Enrollment forecasting methodology

Virtually, call plays everyplace a major role in kind-hearted life, specially in making in store(predicate) decisions such as weather call, university enrollment, production, sales and finance, and so forth Based on these forecasting results, we can prevent damages to issue forth or get benefits from the forecasting activities.Up to now, legion(predicate) qualitative and quantitative forecasting mildews were proposed. However, these posers are unable to deal with problems in which historical selective information debate form of linguistic constructs instead of numerical set. In recent years, m whatever a(prenominal) an(prenominal) orders have been proposed to deal with forecasting problems using hazy beat serial publication. In this paper, we present a untested method to predict the calendar berthreal day for average Arabian Gulf Oil Company using brumous quantify series approach based on average distances of intervals. A visual-based course of studyming i s apply in the implementation of the proposed model.Results obtained demonstrate that the proposed forecasting model can forecast the data effectively and competently Keywords blurred date series, Forecasting, clouded sets, Average-based durationl . Forecasting the size of any phenomenon in future is of the essence(p) and helpful for understanding behavior of phenomenon along term. It is impossible to make future plans to face the phenomenon without defining its future dimensions and identifying shape and modes of complicated process, especially when it is tie in to future forecasting. Making decisions depends completely on truth of forecasting.It is evident that forecasting plays major role in our daily life. The finished and the most streamlined forecasting may support making correct decisions to raise accuracy of our expectations up to 100%. This may be impossible, yet we try to ignore forecasting errors. In order to authorize forecasting problems, many researchers p roposed few(prenominal) methods and different models. One of these models is traditional time series analysis, uni-variant and multi-variant. However, traditional time series has wide applications, that it moldiness satisfy proper conditions to be successful.For example, 50 up to 100 bservations at least are mandatory to achieve Autoregressive and Integrated Moving Average Models (ARIMA) and average zero is necessary to achieve autoregressive. Traditional time series has been applied in many fields such as pollution monitoring, blood pressure estimation, etc. This problem has been studied widely in statistics areas and neural networks. However, in pragmatical life, there are regression 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 logy sets theory is applied, where variables are foggy i. e. declarative variables are not fixed and scali ng of these variables is not expressed by a point, but by an interval or linguistic variables 1, 3. 2. FUZZY LOGIC Fuzzy logic 1 1, is a form of logic which has used in some expert systems and artificial intelligence applications. It was initiative proposed in 1965 by the Iranian scientist Lutfi Zadeh, at University of California, where he developed it as a better method of data processing.However, his theory didnt find a wide interest until 1974, where addled logic was used to control a steam engine. Since hence, applications of blear logic kept developing until the manufacturing of muddled logic chip which have been used in many products such this science. There are many reasons for scientists to correct groggy logic. For example, development of computers and software founded the need to invent or program systems that are capable of dealing with ambiguous information to mimic human thinking.However, this created a problem since computers can only deal with exact and accura te data. This problem caused occurrence of expert systems and artificial intelligence. Fuzzy logic is a theory for building such systems. Fuzzy set theory has many useful achievements in different fields and it aims at approximation of master key knowledge that contains vagueness in human thinking. Figure 1 illustrates the difference amidst traditional and fogged set theories. Fuzzy logic simply reflects how do people think and try to represent our feelings by words, decisions making and our commonplace sense.So, fuzzy logic models are being increasingly used in time series analysis, where they are important for dealing with linguistic values and other models in order to yield better forecasting results. clipping Series is define as a sequence of events easured in incidental times at definite intervals. It was widely used in scotch systems such as stock index and interest. Also, it was used in metrology, especially in wind speed, temperature, pressure, Figure 1 Traditional an d fuzzy sets 3.FUZZY clock time SERIES Fuzzy time series is another concept to solve forecasting problems in which the historical 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 suppositious framework to model a special dynamic process hosepipe observations are linguistic values. The main difference between the traditional time series and fuzzy time series is that the observed values of the former are real adds while the observed values of the latter(prenominal) are fuzzy sets or linguistic values.In the following, some basic concepts of fuzzy time series are briefly reviewed Definition 1 allow U ,u2 un be a universe of discourse (universal set) a fuzzy set A of U is outlined fA (u ) / u fA (u ) / un ,where fA is a rank escape of a ween set A , fA 0,1. Definition 2 If there exists a fuzzy relationship R(t 1, t), such that F(t) =F(t ), where is an arith metic operator, then F(t) is said to be caused by F(t 1). The relationship 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 considered a timeinvariant fuzzy time series. Otherwise, F(t) is timevariant. Definition 4 Suppose 1) and F(t)= A, a fuzzy logical relationship can be defined as Ai AJ where Ai and AJ are called the leftfield side and the right-hand side of the fuzzy logical relationship, respectively. 4. REVIEW OF RELATED plant Many studies have interested in fuzzy time series and have been applied in various fields including university enrollment.Fuzzy time series had proved its efficiency in forecasting as a cheeseparing new method for predicting linguistic values. Song and Chisson 9, 10 first introduced 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 historical 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, due to the fact that the proposed method uses simplified arithmetic operation rather than the complicated MaxMin composition 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 find out an interval of xtension from both sides of crisp value in triangle social status function to get a variant floor of rank. 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 detailsStep 2 delimitate the universe of discourse U. Find the uttermost Dmax and the minimum Dmin among all Dh. For easy partitioning of U, choose two fine numbers Dl and D2 as two proper positive numbers. The economic consumption of Dl and D2 is to make the lower and upper bounds of U bring about multiple of hundreds, thousands, etc. The universe of discourse U is then defined by U = Dt-ntn -Dl , Drnax+D2 Step 3 Determine the appropriate length of interval L. Here, the average-based length method (Huarng, 2001 b) can be applied to designate the appropriate L.The length of interval L is computed according to the tabularize 1 Base mapping table Range Base 0. 1-1. 0 0. 1 1. -10 11-100 10 101-1000 a) Calculate all the absolute differences between the values Dh-l and Dh as the first differences, and the n compute the average of the first differences. b) Take half of the average as the length. c) Find the located range of the length and put the base from Table 1 d) According to the assigned base, round the length as the appropriate L. thus the number of intervals m, is computed by D max+D2-D indeed 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 historical 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, fuzzify 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 usually one historical data to ifferent A1, the need to find out maximum degree of each years historical data belonging to each A1. Step 6 Establish fuzzy logical relationships (FLRs) for all fuzzified data, derive 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 constituent and the number below /is the membership of ui to Then follow the rules for determining the degree of the membership of the istorical data Yi belonging to interval u. The general triangular membership function is expressed as below Step 7 have the fuzzy logic relationship groups (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.