International Journal on Advanced Computer Theory and Engineering (IJACTE)
________________________________________________________________________________________________
Forecasting Lahi Production in India using Fuzzy Time Series and
Diffusion of Innovation
1
Priya Shrivastava, 2Sonam Sharma
Assistant Professor Dept of CSE
ITM University Gwalior, M.P., India
Email: 1priyashrivastava.cse@itmuniversity.ac.in, 2sonamsharma.cse@itmuniversity.ac.in
Abstract -Most of the existing forecasting techniques give
the basic idea of crop production per year. There are
various forecasting techniques, we have worked on two
techniques one is Fuzzy Time Series and another one is
Diffusion of Innovation. Research paper will focus on
(SAII) study, analyze, improve and implement strategies of
forecasting techniques depending on nature of data and we
have done SAII for lahi (crop) production.
I. INTRODUCTION
India ranks second worldwide in farm output.
Agriculture and allied sectors like forestry and fisheries
accounted for 13.7% of the GDP in 2013, about 50 % of
the total workforce. Still there is a great uncertainty
about the outcome for any crop year [5]. It depends upon
various factors like fertilizers, irrigation, climate,
environment, agricultural policies, and economic growth
of India. Certainty of crop production should be present
because it plays significance role in various other areas
and one report from 2008 claimed India’s population is
growing faster than the production of wheat, rice, dal,
lahi etc. India can easily get rid of this problem by using
some policies like reduce food spoilage, increase farm
productivity and by improve its infrastructure.
Similarly if a farmer has prior knowledge about the use
of grains then accordingly he can prepare for his next
year crop. Another point of attention is for land whether
it is fertile or not. So that the government can emphasis
on most fertile lands for agriculture.
II. LITERATURE REVIEW
Various researches have been made in the field of
forecasting using fuzzy time series and diffusion of
innovation and provide result accordingly. As we are
giving comment or observations about the future which
is uncertain, vague, unknown, difficult to perceive,
therefore our main focus is on accuracy. On the basis of
accuracy we can rely on the forecasted result. So here
we are discussing some basic terminology which we
used in implementing our work.
2.1 FUZZY LOGIC
Fuzzy logic is a superset of Boolean logic that has been
extended to handle the concept of partial truth i.e. truth
values lies between completely true and completely
false. Truth values ranges in degree between 0 and 1. It
is the logic underlying modes of reasoning which are
approximate rather than exact[1].
For Example, a temperature can be very cold, cold,
normal, hot and very hot. This type of information can
be comes under fuzzy logic because can have values
between 0 and1 i.e. will assign values to each
information between 0 and 1 but can’t be used by
Boolean algebra.
2.2 Fuzzy Set
A fuzzy set [2] is a set that allows its member to have
different grades of membership (membership function)
in the interval [0, 1]. A membership function provides a
measure of the degree of similarity of an element to a
fuzzy set.
2.3 Fuzzy Time Series
Time Series is a sequence of data points, measured
typically at successive points in time spaced at uniform
time intervals [3].
For example annual flow volume of the Nile river at
Aswan. Fuzzy Time Series is a time series of fuzzy
variables where we predict future values based on
previously observed fuzzy values.
Definition 1
Let Y(t) (t= 0, 1, 2, 3, . . .), a subset of R, be the universe
of discourse on which fuzzy sets fi(t) (i= 1,2, 3, . . .) are
defined and F(t) the collection of fi , then F(t) is defined
as fuzzy time series on Y(t) [4].
2.4 Diffusion of Innovation
Diffusion is a process of spreading or moving of
something from one society to another. Innovation is a
creation of a new thing, idea, product, that is a process
of translating an idea or invention into a good or service
_______________________________________________________________________________________________
ISSN (Print): 2319-2526, Volume -3, Issue -5, 2014
51
International Journal on Advanced Computer Theory and Engineering (IJACTE)
________________________________________________________________________________________________
that creates value. Diffusion of innovation is a process
of dissemination a new product into the society that
must satisfy a specific task for which customer will pay.
During the process of diffusion of innovation [7],
innovations are diffused to members of the society in a
certain moment in time through the media- i.e.
communication channels. The following elements of
diffusion of innovation are identified in scientific
literature: innovation, communication channels, social
system and time.
A1= [400, 500]
2.5 Adoption of Innovation
Similarly for next_year_production (output variable)
shown in figure 3.3 .The historical time series data is
fuzzified with triangular membership function in order
to have the fuzzy logical relations. The historical time
series data of actual lahi production and the
corresponding fuzzified production in linguistic terms
are given in Table I.
Adoption of innovation is a process of accepting the new
product, thing, idea with approval. Thais firstly we
promote a new product in the market and then accept
that new product or technology. Innovation is
synonymous with risk taking while imitators take less
risk because they will start with an innovator’s product
and take a more effective approach. For example IBM
with its PC against Apple Computer, Compaq with its
cheaper PC’s against IBM and Dell with its still cheaper
clones against Compaq.
