Virtually, forecasting plays everywhere a major role in human life, especially in making future decisions such as weather forecasting, university enrollment, production, sales and finance, etc. Based on these forecasting results, we can prevent damages to occur or get benefits from the forecasting activities. Up to now, many qualitative and quantitative forecasting models were proposed. However, these models are unable to deal with problems in which historical data take form of linguistic constructs instead of numerical values. In recent years, many methods have been proposed to deal with forecasting problems using fuzzy time series.
In this paper, we present a new method to predict the calendar day for average Arabian Gulf Oil Company using fuzzy time series approach based on average lengths of intervals. A visual-based programming is used in the implementation of the proposed model. Results obtained demonstrate that the proposed forecasting model can forecast the data effectively and efficiently Keywords: Fuzzy time series, Forecasting, Fuzzy sets, Average-based length1. 1. FORECASTING Forecasting the size of any phenomenon in future is important and helpful for understanding behavior of phenomenon along time. It is impossible to make future
The Term Paper on Financial Forecasting – Time Series Models
The economic recession felt in the United States since the collapse of the housing market in 2007 can be seen by various trends in the housing market. This collapse claimed some of the largest financial institutions in the U.S. such as Bear Sterns and Lehman Brothers, as they held over-leveraged positions in the mortgage backed securities market. Credit became widely available to unqualified ...
plans to face the phenomenon without defining its future dimensions and identifying shape and modes of these dimensions. In addition, making decisions is complicated process, especially when it is related to future forecasting. Making decisions depends completely on accuracy of forecasting. It is evident that forecasting plays major role in our daily life. The accurate and the most efficient forecasting may support making correct decisions to raise accuracy of our expectations up to 100%. This may be impossible, yet we try to reduce forecasting errors. In order to solve forecasting problems, many researchers proposed
several 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, but it must satisfy proper conditions to be successful. For example, 50 up to 100 observations at least are needed to achieve Autoregressive and Integrated Moving Average Models (ARIMA) and average zero is needed 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 practical 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 applied and fuzzy sets theory is applied, where variables are foggy i. e. declarative 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 logic [11], is a form of logic which has used in some expert 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 better method of data processing. However, his theory didn’t find a wide interest until 1974, where fuzzy logic was used to control a steam engine. Since then, applications of fuzzy logic kept developing until the manufacturing of fuzzy logic chip which have been used in many products such as cameras. Nowadays, there are various applications of this science. There are many reasons for scientists to improve fuzzy logic. For example, development of computers and software founded the need to invent or program systems that are capable of dealing with
The Business plan on Forecasting 2
1. Tupperware only uses both qualitative and quantitative forecasting techniques, culminating in a final forecast that is the consensus of all participating managers. False (Global company profile: Tupperware Corporation, moderate) 2. The forecasting time horizon and the forecasting techniques used tend to vary over the life cycle of a product. True (What is forecasting? moderate) 3. Sales ...
ambiguous information to mimic human thinking. However, this created a problem since computers can only deal with exact and accurate 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 professional knowledge that contains vagueness in human thinking. Figure 1 illustrates the difference between traditional and fuzzy set theories. Fuzzy logic simply reflects how do people think and try to represent our feelings by words, decisions making and our
common 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. Time Series is defined as a sequence of events measured in successive times at definite intervals. It was widely used in economic systems such as stock index and interest. Also, it was used in metrology, especially in wind 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 historical data are linguistic
values. Fuzzy time series based on Zadeh’s works [11], Song and Chissom [7], first proposed a forecasting model called Fuzzy Time Series, which provided a theoretic framework to model a special dynamic process whose 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 numbers while the observed values of the latter are fuzzy sets or linguistic values. In the following, some basic concepts of fuzzy time series are briefly reviewed [1-5, 7-10]. Definition 1: Let U ={ u1 ,u2 ,… , un } be a universe of
discourse (universal set); a fuzzy set A of U is defined A= fA (u ) / u fA (u ) / u … fA (u ) / un ,where fA is a membership function of a given set A , fA :U [0,1] . Definition 2 If there exists a fuzzy relationship R(t ? 1, t), such that F(t) =F(t ? 1) R(t ? 1, t), where is an arithmetic operator, then F(t) is said to be caused by F(t ? 1).
The Essay on Desi Arnaz Lucy Time Series
Cuban bandleader and singer-turned savvy TV mogul who, after his marriage to comedienne Lucille Ball in 1940, parlayed their successful "I Love Lucy" series into the Desilu TV production empire, which in its heyday also produced the successful and highly lucrative "The Untouchables" and "Star Trek" series. p Desiderio Alberto Arnaz y de A cha III was born in 1917 to wealthy Cuban landowners. His ...
The relationship between F(t) and F(t ? 1) can be denoted by F(t ? 1) F(t).
