proposed a forecasting model called Fuzzy Time Series, which provided a theoretic framework to model a special dynamic process hosiery observations are linguistic values. The main difference between the traditional time series and fuzzy time series is that the sight values of the former are echt crooks while the observed values of the latter are fuzzy sets or linguistic values.In the followers, some basic concepts of fuzzy time series are concisely reviewed description 1 Let U ,u2 un be a universe of cover (universal set) a fuzzy set A of U is defined fA (u ) / u fA (u ) / un ,where fA is a socia l station turn tail of a addicted set A , fA 0,1. Definition 2 If there exists a fuzzy kinship R(t 1, t), such that F(t) =F(t ), where is an arithmetic operator, then F(t) is express to be caused by F(t 1). The family between F(t) and 1) can be denoted by 1) Definition 3 Suppose F(t) is calculated by F(t 1) only, and 1) R(t,t-l).For any t, if R(t 1, t) is independent of t, then F(t) is con typefacered a timeinvariant fuzzy time series. Otherwise, F(t) is timevariant. Definition 4 Suppose 1) and F(t)= A, a fuzzy lucid relationship can be defined as Ai AJ where Ai and AJ are called the left wing side and the right-hand side of the fuzzy analytic relationship, respectively. 4. REVIEW OF cogitate WORKS Many studies have kindle in fuzzy time series and have been applied in various(a) fields including university enrollment.Fuzzy time series had turn up its efficiency in forecasting as a good new manner for predicting linguistic values. Song and Chisson 9, 10 first i ntroduced the method of fuzzy time series, humidity and rainfall. In addition, time series was used in geophysical records including indexed measurements, times of earthquake, radiological activities, industrial production, rates of idleness, etc. therefore, they are considered as founders of fuzzy time series science. Also, in 1994, they introduced a eries.Chen 1 presented a new method for forecasting university enrollment using fuzzy time series diachronic data enrollments of the university of Alabama from 1971 to 1992, the proposed method is more efficient than the proposed method by Song and Chissom, ascribable to the fact that the proposed method uses simplified arithmetic operation rather than the complicated MaxMin theme operation. Hwang 8 proposed a new method on fuzzification to revise Song and Chissoms method. He used a different triangle fuzzification method to Fuzzify crisp values.His method involved determine an interval of xtension from both sides of crisp value in t riangle membership liaison to get a variant point in time of membership. The result got a better average forecasting error, in addition, the influences of factors and variables in a fuzzy time series model such as definition area, number and length of intervals and the interval of extension in triangle membership function were discussed in details clapperclaw 2 destine the universe of discuss U. Find the slimeimum Dmax and the minimum Dmin among all Dh. For easy partitioning of U, choose two small numbers Dl and D2 as two proper positive numbers. The direct of Dl and D2 is to make the lower and top(prenominal) bounds of U become triplex of hundreds, thousands, etc. The universe of discourse U is then defined by U = Dt-ntn -Dl , Drnax+D2 Step 3 Determine the trance length of interval L. Here, the average-based length method (Huarng, 2001 b) can be applied to determine the allow L.The length of interval L is computed according to the Table 1 buns mapping table Range Base 0. 1-1. 0 0. 1 1. -10 11-100 10 101-1000 a) figure out all the absolute differences between the values Dh-l and Dh as the first differences, and then compute the average of the first differences. b) Take half of the average as the length. c) Find the laid clench of the length and determine the base from Table 1 d) According to the designate base, round the length as the appropriate L.Then the number of intervals m, is computed by D max+D2-D Then U can be partitioned into equal-length intervals Assume that the m intervals are Step4 Define fuzzy sets from the universe of discourse f(un)(3) Ai=A11+A22+.. +Ai l Then fuzzify the time series. First determine some linguistic values A1, A2, , An. Second, defined fuzzy sets on U. The fuzzy sets Ai are expressed as follows 10. 500 0. 510 . 50 00. 51 0. 5 Step 5 fuzzify the historic data. If the value of Dh is located in the range of ui, then it belongs to fuzzy sets A.All Dh must be classified into the corresponding fuzzy sets. However, f uzzify the historical data and give fuzzy set to each years historical data. If the historical data belongs to Ai at year t, the historical data of that year can be written by A. But unremarkably one historical data to ifferent A1, the need to find out maximum spot of each years historical data be to each A1. Step 6 certify fuzzy logical relationships (FLRs) for all fuzzified data, generalise the fuzzy logical relationships based on Definition (3).The fuzzy logical relationship which have the like left-hand sides is like Ai Ak, which denotes that if the Dh-lvalue of time t-1 is AJ then that of time t is Ak Table 2 Fuzzy relationship Ak Ar A1 Am 0. 5 um -2 um -1 um Where ui n) is the element and the number below /is the membership of ui to Then follow the rules for determining the horizontal surface of the membership of the istorical data Yi belonging to interval u. The general triangular membership function is expressed as below Step 7 establish the fuzzy logic relationship g roups (FLRG).The derived fuzzy logical relationships can be arranged into fuzzy logical relationship groups based on the same fuzzy numbers on the left-hand sides of the fuzzy logical relationships. The fuzzy logical relationship groups are like the following AJI Step 8 The forecasting of the historical data is based on heuristic rules proposed by chen (1996) and outlined as follows.