III. PROPOSED ALGORITHM WITH
IMPLEMENTATION
Algorithm1: Based on Fuzzy time Series
The proposed method is implemented in to real life
problem of a dynamical system containing fuzziness like
crop production. The historical time series data of lahi
production is in terms linguistic values.
STEP I: Make a model in which define input values,
output values and relation between them:
In lahi production the inputs are the linguistic values
which define the current lahi production and through
fuzzy inference we will find the next year lahi
production as in linguistic term. Figure 3.1 shows the
FIS Editor which defines the input, output and fuzzy
inference.
STEP II: Defines the membership function for input
variable and output variable.
The input and output variables have A1, A2…A7
linguistic values as given below:
A2= [500, 600]
A3= [600,700]
A4= [700,800]
A5= [800, 900]
A6= [900, 1000]
A7= [1000, 1100]
Table I: Lahi Production
Year
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
Actual Production
(kg/ha)
1025
512
1005
852
440
502
775
465
795
970
742
635
994
759
883
599
499
590
911
862
801
1067
917
Production
in
Linguistic Term
A7
A2
A7
A5
A1
A2
A4
A1
A4
A1
A4
A3
A6
A4
A5
A2
A1
A2
A6
A5
A5
A7
A6
A1 = poor production
A2 = below average production
A3 = average production
A4 = good production
A5 = very good production
A6 = excellent production
A7 = extraordinary production
We define range of the current_year_production (input
variable) from 400 to 1100 shown in figure 3.2 treated
as universe of discourse i.e.
STEP III: Converting Production in Linguistic Term into
IFTHEN Statements.
Defuzzified output, Y (t), is obtained by matching
production in linguistic term given in Table I with a
corresponding if then rule. The IF statements are
generated on basis of the contents present in linguistic
term of production in above table as shown in figure 3.4.
That is,
IF f (t-1) is A7 THEN f (t) is A2.
IF f (t-1) is A2 THEN f (t) is A7.
U= [400, 1100]
_______________________________________________________________________________________________
ISSN (Print): 2319-2526, Volume -3, Issue -5, 2014
52
International Journal on Advanced Computer Theory and Engineering (IJACTE)
________________________________________________________________________________________________
……………..
IF f (t-1) is A7 THEN f (t) is A6.
STEP IV: Derive Forecast
The forecasted lahi has calculated using rule viewer.
Here the current_year_production is 750 (calculated by
using IF-THEN rules of step III) then the
next_year_production will be 725. So as you change the
current_year_production(input)
then
the
next_year_production(output) will be changed as if
input is 554 then the output will be 800 and so on ;
shown in figure 3.5 and 3.6.
Figure 3.1: Fuzzy Inference System One Input and One Output.
3.2: Membership Function of Current_Year_Production i.e. input variable
Figure 3.3: Membership Function of Next_Year_Production i.e. output variable
_______________________________________________________________________________________________
ISSN (Print): 2319-2526, Volume -3, Issue -5, 2014
53
International Journal on Advanced Computer Theory and Engineering (IJACTE)
________________________________________________________________________________________________
3.4:IF THEN rules of Production of Lahi
3.5: Forecasted Lahi Production When Input=554 Then Output= 800
3.6: Forecasted Lahi Production When Input = 455 Then Output=650.
_______________________________________________________________________________________________
ISSN (Print): 2319-2526, Volume -3, Issue -5, 2014
54
International Journal on Advanced Computer Theory and Engineering (IJACTE)
________________________________________________________________________________________________
Algorithm 2: Based on Diffusion of Innovation
Step I: Identify analogy products.
Step II: Estimate Bass Model parameters for each
analogy.
Step III: Assess importance of the new product’s
attributes
Step IV: Calculate parameters for the new product
a. R squared = 1 - (Residual Sum of Squares) /
(Corrected Sum of Squares) = .019.
Bass Model says that the life cycle of a product should
follow a bell shaped graphical structure as given in
figure 3.7 which shows that the production of any
product increases initially and then attain a peak level
that is maximum production and then its graph goes
down shows the declination of the product.
Step V: Estimate the new product’s market potential
Step VI: Simulate the new product’s diffusion.
The diffusion history of products is to be approximated
by a model simulation [9]. Considering these
requirements the best Bass model simulation fit to the
historical data is achieved for α = 0.03 and β = 0.32.
Bass Model Mathematical Expression:
d N(t)/dt = α *(N-N(t))+ β *(N(t)/N)*(N-N(t))
Where,
d N(t)/dt = rate of diffusion at time t.
N (t) = cumulative number of adopters at time t.