Definition 3 Suppose F(t) is calculated by F(t ? 1) only, and F(t) = F(t ? 1) R(t,t-1).
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 F(t ? 1) =Ai and F(t) = Aj, a fuzzy logical relationship can be defined as Ai Aj where Ai and Aj are called the left-hand side and the right-hand side of the fuzzy logical relationship, respectively. 4. REVIEW OF RELATED WORKS 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 good 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 model for forecasting enrollments using fuzzy time series. 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 Chissom’s method. He used a different triangle fuzzification method to Fuzzify crisp values. His method involved determining an interval of extension from both sides of crisp value in triangle membership function to get a variant degree 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
The Term Paper on The UG And PG Time Table
INDIAN INSTITUTE OF TECHNOLOGY DELHI ACADEMIC & EXAMINATION-(UG, PG) Date: 2 July 2012 Sub.: UG and PG Time Table, 1st semester 2012-2013 1. The UG and PG Time Table for 1st semester 2012-2013 is shown in the following pages. Time-table for all the first year courses is given in the first four pages (M courses and P courses). 2. Starting time has been indicated by first letter of the day and ...
were discussed in details 5. THE PROPOSED FUZZY TIME SERIES ALGORITHM The proposed fuzzy time series algorithm in this paper can be summarized as follows: Step 1: Collect the historical data (Dh).
Step 2: Define the universe of discourse U. Find the maximum Dmax and the minimum Dmin among all Dh. For easy partitioning of U, choose two small numbers D1 and D2 as two proper positive numbers. The purpose of D1 and D2 is to make the lower and upper bounds of U become multiple of hundreds, thousands, etc. The universe of discourse U is then defined by: U = Dmin ? D1 , Dmax + D2 (1) [ ] Step 3: Determine the appropriate length of interval L.
Here, the average-based length method (Huarng, 2001b) can be applied to determine the appropriate L. The length of interval L is computed according to the following steps: Table 1: Base mapping table Range Base 0. 1-1. 0 0. 1 1. 1-10 1 11-100 10 101-1000 100 a) Calculate all the absolute differences between the values Dh-1 and Dh as the first differences, and then compute the average of the first differences. b) Take one-half of the average as the length. c) Find the located range of the length and determine the base from Table 1 d) According to the assigned base, round the length as the appropriate L. Then the number of intervals m,
is computed by: D max + D 2 ? D min + D 1 (2) m = I Then U can be partitioned into equal-length intervals U={u1,u2,…….. un}. Assume that the m intervals are u 1 = [ d 1 , d 2 ], u 2 = [ d 2 , d 3 ],…….. ., u m = [ d m , d m +1 ]. Step4: Define fuzzy sets from the universe of discourse: f (u ) f (u ) f ( u n ) (3) A i = A 1 1 + A 2 2 + ….. + Ai u1 u2 un 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: A1 = 1 0 . 5 0 0 0 + + + + …. + u1 u2 u3 u4 um A2 = 0 . 5 1 0 . 5 0 0 + + + + …. + u1 u2 u3 u4 um
A3 = 0 0 . 5 1 0 . 5 0 + + + + …. + u1 u2 u3 u4 um Step 5: fuzzify the historical data. If the value of Dh is located in the range of ui, then it belongs to fuzzy sets Ai. All Dh must be classified into the corresponding fuzzy sets. However, fuzzify the historical data and give fuzzy set to each year’s historical data. If the historical data belongs to Ai at year t, the historical data of that year can be written by Ai. But usually one historical data to different Ai, the need to find out maximum degree of each year’s historical data belonging to each Ai. Step 6: Establish fuzzy logical relationships (FLRs) for
The Essay on Data Table Analysis
This brief will evaluate the design elements of the data tables from an accounting perspective for Kudler Fine Foods. An entity relationship diagram illustrating the existing data tables will be created. Recommendations that are needed for improvements to the data tables will also be outlined. This brief will show a pivot table using Kudler’s general ledger inventory data and there will be an ...
all fuzzified data, derive the fuzzy logical relationships based on Definition (3).
The fuzzy logical relationship which have the same left-hand sides is like Ai Ak, which denotes that if the Dh-1value of time t-1 is Aj then that of time t is Ak which shown in Table 1. Table 2: Fuzzy relationship Ai Aj Aj Ak Ar ….. Al Am ………….. 0 0 0 . 5 1 0 . 5 Am = + + ….. + + u1 u2 um ? 2 um ? 1 um Where ui (i=1,2, … n) is the element and the number below ‘/’is the membership of ui to Then follow the rules for A i ( i = 1, 2 ,…….. n ) determining the degree of the membership of the historical data Yi belonging to interval ui.
The general triangular membership function is expressed as below: Step 7: establish 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: Ai A j1 Ai Aj 2 } Ai > Aj1 , Aj 2 ,….. (6) (4) Step 8: The forecasting of the historical data is based on heuristic rules proposed by chen (1996) and outlined as follows: Where µ ij is the membership degree of ui belonging to Ai, which is defined by
Rule 1: If F(t) = Ai and Group (Ai) = , then The forecast is mi, the midpoint of ui, and Forecasting-valuei = m Ai = n µij j =1 uij 1 µij = 0. 5 0 i= j j = i ? 1 or i = 1 otherwise (5) It is sketched out as follows: Rule 1: If the historical data Yi belong to ui, then the membership degree is 1 of ui, is 0. 5 of u2, and otherwise is zero. Rule 2: If the historical data Yi belong ui, 1 < i < n, then the membership degree is 1 of ui, is 0. 5 of ui-1 and ui+1, otherwise is zero Rule 3: If the historical data Yi, belong to un, then the membership degree is 1 of un, is 0. 5 of un-1, and otherwise zero.
By the form of fuzzy set Ai, fuzzify the time series to the fuzzy set Ai, while the membership is 1 at ui. Rule 2: If the current fuzzy set is Ai, and the fuzzy logical relationship group of Ai is one-to-one, i. e, Ai Ap1, then the forecast is mp1, the midpoint of up1, and Forecastingvaluei = mp1. Rule 3: If the current fuzzy set is Ai, and the fuzzy logical relationship group of Ai is one-to-many, i. e, Ai Ap1, Ap2, ….. Apk, then the forecast is equal to the average of mp1, mp2,….. ,mpk, the midpoint of up1, up2,……,upk, respectively. k Forecasting ? valuei = x =1 m px k (7) Step 9: MSE (Mean Squared Error), defined in eq.
The Essay on Angel At My Table Time Viewer Janet
An Angel at my Table and The Sweet Hereafter: a Difference in Time The two movies An Angel at my Table and The Sweet Hereafter tell stories about the trials of being human. They both show the viewer a world that they with any luck do not have first hand knowledge. Though they both talk of the human condition, they do so by using stylistic differences that in their own right pull the viewer into ...
(8).
MSE = n ? ( Forecastin g _ data i =1 Actual _ data ) 2 (8) n 6. FORECASTING CALENDAR DAY FOR A4 = 0 0 0. 5 1 0. 5 0 0 0 0 0 + + + + + + + + + . u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 A5 = 0 0 0 0. 5 1 0. 5 0 0 0 0 + + + + + + + + + . u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 A6 = 0 0 0 0 0. 5 1 0. 5 0 0 0 + + + + + + + + + . u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 A7 = 0 0 0 0 0 0. 5 1 0. 5 0 0 + + + + + + + + + . u1 u 2 u3 u 4 u5 u 6 u7 u8 u9 u10 A8 = 0 0 0 0 0 0 0. 5 1 0. 5 0 + + + + + + + + + . u1 u 2 u3 u 4 u5 u6 u7 u8 u9 u10 A9 = 0 0 0 0 0 0 0 0. 5 1 0. 5 + + + + + + + + + . u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 AVERAGE ARABIAN GULF OIL COMPANY
As shown in Table 3, there are 23 observations, and two attributes that are year and oil, The method has been implemented and computed by the following: Table 3 Historical data of Arabian Gulf Oil Year 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 Historical data 723 418 560 945 945 782 643 230 460 306 417 599 Year 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 Historical data 811 738 488 486 301 498 248 247 206 200 277 Step1-2: The minimum and the maximum of oil are 200 (Dmin) and 738 (Dmax) and d1= 0 and d2= 55. The universe of discourse can be defined by U =[200,1000]. M=10, there are M intervals, which
are: u1 =[200280 u2 =[280360 u3 =[360440 u4 =[440520 , ], , ], , ], , ], , ], , ], , ], , ], u5 =[520600 u6 =[600680 u7 =[680760 u8 =[760840 u9 =[840920 u10[920 ]. , ], ,1000 Linguistic values were fuzzified and presented in Table 4. Table 4: The results of linguistic and fuzzified values. Fuzzified Linguistic value A1 Not many A2 Not too many A3 Not too- too many A4 Many A5 Too many A6 Too- too many A7 Many many A8 Too many many A9 Very many A10 Very very many many The results of fuzzy sets are: A1 = 1 0. 5 0 0 0 0 0 0 0 0 + + + + + + + + + . u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 A2 = 0. 5 1 0. 5 0 0 0 0 0 0 0
+ + + + + + + + + . u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 A3 = 0 0. 5 1 0. 5 0 0 0 0 0 0 + + + + + + + + + . u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 A10 = 0 0 0 0 0 0 0 0 0. 5 1 + + + + + + + + + . u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 Step 6-7: The derived fuzzy relationship shown in Table 5 and fuzzy logical relationship groups are generated as shown in, Table 6. Table 5: The fuzzy logic relationships A8 > A4 A4 > A2 A5 > A2 A4 > A6 A2 > A4 A2 > A5 A6 > A11 A4 > A6 A5 > A1 A11 > A9 A6 > A9 A1 > A1 A9 > A7 A9 > A8 A1 > A1 A7 > A4 A8 > A5 A1 > A1 A4 > A4 A5 > A5 A1 > A1 Table 6: Fuzzy logical relationship groups Group Fuzzy logical relationship
1 A8 A4,A5 2 A4 A6,A4,A2 3 4 A6 A11 A11,A9 A9 5 6 7 8 9 A9 A7 A2 A5 A1 A7,A8 A4 A4,A5 A5, A2,A1 A1 Step 8: In this step, all forecasted intervals and errors will be computed as shown in, Table 7. Table 7: Historical, forecasted, and error values Year 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 Historical data 723 418 560 945 782 643 430 460 306 417 599 811 738 488 486 301 498 248 247 206 200 277 Predicated value 480 445 865 795 690 445 445 445 480 445 865 690 480 352 352 352 235 235 235 235 235 235 Forecasting error 18. 048 1. 621 2. 634 7. 634 2.