Figure 3.7: Bass modelled life cycle of a product
For lahi production graph does not come under category
of bell shaped curve, its graph is shown in figure 3.8,
follows the turbulence in its production that is a zigzag
or up-down pattern, sometimes productions is increasing
and sometimes decreasing.
N= total number of potential adopters in the social
system at time t.
α = coefficient of innovation or external influence.
β = coefficient of imitation, internal influence or
Word-of-mouth effect.
Typical values of α and β when time t is measured in
years.


The average value of α has been found to be 0.03,
and is often less than 0.01.
The average value of β has been found to be 0.38,
with a typical range between 0.3 and 0.5.
The global market potential of lahi crop is 60,000kg/ha.
The Bass model finds the best approximation to the
historical data with parameters α =0.013 and β=0.008.
Table II: Parameter Estimates of Lahi Crop
Paramet
er
Estim
ate
Std.
Error
95% Confidence Interval
Lower
Upper
Bound
Bound
.009
.017
-.023
.139
Alpha
.013
.002
Beta
.008
.015
ANOVAa
Source
Sum
of
Squares
Regression
9462811.763
Residual
674762.237
Uncorrected 10137574.000
Total
Corrected
687920.444
Total
Df
Mean Squares
2
16
18
4731405.882
4731405.882
Figure 3.8: Life cycle of Lahi production
IV. CONCLUSION
Analyzed and implemented the forecasting of lahi
production through two different forecasting techniques
and come to know that the choice of forecasting
technique depends upon the nature of data, if production
increases with respect to time and when the input data
about the innovations are given in linguistic terms that
defines the characteristics of novelty then we prefer to
use Diffusion of Innovation for better accuracy. And
Fuzzy Time Series has been used when there are
turbulence in given data. from 3.8 fig we come to know
that Lahi production increases and decreases with time,
possessing turbulent nature .the forecasting of lahi
production by FTS gives more accurate forecasted
result. Figure 3.9 shows the comparison of FTS’s and
DOI with actual data .
17
Dependent variable: Actual_Production
_______________________________________________________________________________________________
ISSN (Print): 2319-2526, Volume -3, Issue -5, 2014
55
International Journal on Advanced Computer Theory and Engineering (IJACTE)
________________________________________________________________________________________________
Figure 3.9: Diffusion Curve by Bass Model and FTS
Model.
For lahi production graph does not come under category
of bell shaped curve, its graph is shown in figure 3.9,
follows the turbulence in its production that is a zigzag
or up-down pattern, sometimes productions is increasing
and sometimes decreasing.
[4]
Shiva Raj Singh, “A Simple Time Variant
Method for Fuzzy Time Series Forecasting”,
Dept of Mathematics, BHU, Varanasi, ISSN,
2007.
[5]
Sachin Kumar, Narendra Kumar, “Fuzzy time
Series Method for Wheat Production
Forecasting”, International Journal of Computer
Application, 2012.
[6]
Li-Hui Wang, Shyi-Ming Chen, senior member,
IEEE and Yung-Ho Lee, “Handling Forecasting
Problems Based on Two Factors High Order
Fuzzy Time Series for TAIEX forecasting”,
IEEE Transaction on fuzzy systems, 2009.
[7]
Eva-Maria Cronrath and Alexander Zock.
“Forecasting the Diffusion of Innovations by
Analogies:Examples
of
the
Mobile
Telecommunication Market”. Journal of
Marketing Research, 2006.
[8]
C.H. Cheng, J.R. Chang and C.A. Yeh, “
Entropybased and trapezoid fuzzification fuzzy
time series approaches for forecasting IT
project cost”, Technological Forecasting &
Social Change, 2006.
[9]
Cheng, C.H., Chen, Y.S. , “Forecasting
Innovation Diffusion of Products using Trend
Weighted Fuzzy Time Series Model”, Expert
Systems with Applications, 2009.
[10]
Tsaur, R.C., J.C.O.Yang, and H.F. Wang,
“Fuzzy Relation and Analysis in Fuzzy Time
Series Model”, Computer and Mathematics
with Applications, 49: 539- 548, 2005.
REFERENCES
[1]
Q. Song and B.S. Chissom, “Fuzzy Time Series
and its Models”, fuzzy sets systems, 54(1993)
269-277.
[2]
Q. Song and B.S. Chissiom, “Forecasting
Enrolments with Fuzzy Time Series -part
1”,fuzzy sets and systems,54(1), 1-9 in 1993.
[3]
Q. Song and B.S. Chissom, “Forecasting
Enrolment with Fuzzy Time Series- part
2”,fuzzy sets and systems, vol 62, no1,pp 18,1994.

_______________________________________________________________________________________________
ISSN (Print): 2319-2526, Volume -3, Issue -5, 2014
56