675 3. 035 1. 463 8. 94 5. 593 7. 865 6. 667 7. 487 2. 619 0. 165 4. 112 0. 78 2. 972 11. 537 4. 887 1. 185 7. 464 5. 458 From Table 7, it can be seen that all forecasted values are very near to the actual values. This confirms that the model gives good forecasting. Step 9: Evaluate forecasting performance. The MSE (Mean Squared Error) shown in Table 8. Table 8: Mean Squared Error and Forecasting Error MSE(Mean Squared Error) 2. 18 F. E(Forecasting Error) 31. 8 From Tables 8, it can be seen that small value of the MSE, this confirms the goodness of forecasting model. Figure2: Forecasting observation 7. CONCLUSIONS
The objective of this research paper has been to use fuzzy time series technique for forecasting problems based on average lengths of intervals. It has been successfully implemented to the forecasting of the average calendar day of Arabian Gulf Oil Company. The company can have some early prediction for their average calendar day. Results obtained demonstrate the effectiveness of the proposed model compared to previous works in accuracy and simplicity. Using and analyzing of fuzzy time series that uses linguistic values enhances the power of decision making systems, thus introduces more accuracy than traditional methods.
Further study on performance comparison with other models and experimenting more complicated problems are under investigation. REFERENCES [1] Chen, S. M. , “Forecasting enrollments based on fuzzy time series”, Fuzzy Sets and Systems, Vol. 81, pp. 311-319, 1996. [2] Cheng. C. H. , and Hwang, J. R. , “Temperature prediction using fuzzy time series”, IEEE Trasnactions on Systems, Vol. 30, pp. 263-275, 2000. [3] Hsu, C. C. and Chen, S. M. , “A new method for forecasting enrollments based on fuzzy time series”, in Proceedings of the Seventh Conference on Artificial Intelligence and Applications, Taichung, Taiwan, Republic of China, pp.
17-22, 2002 [4] Jilani T. A. and Ardil. C. , “Fuzzy metric approach for fuzzy time series forecasting based on frequency density based partitioning”, in proceedings of world academy of science, engineering and technology, Vol. 23, pp. 13076884, 2007 [5] Lee, C. H, Huarng, K. & Chen, S. M. , “Forecasting problem using fuzzy time series”, Fuzzy sets and system, Vol. 100, pp. 217-228, 1998. [6] Singgh, S. R. “A simple method of forecasting based on fuzzy time series”, Applied Mathematics and Computation, Vol. 186, pp. 330-339, 2007. [7] Song, Q. and Chissom, B. S. , “Fuzzy time series and its models”, Fuzzy Sets and Systems, Vol.
54, pp. 269-277, 1993. [8] Hwang, J. R. , Chen, S. M. , and Lee, C. H. , “Handling forecasting problems using fuzzy time series”, Fuzzy Sets and Systems, Vol. 100, PP. 217228, 1998. [9] Song, Q. and Chissom, B. S. , “Forecasting enrollments with fuzzy time series – Part I”, Fuzzy Sets and Systems, Vol. 54, pp. 1-9, 1994. [10] Song, Q. and Chissom, B. S. ,” Forecasting enrollments with fuzzy time series – Part II”, Fuzzy Sets and Systems, Vol. 62, pp. 1-8, 1994 [11] Zadeh, L. A. , “The concept of a linguistic variable and its application to approximate reasoning-Part I”, Information Sciences, Vol. 8, pp. 199-249, 1975.
